# 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 EngineersThe contents of this report are not to be used for advertising, publication, orpromotional purposes. Citation of tradenames does not constitute anofficial endorsement orapproval oftheuse ofsuch 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 PAPERWater 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 ExperimentStation 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
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...4-53Documented Session
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-59 Instructional Cases
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-79 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..R-1 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..B-1 Appendix A: Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..A1 Appendix B: Conversion Factors
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..B1 SF298 

### 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 inempirical eutrophication models developed fornorthem lakeapplications
. . . . . . . . . . . . . . . . . 1-4 Control pathways inempirical eutrophication models developed forCEreservoirapplications
. . . . . . . . . . . . . . . . . 1-5 Sensitivity analysis offirst-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 forBeaver Reservoir
. . . . . . . . . . . . . . . . . 3-7 Schematic ofBATHTUB calculations
. . . . . . . . . . . . . . . . . . 4-3 Control pathways inempirica.l eutrophication models developed for CEreservoir 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 inRemodel 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

ivFigure 4.7. Phosphorus, chlorophyll a, and transparency relationships for CE reservoirs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-31 Figure 4.8. Calibration factor for linearphosphorus/chlorophyll model versus lightlimitation factors
. . . . . . . . . . . . . . . . . . . 4-34 Figure 4.9. Model segmentation forLake 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 ofLake and Reservoir Empirical Eutrophication Models
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6 Mass Balance Terrnsand Data Sources
. . . . . . . . . . . . . . . . 1-22 Minimal and Desirable Designs forTributary Monitoring Programs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-23 General Guidelines for Designing Reservoir Pool Monitoring Programs
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-27 Estimation Algorithms Used inFLUX Program
. . . . . . . . . . . 2-5 Stratified Sample Algorithm (Cochran 1977; Bodo and Unny 1983)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10 Breakdown byFlow 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 SpatiallyAveraged CEReservoir Data
. . . . . . . . . . . . . . . . . . . . 4-13 Diagnostic Variables andTheir Interpretation
. . . . . . . . . . . . 4-14 Equations forEstimating Nonalgal Turbidity, Mixed Depth, andHypolimnetic Depths inAbsence of Direct Measurements
. . . . . . . . . . . . . . . . . . . . . . . . . . . ...4-33

# Preface

The information reported herein isbased on aseries oftechnical reports written byDr. William W. Walker and published bythe U.S. Army Engineer Waterways Experiment Station (WES). These previous reports summarized work conducted aspart oftheEnvironmental andWater Quality Operational Studies Program, sponsored bythe Headquarters, U.S. Army Corps ofEngineers (HQUSACE). Preparation ofthis report was sponsored byHQUSACE, aspart oftheWater Operations Technical Support (WOTS) Program. The WOTS Program was assigned to WES under the purview ofthe Environmental Laboratory (EL). Funding was provided under Department ofthe 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, fortheWOTS. Program Monitors forWOTS were Messrs. Frederick B. Juhle and RixieHardy, 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 ofDr. Richard E. Price, Chief, EPEB, Mr. Donald L. Robey, Chief, EPED, and Dr. John W. Keeley, Director, EL. Atthetime ofpublication ofthis report, Director ofWES was Dr. Robert W. Whalin. Commander was COL Bruce K. Howard, EN. This report was updated inApril 1999. This report should becited 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 ofthis report are not to be usedfor adver~ising, publication, orpromotional putposes. Citation oftrade names does not constitute an oficial endorsement or approval ofthe use ofsuch commercial products. vi

### Background 

# 1 Introduction

This report describes simplified procedures foreutrophication assessment and prediction. These techniques, initially developed foruse atU.S. Army Corps ofEngineer (CE) reservoirs, are based upon research previously described ina series oftechnical 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 isdetailed itiormation concerning application ofthe latest versions ofthese techniques using aDOS-based personal computer and also reported isanupdate ofthe 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 inthis report, their intelligent “use” requires an understanding ofbasic modeling concepts and familiarity with the supporting research. Review ofthe above research reports and related references onthis topic (see References andBibliography) willfacilitate proper use ofthetechniques described below. Eutrophication canbe defined asthe enrichment ofwater bodies leading to an excessive production oforganic materials byalgae and/or aquatic plants. This process has several direct and indirect impacts onreservoir water quality and beneficial uses. Common measures ofeutrophication include total nutrient concentrations (phosphorus and nitrogen), chlorophyll a (ameasure ofalgal density), Secchi depth (ameasure oftransparency), organic nutrient forms (nitrogen and carbon), andhypolimnetic dissolved oxygen depletion. The basis ofthe modeling approach described below isto relate eutrophication symptoms to external nutrient loadings, hydrology, and reservoir morphometry using statistical models derived from arepresentative cross section of reservoirs. When applied to existing reservoirs, the models provide aframework for interpreting water quality monitoring data and predicting

Chapter 1 Introduction 1-1effects offhture changes inexternal nutrient loadings. The models can also be used to predict water quality conditions inaproposed reservoir. Three basic phases are involved inapplying the methodolo~ to anexisting orproposed reservoir:
a. Analysis and reduction oftributary water quality data. b. Analysis and reduction ofpool water quality data.
c. Model implementation, A separate computer program has been developed for each phase. The datareduction phases are critical steps inthe modeling process. The programs can also be used inother aspects ofreservoir operation and management, including monitoring program design and generalized data analysis. The model implementation program isdesigned so that itcanbe applied to asingle reservoir (mixed or spatially segmented), networks ofreservoirs (hydrologically linked), orcollections ofreservoirs (hydrologically independent). The lasttype of application can support regional comparative assessments ofreservoir conditions and controlling factors. This report isorganized infour chapters. Chapter 1reviews basic empirical modeling concepts, presents anoverview ofthe assessment procedures which have been developed forreservoir application, and summarizes basic data requirements and recommended monitoring strategies. Chapter 2 describes the FLUX program, which isdesigned for analysis and reduction oftributary monitoring data. Chapter 3 describes PROFILE, aprogram designed for analysis and reduction ofpool monitoring data. Chapter 4 describes BATHTUB, a program designed for model implementation. Appendix Adescribes the necessaryprocedures for installing theprograms on anIBM-compatible personal computer. Several levels ofinvolvement are offered to potential users ofthis methodology. The following steps are suggested: Step 1: Review summary information (Chapter 1). Step 2: Review supporting research andbasic 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 IntroductionStep 7: Apply program to user-defined problems. The above procedures provide agradual and logical introduction ofthe techniques and afoundation fortheir application inareservoir management context. 

### Eutrophication Modeling Techniques Models for reservoir eutrophication can bebroadly classified astheoretical orempirical. While allmodels are empirical to some extent, they are distinguished bytheir levels ofempiricism. General characteristics and limitations of these model types are discussed below. Theoretical models generally involve direct simulation ofphysical, chemical, andbiological processes superimposed upon asimulation ofreservoir hydrodynamics. These methods generally have extensive resource requirements in terms ofinput dat~ computing facilities, and user expertise. They can beusefblfor problems requiring high spatial and temporal resolution and/or simulation ofcause-effect relationships which cannot berepresented 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 asmass balance and nutrient limitation ofalgalgrowth), empirical models do not attempt explicit simulation ofbiochemical processes and use simplified hydrodynamic representations. They generally deal with spatially and temporally averaged conditions. The simple structures, low resolution, limited number ofinput variables, and initial calibration to data from groups ofimpoundments result inrelatively low data requirements. Atthe same time, the above characteristics limit model applicability. Inone sense, empirical models attempt to “interpolate” the gross responses ofagiven impoundment, based upon observed responses ofother impoundments and levels ofcertain controlling variables. They also provide a quantitative framework for interpreting monitoring data from agiven impoundment and describing eutrophication-related water quality conditions and controlling factors both inabsolute and relative terms. Empirical model structures and evolution Empirical prediction ofreservoir eutrophication canbe described as atwostage procedure involving the following types ofmodels:
a. Nutrient Balance Models. These relate pool or discharge nutrient levels to external nutrient loadings, morphometry, andhydrology. (Note that theterm “pool” refers to the lake orreservoir impounded byadam.)

Chapter 1 Introduction 1-3b. Eutrophication Response Models. These describe relationships among eutrophication indicators within the pool, including nutrient levels, chlorophyll a, transparency, andhypolimnetic oxygen depletion. Generally, models ofeach type must be linked to relate external nutrient loadings to reservoir water quality responses. Inthe absence ofloading information, however, application ofeutrophication response models alone can provide useful diagnostic tiormation on existing water quality conditions and controlling factors. The literature contains awide array ofempirical eutrophication models which have been calibrated and tested using data from various lake and/or reservoir data sets. Many ofthese models, particularly the earlyones, 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 ofvariables and basic assumptions, as depicted inFigure 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 canbe summarized inthree terms:
a. Inflow total phosphorus concentration. External loading/discharge rate, anutrient supply factor. b. Mean depth. Reservoir volume/surface are% amorphometric factor.
c. Hydraulic residence time. Reservoir volume/discharge rate, ahydrologic fwtor. Empirical nutrient balance models have generally evolved from asimplistic “black-box” model which represents the impoundment as acontinuous stirredtank reactor atsteady state andthe sedimentation ofphosphorus as afirst order reaction. Phosphorus isassumed to control algalgrowth and other eutrophication-related water quality conditions. Response models generally consist ofbivariate regression equations relating each pair ofresponse measurements (e.g., phosphorus/chlorophyll, chlorophyllk.nsparency). 1-4 Chapter 1 IntroductionInadapting these models foruse inCE and other reservoirs (Walker 1981, 1982, 1985), modifications have been designed to include additional input variables, controlling factors, and response variables, as depicted inFigure 1.2. Table 1.1 compares the variables and assumptions ofthe reservoir models documented inthis manual. The reservoir modifications are designed to improve generality byincorporating additional independent variables and controlling factors found to be important inmodel testing.

INFLOW TOTAL **METALIMNETIC ~**  **DEPLETION RATE**  **INFLOW ORTHO-P** 
MEAN **TOTAL 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 inthe following areas:
a. Effects ofnonlinear sedimentation kinetics onnutrient balances. A second-order kinetic model appears to be more general than afirstorder model forpredicting both among-reservoir, spatially averaged variations andwithin-reservoir, spatial variations. b. Effects ofinflow nutrient partitioning (dissolved versus particulate or organic versus inorganic) onnutrient balances and chlorophyll a levels. Because ofdifferences inbiological availability and sedimentation rates, reservoir responses appear to be much more sensitive to the orthophosphorus loading component than tothenonortho (total minus ortho) component.

Chapter 1 Introduction 1-5Table 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 ofseasonal variations innutrient loadings, morphomet~, and hydrology onnutrient balances. Pool water quality conditions are related more directly to seasonal than to annual nutrient balances in impoundments with relativelyhigh flushing rates.

Chapter 1 Introductiond Effects ofalgalgrowth limitation byphosphorus, nitrogen, light, and flushing rate on chlorophyll a concentrations. Simple phosphorus/ chlorophyll a relationships are oflimited use inreservoirs because nitrogen, light, and/or flushing rate may also regulate algal growth, depending upon site-specific conditions.
e. Effects ofspatial variations innutrients and related variables, as controlled byreservoir morphometry, hydrology, andthe spatial distribution oftributary nutrient loads. Nutrient-balance models can be implemented inaspatially 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 ofwater-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 andtesting are described inthe supporting research reports (Walker 1982, 1985).
Applications Potential model applications can be classified into two general categories: diagnostic and predictive. Characteristics and limitations ofthese applications are described below. In adiagnostic mode, the models provide aframework for analysis and interpretation ofmonitoring data from agiven reservoir. This yields perspective on eutrophication-related water quality conditions and controlling factors. Assessments can be expressed inabsolute terms (nationwide, e.g., with respect to water quality objectives, criteri~ or standards) and/or relative terms (e.g., comparisons with other impoundments, orregionally). Using routines and statistical summaries included inthe BATHTUB program, observed orpredicted reservoir characteristics can beranked against characteristics ofCE reservoirs used inmodel development. In apredictive mode, the models are used to project fiture conditions in either existing or planned reservoirs. The distinction between the two types of predictive applications isimportant. Inthe first case, monitoring data from an existing reservoir can beused, incombination with the models and diagnostic analyses, as a“starting point” for “extrapolation” tofuture conditions. Because ofthe opportunity for site-specific calibration, projections offuture conditions inanexisting reservoir aregenerally subject to less uncertainty than projections ofwater quality conditions inaproposed reservoir. In apredictive mode, the models project steady-state responses to changes incontrolling variables which are explicitly represented inthe model network
Chapter 1 Introduction 1-7(Figure 1.2). Such projections canbeused inimpact assessments and inevaluations ofwater-quality-control strategies. For example, fhture scenarios involving changes inseasonal or annual-mean values ofthe following factors can be evaluated:
a. Inflow nutrient concentrations orloadings (total phosphorus, ortho phosphorus, total nitrogen, and/or inorganic nitrogen). b. Pool elevation, as itinfluences mean depth, mixed-layer depth, mean hypolimnetic depth, andhydraulic residence time.
c. Inflow volume and changes inhydraulic residence time. d. Pool segmentation, asitinfluences longitudinal nutrient transport, sedimentation, andthe spatial distribution ofnutrients and related water quality conditions. Applications ofthe firsttype are ofprimary importance because control strategies forreservoir eutrophication areusually focused on external nutrient (especially, phosphorus) supplies. Examples ofimpacts and control strategies which cannot be explicitly evaluated with these models include the following:
a. Variations inpool level orother model input variables which occur over time scales shorter than the growing season (typically, 6months). b. Changes inoutlet levels.
c. Structural modifications, such asthe construction ofweirs. 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 ofthe models inadiagnostic mode can provide useful baseline water quality perspectives; however, simulation orother approaches must beused forpredictive purposes. Although the supporting research has focused onreservoirs, the computational framework can also be applied tonatural lakes. Certain procedures and concepts are essential to evaluating eutrophication problems inlakes orreservoirs. These include calculation oftributary nutrient loads, summary of observed water quality conditions, construction ofwater balances, and construction ofmass balances. Inadapting the empirical lake models (Figure 1.1) for use inreservoirs, the goal has been to increase model generality, so that the resulting formulations can be applied within certain constraints to lakes orto 1-8 Chapter 1 Introductionreservoirs. The limits and extent ofmodel testing against lake data sets are summarized inthe supporting research reports (Walker 1982, 1985). Options for implementing empirical models previously developed exclusively from lake data sets are also included inthe software.
Error, variability, and sensitivity analysis The distinction between “error” and “variability” isimportant. Error refers to adifference between anobserved and apredicted mean value. Variability refers to spatial ortemporal fluctuations inconcentration about the mean. Prediction oftemporal variability isgenerally beyond the scope ofempirical modeling efforts, although such variability isimportant because itinfluences the precision ofobserved 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 apercentage basis or logarithmic scales. This stabilizes variance overthe ranges ofconcentration encountered, animportant requirement for application ofcommon statistical techniques (e.g., regression). This report frequently uses the mean coefllcient ofvariation (CV) as ameasure oferror. The CV equals the standard error of the estimate expressed as afraction ofthe predicted value. For example, aCV of0.2 indicates that the standard error is20 percent ofthe 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 ofvariation

Y = 95-percent confidence range for mean value Magnitudes, sources, and interpretations oferror are discussed below. Error CVSfor the reservoir model network (Figure 1.2) are onthe order of 0.27 forpredicting total phosphorus and 0.35 forpredicting mean chlorophylla. According to the above equation, these statistics translate into 95-percent confidence factors of 1.72 and 2.00, respectively. Inapplying these models inareservoir management context, limitations imposed byerrors ofthis magnitude are less severe than immediately apparent because ofthe following factors:

Chapter 1 Introduction 1-9a. Despite the relatively wide confidence bands, the models explain 91 percent and 79percent ofthe observed variances in totalphosphorus and chlorophyll aacross reservoirs, respectively. This reflects the relatively wide ranges ofconditions encountered and suggests that the models are adequate forbroad comparative analyses ofreservoir conditions (i.e., ranking). b. Error statistics are calculatedfiom “imperfect” data sets. Errors are partially attributed to random sampling, measurement, and estimation errors inthe input and output (i.e., observed) conditions, which inflate the total error but do not reflect model performance.
c. Error magnitudes refer topredictions which are made without the beneJt ofsite-specl@cwater quality information. In applications to existing reservoirs, prediction errors can bereduced bycalibrating the model (adjusting certain model coefficients) so that predictions match observed water quality conditions. The calibrated model can subsequently beused to project water quality changes likelyto result from changes innutrient loads orother controlling factors. d. Year-to-year water quality variations induced by climate, hydrology, nutrient loading, and otherfactors are substantial inmany reservoirs. Itwould be difficult to detect modest errors inpredicting average conditions without several years ofintensive monitoring.
e. Ability tode$ne objective criteria orstandards islimited. The “penalty” or “risk” associated with modest errors inpredicting average responses may be low when expressed interms ofimpacts onwater uses. The measured and modeled variables (chlorophyll a, etc.) are reasonable and practical, but impefiect, surrogates forpotential wateruse impacts. $ Ability topredict changes in loading resultingfiom adoption ofspecl~c management strategies is limited. This applies particularly to implementation ofnonpoint source loading controls with performances evaluated using watershed simulation models. Insuch situations, errors associated with predicting reservoir response maybe swamped byerrors associated with predicting loadings; i.e., the reservoir response model may not bethe limiting factor inthe analysis. Error-analysis concepts discussed below provide additional perspectives onthe above points.



### 1-1o Differences between observed and predicted reservoir conditions can be attributed to the combined effects ofanumber oferror sources, as described below:

Chapter 1 Introductiona. Independent variable error. These areerrors inthe estimates ofmodel input variables, including external nutrient loadings, flows, and reservoir morphometry. b. Dependent variable error. These areerrors inthe estimates ofmean observed reservoir water quality conditions, based upon limited monitoring data.
c. Parameter error. These errors are attributed to biases orrandom errors inthe model coefficients estimated from cross-sectional data sets. d. Model error. These errors are attributed to errors inmodel structure or effects offactors which arenot explicitly represented. The user has direct control over the firsttwo error sources (i.e., independent and dependent variable error), primarily through design and implementation of appropriate monitoring programs and use ofproper data reduction techniques. The lasttwo sources (i.e., parameter and model error) are also under user control to the extent thatthe user selects the model(s) deemed appropriate for specific application. Research (Walker 1981, 1982, 1985) has been directed at minimizing the lasttwo error sources byreviewing, screening, refining, calibrating, and testing arrays ofmodels which are appropriate forreservoir applications under specific conditions. The impacts oferrors inspeci$ing model input variables orcoefficients depend upon the sensitivities ofmodel predictions to those inputs. Sensitivities, inturn, reflect model structure and variable ranges. Asensitivity coefficient can be conveniently expressed as anormalized first derivative, or asthe percent change inamodel output variable induced bya 1-percent change inamodel input. For example, a sensitivity coefficient of 1.0would indicate thatthe output isproportional to the input; inthis situation, for example, a5-percent error inspeci&ing the input would propagate through the model and cause a 5-percent error inthe predicted output. For asensitivity coefficient of0.2, however, a5-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 orestimate accurately. Figures 1.3 and 1.4display sensitivity coefficients for models predicting mean phosphorus concentrations inreservoirs assuming first- and second-order sedimentation reactions, respectively. Inboth cases, the output variable isthe error term orthe ratio ofthe observed to the predicted mean phosphorus concentration. Input variables used to calculate this ratio include the observed pool concentration, inflow concentration (flow-weighted over allsources), flushing rate (outflow/volume), and sedimentation coefficient. Sensitivities varywith flushing rate overthe approximate range encountered inCE impoundments (median value forreservoirs used inmodel testing
= 7/year. At low flushing rates (or longhydraulic residence times), sensitivities
Chapter 1 Introduction 1-111.0

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 andflushing rate arerelatively high (approach ing 1.0forthe first-order model and0.5 forthe second-order model). This reflects the relative importance ofthe sedimentation term inthe overall phosphorus balance ofthe reservoir. Athigh flushing rates, sensitivities to the sedimentation coefficient and flushing rate approach zero forboth models. Inthis situation, the sedimentation process isrelatively unimportant, and modest errors inthe specified flushing rate a.dor sedimentation coefficient canbe tolerated without having major impacts onthe predicted pool concentration. Because the sedimentation coefficient isestimated from highly simplified empirical models (whereas the other input terms canbe directly measured), its sensitivity characteristics have astrong influence on model performance and uncertainty over the range offlushing rates.
1-12 Chapter 1 Introduction1.0

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 1.4are intended primarily to demonstrate sensitivity analysis concepts. They also illustrate some important basic characteristics of empirical nutrient balance models:

a. Sensitivities arehighest for inflow and pool phosphorus concentrations over the entire range offlushing rates. This emphasizes the importance ofmonitoring programs (tributary and pool) and data reduction procedures to modeling efforts. b. Because ofahigher sensitivity to phosphorus sedimentation, potential prediction errors aregreater forreservoirs with lower flushing rates.

Chapter 1 introduction 1-13While pool nutrient concentrations can bepredicted relatively easilyfrom inflow concentrations inreservoirs with high flushing rates, predictions ofbiological responses (as measured bychlorophyll a) may be more difficult because oftemporal variability innutrient levels (induced bystorm events, for example) and/or controlling effects ofturbidity andflushing rate. The importance of obtaining accurate inflow and pool concentration estimates for model implementation has ledto the development ofthe computer programs described in subsequent chapters. FLUX andPROFILE are designed to make efficient use oftributary and pool monitoring da~ respectively, incalculating the required summary statistics. 

### Summary of Assessment Procedures Figure 1.5 depicts the basic steps involved inapplying the eutrophication assessment procedures described inthis and subsequent chapters. The “pathway” comprises four general stages:
a. Problem identification. b. Data compilation.
c. Data reduction. d. Model implementation. Once the userhas developed aworking understanding ofthemodel structures, assumptions, and limitations byreviewing basic references and supporting research (see References and Bibliography), most ofthe effort and cost would typically be involved inthe data compilation and data reduction stages. Three computer programs have been written to assist at various stages ofthe analysis. The functions ofthese programs are outlined below:

a. FLUX

-estimation oftributary mass discharges (loadings) from grab sample concentration data and continuous flow records. b. PROFILE

-display and reduction ofpool water quality data.
c. BATHTUB

- implementation ofnutrient balance and eutrophication response models. Figure 1.5 summarizes the basic inputs, functions, and outputs ofeach supporting program. This chapter provides anoverview ofeach analytical stage. Details aregiven insubsequent chapters, along with examples and guidance for use ofthe 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, andwater uses. b. Water quality standards andmanagement objectives.
c. Whether the reservoir isexisting orplanned. d. Specific managementstrategies orimpacts to reevaluated.

Chapterl Introduction 1-15e. Types ofevaluations to beperformed. (1) Diagnostic. (2) Predictive. J Classes ofmodels to beused. (1) Nutrient balance. (2) Eutrophication response. Ifthe analysis isnot directed toward evaluating specific management strategies orimpacts, the general objective maybeto develop perspectives onreservoir water quality conditions and controlling factors aspart ofa“diagnostic” study. This may lead, inturn, to future evaluations ofspecific management strategies designed for water quality control. Two general types ofevaluations maybe pefiormed. Inadiagnostic mode, the models are used as aframework forinterpreting monitoring data from the reservoir and/or itstributaries. Adiagnostic study provides insights into factors controlling algal productivity and rankings oftrophic state indicators versus water quality criteria and/or data from other CE reservoirs. Inapredictive mode, the models are applied to predict future conditions inaplanned reservoir orinan existing reservoir undergoing changes innutrient loading regime and/or other controlling factors. Model classes are determined bythetypes ofanalyses to beperformed. Both nutrient balance and eutrophication response models arerequired for a predictive analysis. Diagnostic studies ofexisting 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 orload/response relationships. Monitoring requirements aregenerally more stringent for implementing nutrient-balance models than for implementing eutrophication-response models. Response models and pool monitoring data may be used inpreliminary diagnostic studies aimed atdefining reservoir conditions. Insome reservoirs, this may be followed byimplementation ofamore elaborate monitoring program designed to quanti~ nutrient loadings and to support nutrient-balance modeling. Priorities can be established based upon the severities ofexisting eutrophication-related problems (ifany), intensities and types ofwater use, and potential for future improvement or degradation owing to changes inloading regime.

1-16 Chapter 1 IntroductionData compilation As shown inFigure 1.5data compilation occurs intwo general areas. The reservoir data required for implementation ofeutrophication-response models include morphometric characteristics, outflow hydrology, and pool water qualityobtained over atleast one complete growing season (three preferred). The watershed data required for implementation ofnutrient-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 atreservoir entrypoints over atleast one full water year (three preferred). Details on data requirements and suggested monitoring designs are given later inthis chapter.

Data reduction Inthe data reduction phase, pool andtributary water quality data are reduced or summarized informs which can serve as model input. Since the models generally deal with conditions averaged over agrowing season within defined reservoir areas (segments), data reduction involves the averaging or integration ofindividual measurements, sometimes with appropriate weighting factors. The FLUX program isdesigned to facilitate reduction oftributary inflow monitoring data and reservoir outflow monitoring data. Using avariety ofcalculation techniques, FLUX estimates the average mass discharge orloading that passes agiven tributary monitoring station, based upon grab-sample concentration data and acontinuous flow record. Potential errors inthe estimates are also quantified and canbeused to (a) selectthe “best” orleast error loading estimate, (b) assess data adequacy, and (c) improve future tributary monitoring efficiency viaoptimal allocation ofsampling effort among seasons and/or flow regimes. Graphic displays ofconcentration, flow, and loading data are also provided for diagnostic purposes. The PROFILE program facilitates analysis and reduction ofpool water qualitydata from existing reservoirs. A variety ofdisplay formats are provided to assist the user indeveloping perspectives on spatial andtemporal water quality variations within agiven reservoir. Algorithms are included for calculation of hypolirnnetic oxygen depletion rates and forrobust estimation ofareaweighted, surface-layer mean concentrations ofnutrients and other response measurements used insubsequent modeling steps.
ModeI implementation The BATHTUB program applies empirical eutrophication models to morphometncally complex reservoirs orto collections ofreservoirs. The program performs water and nutrient balance calculations inasteady-state,
Chapter 1 Introduction 1-17spatially segmented hydraulic network which accounts for advective transport, diilbsive transport, and nutrient sedimentation. Eutrophication-related water quality conditions (expressed interms oftotal phosphorus, total nitrogen, chlorophyll a, transparency, organic nitrogen, particulate phosphorus, and hypolimnetic oxygen depletion rate) arepredicted using empirical relationships previously developed and tested forreservoir applications (Walker 1983). To reflect data limitations orother sources ofuncertainty, keyinputs to the model can be specified inprobabilistic terms (mean and CV). Outputs are expressed interms ofamean value and CVfor each mass balance term and response variable. Output CVSare based upon afirst-order error analysis which accounts for input variable uncertainty and inherent model error. As shown inFigure 1.5, applications ofBATHTUB would normally follow use ofthe FLUX program for reducing tributary monitoring data and use ofthe PROFILE program forreducing pool monitoring data. Use ofthe data reduction programs is optional ifindependent estimates oftributary loadings and/or average pool water quality conditions are used. 

### Data Requirements This section summarizes datarequirements to support model applications. The following categories are discussed:

a. Watershed characteristics. b. Water and nutrient loadings.
c. Reservoir morphometry. d Pool water quality andhydrology. Before describing each area indetail, itisappropriate to discuss some general concepts and guidelines that may behelpful inthe design ofareservoir study. IrIatypical application, most ofthe 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 forthe study. Data requirements can begiven rather explicitly, as determined bythe listof model input variables. Specific data sources and monitoring program designs cannot be dictated, however, because they are influenced byunique aspects of each reservoir and itswatersheds, the extent ofexisting dat~ logistic considerations, and study resources.

1-18 Chapter 1 IntroductionCompilation and review ofexisting data are important initial steps inconducting areservoir study. Preliminary application ofmodels using existing data (even ifinadequate) canhighlight data strengths and weaknesses andhelp to focus fhture monitoring activities. Insome cases, existing data maybe adequate to support modeling efforts. When existing data are inadequate or unavailable, aphased monitoring program isgenerally indicated. The first phase involves asmall-scale program designed to obtain preliminary data for use indesigning efficient monitoring programs for subsequent years. Aphased study can be arelatively cost-effective means of data acquisition. Given specific objectives (e.g., quanti@ng annual total phosphorus load or growing-season mean chlorophyll a concentration inan existing reservoir), statistical methods can be applied to improve monitoring efficiency. Asthe efficiency ofamonitoring program increases, the amount ofuncertainty (variance) inthe measured variable decreases. Monitoring efficiency may be improved byoptimizing the allocation ofsampling effort, subject to logistic and economic constraints. Examples ofsuch optimization procedures include the following:
a. Allocation ofsamples among flow regimes to estimate loadings from a given tributary. b. Allocation ofsamples among tributaries to estimate total reservoir loading.
c. Allocation ofsamples among stations, depths, and dates to estimate reservoir-mean concentrations. Phased studies oruseful existing databases are required to implement these optimization procedures. Because oflogistic 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 isused inthe development and interpretation ofhydrologic and nutrient loading dat~ inthe design oftributary monitoring programs, and inthe assessment ofproblem sources and control strategies. Maps (U.S. Geological Survey topographic orother) arethe most useful formats forthis type ofinformation. Separate maps (or aseries oftransparent overlays) can be used to summarize the following types ofwatershed tiormation:

a. Elevation contours. b. Subwatershed delineations.
Chapter 1 Introduction 1-19c. d.

e. J Dominant land uses. Soiltypes. (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 aregenerallyusefid sources ofwatershed Mormation. Soils information would also be available from the Soil Conservation Service. The information should be summarized inatabular form bysubwatershed. Land uses, soiltypes, topography, and point sources are important factors in determining runoff and nutrient export from agiven subwatershed. This type oftiormation isused 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 orproportion monitored loads from anearby watershed with similar land uses and soiltypes, based upon drainage area). Projections offuture land use and point-source nutrient loads are also required forpredicting impacts ofwatershed development.

Water and nutrient loadings The formulation ofwater andnutrient balances forthe reservoir is acritical step inthe empirical modeling process. The following components are of concern:

1-20 a. Water. b. Total phosphorus.
c. ortho phosphorus.

Chapter 1 Introductiond. 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 maybe omitted ifmonitoring data and/or preliminary mass balance calculations indicate thatthe 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 ofnutrient sedimentation models which account forthe “availability” orpartitioning oftotal nutrient loads between dissolved and particulate (or inorganic and organic) fractions. Conservative substance balances are useful fortesting water balances and calibrating diffhsive transport rates insegmented reservoirs. The nutrient species listed above correspond tothose monitored bythe U.S. Environmental Protection Agency (EPA) National Eutrophication Survey, theprimary data source used inmodel development andtesting. Monitoring of other species (particularly, total dissolved phosphorus) maybe desirable for deftig inflow nutrient partitioning and availability. Because ofexisting data constraints, however, the models are based upon the above species. Generally, balances should beformulated over both annual and seasonal (e.g., May-September) time periods. Annual balances should be calculated on awater-year (versus calendar-year) basis. While traditional nutrient loading models deal with annual time scales, seasonal loadings arebetter predictors of trophic status inmany reservoirs. The methodologies presented in subsequent sections can be applied separately to annual and seasonal nutrient balance data. Nutrient residence time criteria areused to assess the appropriate time scale for each reservoir. The nominal definition ofseasonal (May-September) canbe adjusted in specific applications, depending upon seasonal variations ininflow hydrology and, especially, pool level. For example, ifafull recreational pool were maintained June through August and much lower elevations were maintained during other months for flood control purposes, then aJune-August time scale may be more appropriate for seasonal nutrient balances. Generally, seasonal balances are less important inprojects with little orno inflow or outflow during the summer months. The formulation ofboth seasonal and annual balances isgenerally recommended for allapplications and does not substantially increase monitoring requirements, since both sets ofloading estimates can be derived from the same monitoring program. For each component and time scale, acontrol volume is drawn around the reservoir (or reservoir segment) and the following mass balance terms are quantified:
Chapter 1 Introduction 1-21a. Total inputs. b. Total OU@ltS.

c. Increase instorage. d. Net loss. Table 1.2outlines the specific elements ofeachterm and general data sources. Since water isconservative, the net loss term inthe water balance (estimated by difference) reflects errors inthe estimates ofthe other water balance terms. For nutrients, the net loss term canbe estimated bydifference or, inapredictive mode, byusing empirical nutrient sedimentation models which have been calibrated and tested forreservoir 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 Ingeneral, direct monitoring isrecommended to quanti& major flow and nutrient sources. Table 1.3 summarizes “minimal” and “desirable” designs for

1-22 tributary monitoring programs and methods forquanti&ing other loading components. These are intended asgeneral guidelines to be modified based

Chapter 1 IntroductionChapter 1 Introduction 1-231-24 Chapter 1 Introductionupon site-specific conditions. The basic design for major tributaries and outflows consists ofcontinuous flow monitoring and acombination ofperiodic grab-sampling and event monitoring for concentration. A sampling program weighted toward high-flow regimes isgenerally desirable forestimation of loadings. The multiple objectives ofestimating both annual and seasonal loadings should be considered indesigning surveys. The FLUX program can be applied tohistorical and/or preliminary monitoring data to assist insampling design. While balances are formulated forthe study (monitored) period, ahistorical hydrologic record isdesirable to provide perspective on study conditions in relation to long-term averages and extremes. Long-term hydrologic records are usually available forreservoir discharge sites and major tributary inflows. If not, records from anearby, 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 isrequired fornutrient balance and eutrophication response models. Itisusually readily available from project design memoranda and other sources. Amap indicating the following basic idormation isuseful:
a. Distance scale. b. Shoreline fortypical and extreme pool levels.
c. Bottom elevation contours or soundings. d. Tributary inflows and anydirect point sources.
e. Pool and tributary monitoring station locations. The following morphometric data should also be compiled intabular form:
a. Elevation/area volume table. b. Typical operating pool elevations (rule curve).
c. Reservoir bottom elevation ateach pool sampling station. d. Volumes, surface areas, and lengths ofmajor reservoir segments at typical operating elevations. This tiormation isused indata reduction (PROFILE) and modeling (BATHTUB).
Chapter 1 Introduction 1-25Pool water quality and hydrology In studies ofexisting reservoirs, pool water quality andhydrologic data are used forthe following purposes:
a. Assessing trophic state, related water quality conditions, and controlling factors. b. Model testing and calibration. Expressed interms ofmodel variables, the primary objectives ofthe monitoring program are to obtain the data required for calculation ofgrowingseason, mixed-layer, average concentrations ofthe 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 isto estimate hypolimnetic and metalimnetic oxygen depletion rates. Secondary objectives areto develop perspectives on spatial variations, vertical stratification, basic water chemistry, and other variables which are directly orindirectly 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 ofconditions within the reservoir may be obtainable from historical data and canbe veryuseful indesigning future surveys.

1-26 The objectives ofidentifying 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 ofamajor tributary arm are much more important than variations perpendicular to the flow. Ifthey exist, longitudinal gradients innutrients, algal biomass, and transparency areusually steepest inupper pool areas; this
Chapter 1 IntroductionTable 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 1-27suggests that stations should be more closely spaced inupper pool areas to permit adequate resolution ofgradients. Most ofthe reservoir volume, however, isusually located inthe lower pool areas, where width and depth tend to begreater and spatial gradients tend to be less pronounced; this suggests a greater emphasis onlower pool stations forthe purposes ofcalculating reservoir means. Because ofthese trade-offs, itisdifficult touse a statistical approach for optimizing station placement within agiven reservoir.
Ghen multiple sampling objectives, areasonable design rule isto distribute stations throughout representative areas ofthe reservoir. The size, morphometric complexity, and loading distribution ofareservoir largely determine the required number ofstations. Aminimum ofthree stations (upper-pool, midpool, and near-dam) arerecommended for small projects with simple morphometry. Based upon reservoir morphometnc information, weighting factors canbe applied to data from each station incalculating 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 ininformation content) ofmeasurements made ineach reservoir area or segment during each sampling round. There are several ways inwhich replication can bebuilt into survey designs, including the following:
a. Multiple sampling atagiven date, station, and depth. b. Multiple sampling with depth within the mixed layer atagiven date and station.
c. Multiple sampling stations within agiven reservoir segment or area, d. High temporal sampling frequencies, permitting aggregation of data from adjacent sampling dates. Indesigning surveys, combinations ofthe above strategies can be employed to provide data which include atleastthree measurements for each reservoir segment and sampling round. Inthe “desirable” design (see Table 1.4), three samples are suggested within themixed layerfor each station and date. Since the stratum ismixed, onthe average, the three samples can betreated as replicates. Other strategies listed above canbeused inconjunction with depth sampling to provide replication. Another monitoring objective isto sample each station on each sampling round; this greatly simplifies reduction ofthe data and error analysis, asimplemented inthe PROFILE program.

1-28 Assuming representative station distribution and proper sampling and analyticaltechniques, the “precision” ofamean, surface-layer, growing-season value depends largely upon thenumber ofsampling rounds andthe inherent temporal variabilities ofwater quality components inthe reservoir being studied. For sampling periods ofroughly aweek or longer, the variance ofthe
Chapter 1 Introductionmean isroughly inversely proportional to thenumber ofrounds. Based upon analyses ofvariance applied to model development data sets (Walker 1980, 1981),temporal variance components ofphosphorus, transparency, and chlorophylla aretypically 0.31,0.33, and 0.62, respectively, expressed as CVS. Figure 1.6shows the estimated accuracies ofreservoir mean concentrations computed from sampling designs with between 1and 30 sampling rounds over arange oftemporal CVS. The “value” ofeach additional round, as measured bythe reduction inthemean CV, decreases asthetotal number ofrounds increases. This figure provides arough perspective on design sensitivity and a basis for interpreting the reliability of data fromhistorical monitoring activities, provided the sampling regimes were both specified and representative.

TEMPORAL COEPflCKt4TOFVARIATION 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 oftemporal CVS The “adequacy” ofagiven monitoring program ispartially determined by the precision ofthe mean concentration estimates calculated from the data. Because ofthe limited pool sampling schedule employed bythe EPA National Eutrophication Survey (three tofour sampling rounds pergrowing season), typical error CVSwere onthe order of0.18 for mean total phosphorus, 0.18 for mean transparency, and 0.28 for mean chlorophyll a. More precise estimates (e.g., mean CVSless than 0.10 for nutrients andtransparency and 0.15 for mean chlorophyll a) aredesirable for model applications inareservoir management context.
Chapter 1 Introduction 1-29The purpose ofsampling inandbelow thethermocline (Table 1.4) isto provide information onvertical stratification and the accumulation and transformation ofnutrients within thehypolimnion. Many important secondary water quality effects ofeutrophication areexpressed inbottom waters, including oxygen depletion, development ofreducing conditions, nutrient accumulation, iron and manganese releases, and sulfide and ammonia generation. While nutrient data from thehypolimnion arenot used exclusively inthe models, they are important for developing anunderstanding ofnutrient cycling and reservoir processes. Since metaiimnetic andhypolimnetic samples are less important for trophic state assessment and model implementation, however, sampling fi-equencies inand below the thermocline canbe lower than those used forthe mixed layer.

1-30 Chapter 1 Introduction

# 2 FLUX

FLUX Overview
FLUX isaninteractive program designed foruse inestimating the loadings ofnutrients or other water quality components passing atributary sampling station over agiven period oftime. These estimates canbe used informulating reservoir nutrient balances over annual orseasonal averaging periods appropriate for application ofempirical eutrophication models. Data requirements include (a) grab-sample nutrient concentrations, typically measured ataweekly to monthly frequency for aperiod ofatleast 1year, (b) corresponding flow measurements (instantaneous ordailymean values), and (c) acomplete flow record (mean dailyflows) forthe period ofinterest. 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 isalso included. Inmany cases, strati&ing the data increases the accuracy and precision ofloading estimates. Uncertainty ischaracterized byerror variances ofthe loading estimates. Avariety ofgraphic and tabular output formats are available to assist the user inevaluating data adequacy and inselecting the most appropriate calculation method and stratification scheme for each application. FLUX provides Mormation which can beused to improve the efficiencies offuture monitoring programs designed to provide data for calculating loadings and reservoir mass balances. The succeeding sections ofthis chapter contain descriptions ofthe following topics:

a. Input data requirements. b. Theory.
c. Program operation. d Typical application sequence.
Chapter 2 FLUX 2-1e. 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 ofcollection, concentration, and instantaneous flow). The other describes the complete flow record (date, mean dailyflow) over the period of interest. Most ofthe effort inapplying FLUX isgenerally involved insetting up the required data files. To facilitate this effort, FLUX canread files inavariety offormats, as described inasubsequent section (see Data fileformats). The function ofthe program isto usethe water quality information inthe sample data setto estimate the mean (ortotal) loading which corresponds to the complete flow distribution overthe period ofinterest. Allprogram calculations and output are inmetric units, withflows expressed inmillion cubic meters (= cubic hectometers, hm3)peryear, concentration inmilligrams per cubic meter (parts per billion), and loading inkilograms peryear. The data can be stored inother units and converted to the appropriate units when accessed byFLUX (see Appendix B). For atypical nutrient-balance study, sample data sets would include the following components: instantaneous flow, total phosphorus, ortho-phosphorus, total nitrogen, inorganic nitrogen, and aconservative substance such as chloride. Potential applications ofthe program are not restricted to these constituents, however. The sample data arenormally derived from periodic grab-sampling. Flow measurements stored with the water quality data should correspond to the times ofsampling. Daily mean flows canbeused inthe absence ofinstantaneous flow measurements; FLUX can automatically pair sample concentrations with corresponding daily mean flows specified inthe complete flow record. Generally, samples are collected periodically (weekly to monthly) over ayear and over arange offlow regimes. Ifintensive storm-event monitoring has been conducted, resulting discrete orcomposite samples should be summarized before they are accessed byFLUX; inthis case, each record inthe sample data setincludes anevent mean flow and aflow-weighted mean concentration for each component. Differences inthe duration ofcomposite samples are not considered inthe current version ofFLUX. Ifcontinuously sampled events represent asignificant fraction ofthe total loading over the estimation period, the program may overestimate the error variance ofthe loading estimates. To avoid severe biases inthe load estimates, special consideration must begiven to

2-2 Chapter 2 FLUXthe specification ofsample flows insmall, flashy streams or storm sewers (see Typical application sequence). The reliability ofloading estimates strongly reflects monitoring program designs. Water quality samples should betaken overthe ranges offlow regime and season which are represented inthe complete flow record. For agiven number ofconcentration samples, loading estimates willusually be ofgreater precision ifthe sampling schedule isweighted toward high-flow seasons and storm events, which usually account for ahigh percentage ofthe annual or seasonal loading. While the calculation methods described below are designed to make efficient use ofthe available datq they cannot work miracles. Ifthe basin dynamics are such that annual loadings are dominated strongly byafew extreme events, no calculation procedure willgive an acceptable answer without representative samples from atleast some ofthe major events. FLUX provides graphic and tabular output which canhelp to evaluate the adequacy of the sample data set foruse inload 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 atatime. Concentrations which are entered as zero ornegative values are assumed to be missing. Sample records with zero ornegative flow values arenot used inload calculations. AllFLUX calculations are performed incomputer memory; source data files are not modified. The flow data set specifies the complete flow distribution, which isgenerally derived from continuous stage or velocity measurements made atornear the water quality monitoring site. Typically, flow records consist ofamean flow for each dayinthe period ofinterest. Inthe absence ofdailymeasurements, other averaging flow periods can also beused (weekly, monthly), but with some loss ofaccuracy. Ifacontinuous flow record isnot available for aparticular site, one might be constructed using simulation techniques or correlating available flow measurements with simultaneous data from anearby benchmark station with acontinuous flow record and similar watershed. Missing values are permitted inthe flow distribution file, but they should be avoided byestimating 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 byFLUX reflect total transport inthe downstream direction. This maybe different from the nettransport estimates appropriate foruse inBATHTUB or other massbalance models. Ifthe stream contains significant reverse flows, an option is available for calculating total transport intheupstream direction; this essentially involves reversing the sign ofthe sample flow and dailyflow data. The net downstream transport can subsequently be calculated bysubtracting the total upstream transport rates from the total downstream transport rates. Itis convenient to define thetime period represented inthe sample data set asthe “sampling period” and that represented inflow data set asthe “averaging
Chapter 2 FLUX 2-3period.” Normally, these two periods correspond, i.e., the flow data set contains amean dailyflow value for each dayintheyear ofwater quality sampling. Ifthe sampling and averaging periods do not correspond (e.g., the sample set might contain data from 1978 through 1981, andthe flow setmight contain dailyflows for 1981),then the user ismaking the assumption that the flow/ concentration dynamics ofthe stream are stable, i.e., that concentrations measured between 1979 and 1980 are also representative ofthose measured in 1981. Using samples from outside the averaging period canincrease the accuracy and precision ofthe loading estimates (by increasing the number of samples and improving the coverage offlow regimes); this may introduce bias inthe loading estimates, however, ifthere are significantyear-to-year variations inthe flow/concentration relationship caused byvariations inclimate, hydrology, orwatershed land use. Ineach program run, the user specifies the date ranges and/or season ranges to beused for samples andflows; this permits estimation ofboth annual and seasonal loadings from source data files containingdata from 1ormore years ofmonitoring. The flow data setmay include dailyflows from theyear(s) ofwater quality monitoring, as well as other periods which mayrepresent “low-flow,” “average,” and “high-flow” years. Provided that asufficiently wide range of flow regimes are sampled, this permits extrapolation ofthe sample record, i.e., estimation ofyear-to-year variations inloadings based upon sample data from a specific year oryears. FLUX canhandle problems containing upto 900 samples and 8,000 daily flow records (-22 years), These constraints applyto data read into computer memory atthe start ofprogram execution, notthe size ofthe input data files. Since the user isprompted forthe ranges ofsample andflow dates to beused inagiven run, the input data files canbe much largerthan indicated above. Users should checkthe online documentation file (accessed through the HELP option ofthe main menu) for maximum problem dimensions and other program changes inupdated versions ofFLUX (Version 5.0 isdocumented 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 ineach application. Walker (198 1,1987) provides details onthe derivation and testing ofeach method. The FLUX procedure “Calculate/Loads” provides aone-page summary ofloadings calculated using each method. The user must decide which method ismost appropriate for each application, based upon factors discussed below. Inmost cases, particularly ifthe data areproperly stratified (see Data stratification), the calculation methods willgive estimates which are not
2-4 Chapter 2 FLUXTable 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 = qiCi(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 2-5significantly different from each other. Thus, the choice ofmethod willnot be critical. Desired properties ofthe loading estimates include minimum bias and minimum variance. The distinction between bias and variance (analogous to “accuracy” and “precision”) isimportant. Abiased procedure willgive the wrong answer, even for aninfinitenumber ofsamples, whereas variance inthe mean can generally be reduced byincreasing thenumber ofindependent random samples. The seriousness ofbias depends upon its size relative to the variance ofthe mean orthe standard error ofestimate. Biases less than 10percent ofthe standard error account for less than 1percent ofthe total mean squared error and aregenerally considered negligible (Cochran 1977). Bias in aloading estimate can come from two sources: unrepresentative sampling or the use ofaninappropriate calculation method. These sources are discussed below. Consistent problems with sample collection, handling, and analytical procedures can cause one type ofunrepresentative sampling; there islittlethat can be done about these problems atthe calculation stage. Another, more subtle, but generally more common type ofunrepresentative sampling results from differences inthe distributions offlows between the sampling dates and the entire averaging period. Sampled flows maytend to behigher or lower, onthe average, than the complete distribution offlows orcontain ahigher or lower percentage ofextreme flows. This can lead to bias inthe estimate ifthe calculation procedure does not take the relative flow distributions into consideration bydirectly representing the flow/concentration relationship and/or bystrati~ing the sample, as described below. Even ifthe sampled and total flow distributions are equivalent, bias can be introduced as aresult ofthe calculation method. For example, loading calculated asthe product ofthe mean sample concentration andthe mean flow over the averaging period would be badly biased ifflow and concentration are (even weakly) correlated (Walker 1981). Because ofthe potential bias associated with this method, itisnot included intheprogram. The sixincluded methods have been selected and tested sothat, forrepresentative 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 islimited ultimately bythe sample data sets. Method applicability depends upon the relationship between concentration and flow. InFLUX, this characteristic isrepresented bythe slope ofa log(Concentration) versus log(Flow) regression (C/Q slope) derived from the sample data set. Typically, the C/Q slope approaches -1 atmonitoring stations which are downstream ofmajor point sources. The slope may approach or exceed 1atmonitoring stations where the load isgenerated as aresult of runoff orhigh-flow events, particularly forparticulate components. Inmany watersheds, the C/Q slope fortotal phosphorus varies with flow (negative atlow flows to positive athigh flows). FLUX graphic and tabular output helps to
2-6 Chapter 2 FLUXcharacterize the concentratiordflow relationship; this characterization isessential to selecting the appropriate calculation method and developing reliable loading estimates. Method 1(direct load averaging) isthe simplest ofthe calculation schemes. Itgives unbiased results onlyifthe 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 onthe unsampled days isnot considered. This method ismost appropriate for situations inwhich concentration tends to be inversely related to flow (C/Q slope approaching

-1;loading does not varywith flow). This might occur, for example, atastation which isbelow amajor point source and the flow/ concentration relationship iscontrolled bydilution. Method 2bases the loading estimate onthe flow-weighted average concentration times the mean flow overthe 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 orweakly related. Some bias may occur for extreme flow/concentration relationships. Intest simulations ofastream with aC/Q slope 0.75, Method 2 overestimated loadings byan average of 10percent (Walker 1987). This bias can be substantially reduced by stratifying the samples into groups ofrelatively homogeneous concentration and applying the method separately to each group, as described in more detail below. This isperhaps the most robust and widely applicable method, especially when applied to stratified data sets. Method 3 modifies the Method 2estimate byafactor that isdesigned to adjust forpotential bias insituations where concentration varies with flow. The factor was developed byBeale(1962) and applied inaload estimation method developed bythe International Joint Commission(IJC)(1977), as described by Bodo andUnny(1983, 1984). Trial simulations indicate that, compared with Method 2, this procedure ismoderately successful atreducing bias buttends to have slightlyhigher mean squared error for streams with C/Q slopes greater than orequal to zero (Walker 1987). Method 4 isthe regression method developed byWalker (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 incases where the dailyflow data setcontains asignificant number ofzero flow values. This method petiorms well over arange ofC/Q slopes. Some bias isintroduced athigh C/Q slopes. Ata slope of0.75, for example, simulated bias is 13percent ofthe mean loading but accounts for only 6percent ofthetotal mean squared error (Walker 1987). Additional simulations indicate that bias also occurs ifthe C/Q slope ishighly nonlinear (i.e., quadratic orhigher order polynomial). This problem canbe resolved bystrati- &ing the sample so that the relationship isapproximately linear within each group.

Chapter 2 FLUX 2-7Method 5 modifies theMethod 4 estimate byafactor accounting for differences invariance between the sampled andtotal flow distributions (Walker 1987). The derivation ofthe method isbased upon expected value theory (Benjamin and Cornell 1970). Method 5 should not beused incases where the dailyflow data set contains asignificant number ofzero flow values. As for Method 4, bias resulting from nonlinearity inthe log (c) versus log (q) relationship can bereduced bystrati$ing the data. Method 6 isanother regression-based calculation method. For each stratum, the C/Q regression equation isapplied individually to each dailyflow value. In contrast, Methods 4 and 5 use onlythe flow means and variances. A small correction forbias resulting from the logtransformation isalso included. This method is often appropriate forgenerating daily, monthly, or yearly load time series using an optional FLUX procedure designed forthis purpose (Calculate/Series). Relatively intensive sample data sets andwell- defined concentration/flow relationships are required forreliable application ofthis method. Method 6 isgenerally preferred over the other regression-based methods when the flow/concentration relationship iswell defined. Inapplications to small, flashy streams, special consideration must begiven to the specification ofsample flows to avoid bias inMethod 6estimates (see Typical application sequence). Error analysis calculations aretime-consuming relative to the other methods. An option toturn offthe error analysis forMethod 6is included (Utilities/Set/Method 6). For each method, thejackknife procedure (Mosteller andTukey 1978) is used to estimate error variance. This involves excluding each sampling event, one atatime, and recalculating loadings, as described inTable 2.2. While alternative, direct estimators ofvariance are available from classical sampling theory for most ofthe methods (Cochran 1977; Walker 1981; Bodo and Unny 1983, 1984), such formulas tend to relyupon distributional assumptions. The direct estimators are generally applicable to large samples andnormal distributions, neither ofwhich istypical ofthis application. As described byCochran (1977), thejackknife has improved properties for ratio estimators derived from small, skewed samples. Use ofthejackknife procedure also provides auniform basis for comparing calculation methods with respect to estimated variance. Simulations (Walker 1987) indicate thatjackknifing provides areasonably unbiased estimate for error variance for arange ofC/Q slopes. Two important factors should be considered ininterpreting the variance estimates. First, the estimates are themselves subject to error and are oflimited accuracy in small sample sizes, particularly ifthe sampled flow distribution isnot representative. Second, the variance estimates do notreflect effects ofbiases associated with some calculation methods under certain conditions, as discussed above. Thus, while the estimated variances are important factors to consider inselecting the “best” loading estimation method, the sample characteristics and bias potential should also be considered. FLUX diagnostic procedures assist inthis process, as described below.

2-8 Chapter 2 FLUXError variance estimates developed byFLUX assume thatthe samples are statistically independent. This maynot bethe case ifthe filecontains large numbers ofdiscrete samples taken within relatively short periods oftime. One approach to solving this problem isto composite the samples byevent prior to calculating loadings. Important Wormation onthe flow/concentration relationship may be lostincompositing, however. As an alternative to compositing, discrete samples can begrouped byevent onlyforthe purposes oferror analysis. InFLUX, sampling events are defined bythe program parameter T. = Maximum Event Duration (days). Samples collected within T, days ofeach other are considered part ofthe same sampling event. The default setting for T. is 1day. This setting onlyinfluences the error variance estimates (not the mean loading estimates). Itonly influences error variance estimates developed from relatively intensive sample data sets containing multiple samples onthe same dayorwithin the current N~setting.

Data stratification FLUX includes an option to divide the input flow and concentration data into aseries ofgroups 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 ofeach group inthe total flow distribution (see Table 2.2). The groups, or “strat~” canbe defined based upon flow, season, and/or date. Stratification can serve three basic functions:

a. Adjust for differences inthe frequency distributions ofsampled and unsampled flow regimes. b. Reduce potential biases associated with some calculation methods and/ or sampling program designs.
c. Reduce the error variance ofthemean loading estimate. When sample data are adequate, stratification can offer significant advantages over the direct methods and provide insights that canbeused to improve sampling efficiency infuture years. Inmost applications, the groups are defined based upon flow. The “flowinterval” method was developed bythe U.S. Army Engineer District, Buffalo (1975), for use inthe Lake Erie Wastewater Management Study and is described byVerhoff, Yaksich, and Melfi (1980) andWesterdald etal. (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 databased upon flow reduces the loading
Chapter 2 FLUX 2-92-1o 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~. = , / ~ (N&J ntN~Sm~ V*=

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

variance within each group and results inlower variance forthe total loading estimate. Aflow-stratified version ofMethod 2written inSAS (Statistical Analysis System) was developed and applied to estimate phosphorus loadings inaVermont lake study (Walker 1983). The IJC method described byBodo and Unny (1983, 1984) isaflow-stratified version ofMethod 3. InFLUX, data groups or strata can be defined based upon flow range, date range, and/or season range. Generally, flow ranges would beused andthe data would be stratified into two orthree groups based upon flow. In some situations, however, itmaybe desirable to strati~ based upon sampling date or
Chapter 2 FLUXseason. Stratification based upon season may beusefti insituations where there is astrong seasonal variation inconcentration which isindependent of flow orfor streams with highly regulated flows, such as areservoir outflow station (particularly when intake levels are varied seasonally). Flowindependent, seasonal variance components are more likelyto be detected in analysis ofdissolved or inorganic nutrient concentrations (particularly nitrate) than inanalysis ofparticulate ortotal nutrient concentrations. In deftig stra~ one objective isto isolate homogeneous subgroups, based upon the flow/concentration relationship assumed bythe calculation method (constant loading forMethod 1,constant concentration forMethods 2 and 3, and log-linear flow/concentration relationship forMethods 4-6). A second objective isto set stratum boundaries so that the sampled and total flow distributions are equivalent within each stratum. This protects against bias inthe loading estimates and applies particularly tohigh-flow strata. As described above, the method used to estimate error variance does not detect bias. Ifthe flow distributions are not equivalent within each stratum, then minimum variance isless reliable as acriterion for selecting the “best” calculation method and loading estimate. Statistical and graphical tests areprovided to compare flow distributions within each stratum. Robustness ofthe loading estimate decreases asthenumber ofstatistical parameters which must beestimated from the sample data setincreases. The number ofparameters which must be estimated depends upon the calculation method and upon thenumber ofstrata. Methods 1and 2require one parameter estimate for each stratum. Methods 3, 4, 5, and 6require two parameter estimates per stratum. Strati&ing the data into two orthree groups based upon flow and using Method 2isgenerally adequate to capture the flow/ concentration relationship while requiring the fewest parameter estimates (in statistical terms, using up the fewest degrees offreedom). Ifconcentration does not vary systematically with flow, theneed forflow stratification decreases. Uncertainty inthe loading estimate isreflected bythe CV estimate reported for each calculation method. The CV equals the standard error ofthe mean loading divided bythemean loading. The CV reflects sampling error inthe flow-weighted mean concentration. Potential error variance inthe flow measurements are not considered inthese calculations. Inpractice, CV values <0.1 areusually adequate foruse inmass-balance modeling, especially considering that uncertainty inflow measurements isusually inthis range. Depending on stream dynamics, CV values <0.1 may be verydifficult 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. Ifhigher CVSarefound, 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 ifthe CV values arehigh for major tributaries.

Chapter 2 FLUX 2-11For each calculation method, FLUX generates aninvento~ ofsample and flow data inaddition to abreakdown ofthe flow, load, and variance components within each stratum, aswell asforthetotal strat~ as demonstrated in Table 2.3, for the Caddo River example. Samples have been divided into three flow intervals. Complete output forthis example isgiven atthe end ofthis 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 isroughly inversely related to sampling frequency within each stratum, the “breakdown bystratum” given inTable 2.3 is useful for evaluating sampling strategies. The low-flow stratum accounts for 55.4 percent ofthe total samples but only4.6 percent ofthetotal mass discharge. Infuture sampling, moving some ofthesamples fromthelow-flow to thehigh-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 ofthetotal loading estimate. FLUX also provides an estimate ofthe “optimal” sample distribution (expressed as percent ofthetotal sampling effort allocated to each stra~ NEOPTO/O inTable 2.3) which would minimize the variance ofthe total loading estimate for agiven total number ofindependent samples, using the equations specified inTable 2.2. Comparing the observed variance with the optimal variance provides anapproximate indication ofthepotential benefits of optimizing the sample design. Inthis case, shifting from thehistorical sample distribution across flow strata (55%/36%/8%) to the optimal sample distribution (4%/2 1%/76%) would decrease the CV ofthe load estimate from O.118to 0.045. As described byBodo and Umy (1983, 1984), stratum breakdowns can be used to refine monitoring program designs for future years, subject to practical limitations in sample scheduling andtotal budget and to requirements imposed byother monitoring objectives. The “optimal” distribution ofsampling effort indicated bythe program maybedifficult to achieve without automated equipment. An important statistical limitation isthatthe “optimal” allocation assumes that the samples are serially independent, and itmaybe impossible to take the recommended number ofindependent 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 ofthese limitations, the “optimal” design should not be viewed as anabsolute objective, but as ageneral direction for adjusting previous survey designs within practical constraints.
Diagnostics FLUX includes several routines forgenerating scatter plots andhistograms offlow, concentration, loading, and sample dates, asillustrated atthe end of this chapter. The relationship between flow and concentration partially determines the appropriate calculation method and should bereviewed ineach 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 inassessing 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 onthe unsampled days orperiods. For agiven method, observed and predicted fluxes can be compared foreach water quality sample. This provides one measure ofperformance. Ideally, the flux residuals (loglO(observed flux) minus loglO(predicted flux) should berandom and independent offlow season. Inpractice, 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 2-13date. Alternative stratification schemes canbe investigated to reduce the flowdependence and/or time-dependence ofthe residuals. Listings ofresiduals andjackknifed loading estimates areuseful for identi&- ing outliers and determining sensitivity ofthe loading estimates to individual samples. FLUX includes anoutlier detection routine which canbe used to delete suspected outliers from the sample data set. Outliers are detected based upon deviations ofthe residuals from alognormal 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 maybe lost ifanapparent outlier is actually animportant signal. Suspected outliers areusually apparent onthe 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 theFLUX menu structure and operation procedures. When the program isrun (from theDOS prompt), aseries ofhelp screens summarizing model features isfirst encountered. Iferror messages appear, itgenerally means that one oftheFLUX program fileshas been corrupted orthat your computer does nothave enough available memory. TV reinstalling the program. Tryunloading anymemory-resident software. Ifyou aretrying to run the program from Windows, try exiting Windows and running directly from DOS. The program permits selection of ‘user mode’ atstartup after introductory screens. The selection of user mode isfollowed by amenu which provides interactive access to eighttypes ofprocedures 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 Aprocedure category is selected bymoving the cursor (using arrow keys) orby pressing the first letter ofthe procedure name. Selected procedures inthe menu box arehighlighted onthe screen and underlined inthe following documentation. Assistance innavigating around the menu can be obtained by

Chapter 2 FLUXpressing the <F7> fiction key. AHelp screen describing the selected procedure can be viewed bypressing <Fl>. After each procedure is completed, control returns to the above menu screen. Essential features ofthe current data set are summarized below the menu box (not shown here).

Data procedures Data procedures control input, stratification, listing, and other manipulations ofsample and./orflow data used inload 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 innew sample orflow 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 Inthe firstthree procedures, adata-entry screen ispresented for defining all input specifications (data filenames, variable labels, time periods, and units conversion factors). Use Reset to read innew flow data and resetthe stratification scheme. Use Keep to read innew data without changing the current stratification scheme. Use Samples to read innew sample data only, without changing the current dailyflow data or stratification scheme. Use Index to read innew data from astation index file, which isauser-created ASCII file defining the storage locations andformats for concentration and flow data referring to specific stations. Using index files greatly speeds and simplifies the specification ofinput data. (See Data-entry screens.) Ifvariable labels (for dailyflows, sample flows, and concentration) are left blank on data entry screens, the user isprompted to selectthe appropriate field from alistofallfields contained inthe source data file. Screen messages track the progress of data retrieval from diskfiles. Ifthe specified data sethas fewer than three samples orno dailyflows, anerror message appears and control returns to the main menu. Note that this may occur ifthe filenames orvariable labels are entered incorrectly. Ifavalid data setisretrieved, subsequent screens include alisting ofmissing orout-of-sequence dailyflows (Data/List/
Chapter 2 FLUX 2-15Missing procedure) and asummary ofthe current stratification scheme (Data/ Stratify/List procedure). Control then returns tothe main menu. Data/Stratify procedures divide the sample and flow data into groups based upon flow, date, and/or season. Inmany cases, stratification increases the accuracy and precision ofload estimates. At leastthree samples are required ineach 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 isoften appropriate, especially when concentration iscorrelated 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 firstthree procedures defineflow boundaries automatically. Dividing the dataintotwo strata based uponflow(low-flow andhigh-flow)is often appropriate. Three ormore flow stratamaybe appropriate for relatively intensive datasetswithstrongflow/concentration relationships. The lastprocedure 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 avalid stratification scheme is defined orthe stratification scheme isreset. Data/Delete procedures operate only on data stored inmemory; they do not change diskfiles:

**One Delete**  **a Specific**  **Sample Excluded**  **Delete All**  **Sanples Excluded**  **from Current**  **Stratification Sche**  The Data/Composite procedure combines samples collected onthe same date or inthe date interval into asingle composite sample:

2-16 Chapter 2 FLUX**Ccmposite Canposite**  **Sanples** by Date The user isprompted forthetime interval (number ofdays) to be used for compositing samples. This optional procedure maybe appropriate for data derived from intensive monitoring programs providing multiple samples per date. The composite sample concentration isthe flow-weighted mean ofthe individual samples. The composite sample flow isthe average ofthe sample flows. Because ofpossible variations inactual event duration, itisgenerally preferable to composite samples prior to running FLUX; i.e., to specifi event mean flows and event flow-weighted mean concentrations inthe source data files. The Data/FlowSub procedure canbeused to testthe sensitivity ofload estimates to the types offlow measurements which are paired with sample concentrations:

**F 1** **ousub Substitute**  **Dai ly**  **Mean Flows**  **for Sanple**  **Flows** Depending upon source data files, input sample flows maybe instantaneous flows measured atthe time ofsampling. The Data/FlowSub procedure replaces sample flows with daily mean flows onthe corresponding sample dates. Samples are deleted ifthe corresponding dailymean flow ismissing or zero. This flow substitution may also beperformed intheData/Read procedures byentering “Lookup” inthe sample flow field. Data/List procedures summarize the sample and/or flow data which have been retrieved from diskfiles:

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 bereviewed to make sure thatthe correct sample and flow datahave been retrieved from disk files. Both sample flows and corresponding dailymean flows are listed bythe firsttwo procedures. Dailyflow data files read byFLUX are assumed to be sorted bydate. The Data/List/Missing procedure lists missing or out-of sequence dailyflow records. Ifanyare detected, FLUX can still operate. Itis desirable, however, to estimate anymissing flows independently andto sort flow files before running FLUX.

Chapter 2 FLUX 2-17Calculate procedures Calculate procedures canbe accessed tier valid sample andflow data sets have been read and avalid 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 beused 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 forBATHTUB applications. The Calculate/Series procedure listsflow, 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 notinclude error estimates. These procedures are included primarily forgenerating load time series for use inapplications other than BATHTUB which may require dailyormonthly estimates.
Method procedure The Method procedure asks the user to select the loading calculation method to beused ingenerating 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 isinitially selected asthe default calculation method when the program is started. Descriptions ofeach method aregiven above (see Loading calculation methods); summary descriptions can be viewed byselecting a method and pressing theHelp key<F1>orbyrunning the Help procedure.

Plot procedures Plot procedures provide important diagnostic information which canhelp in evaluating the adequacy ofthe 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, orflow as afunction ofcalculation 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 allstrata) 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 orahistogram:

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 firstthree procedures. The``estimated'' sample concentration isbased uponthe currently selected calculation method. Different symbols areusedto 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 dailyflow 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 FLUXInaddition to plotting the dailyflow values, each ofthese formats also indicates dailyflows onthe dates ofsample collection (red squares). These displays are usefhl for identi&ing gaps inthe sample record and for assessing sample coverage ofmajor hydrographyfeatures. The lLinear and 2Log displays use different symbols to identi& strata. The 3Fi11eddisplay does not identifi strata. If zero flows are contained inthe record, these are plotted as one-half ofthe lowestpositive flow value inthe 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**  Inthe first case, they axis reflects the cumulative percentage oftotal samples ortotal flow days. Inthe second case, they axis isthe cumulative percentage ofthe total sample volume ortotal flow volume. Plot/Residuals procedures display residuals forthe 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 isdefined as log10(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 caninfluence the accuracy of error estimates and determine the appropriateness oftime-series methods for estimating loads.
List procedures List procedures can be accessed only ifavalid data setand 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 adescription oftheoutlier detection method. Ifany outliers are detected, the user may electto 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). TheList/Breakdowns procedure provides detailed information onthe distribution offlow, flux, and error variance as afuction ofstratum forthe current calculation method:

Breakdowns List Load & **Flow Breakdowns**  **by Stratun;**  **Optimal** Sample Allot The top halfofthis output screen shows the sample properties. The bottom halfestimates the optimal sample allocation across strata based upon the current sample properties. The optimal allocation isdefined asthe distribution of sampling effort (percentage oftotal sample events ineach stratum) which leads to the lowest error inthe load estimate. This information can beused torefine future data-collection efforts. TheList/Jackknife procedure shows the derivation ofthe error variance estimate forthe current calculation method:

2-22 Jackknife List Jackknife Table for Current Calculation Method

**Chapter 2**  FLUXEach sample event isexcluded, one atatime, from the sample setand the load estimate isrecalculated using data from the remaining sample events. The procedure lists and displays the distribution ofload estimates with each sample event excluded. This can beused to identi~ samples which have arelatively large impact onthe computed average loads.

Utilities procedures Utilities procedures allow theuser 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 TheUtilities/Output procedure redirects program output to adiskfile orto screen:

Screen Send Output to Screen (Default) **File Send**  **Output to**  Disk **File** The selected output destination remains ineffectuntil itisreset. Even if Screen is selected, individual output screens canbe copied to diskfiles after viewing. TheUtilities/View procedure views anyDOS file stored inASCII format:

View View any DOS File Onlythe first 80 columns ofeach record are displayed. Utilities/Set procedures modi~ the default settings forvarious 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
2-23TheUtilities/Set/Events procedure sets the maximum duration ofanindependent sampling event forthe purpose ofestimating error variances:

Events Define Maximum Event Duration (Days) For Grouping Samples This setting does not influence mean load estimates. The default setting is 1day. Iftiesmple record conttis hydro~aptic events l~tig longertim 1day and ifmultiple samples are collected within events, settings longer than 1day maybe appropriate. TheUtilities/Set/Signif setsthe statistical significance levelrequired before flow/concentration regression models are applied incalculating 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 ofO. Otol.O. IfSignif=O.0, the sample regressions arenever used; the slope ofthe log concentration versus logflow relationship isalways setto 0.0 before calculating loads. IfSignif = 1.0(default), the regression slope calculated from the sample record isalways used (regardless ofits significance level). IfSignif = 0.05, the sample regression slope isused only ifitisdifferent from zero atthe 0.05 significance level. TheUtilities/Set/Restrict toggles the option to restrict concentration versus flow regressions to the range ofsampled flows:

Restrict **Toggle Option**  **to Restrict**  **Flow Ranges**  for **Model Application**  This setting only influences loads calculated using Method 6. Ifthe Restrict setting ison (default), dailyflows arerestricted to the range ofsample flows before applying the regression to calculate loads. For example, ifthe maximum sampled flow is98 hm3/year, the predicted concentration ataflow of 98 hm3/yearisapplied to alldays when the flow exceeds 98 hm3/year. Ifthe Restrict setting isoff, extrapolation ofthe regression beyond the range of sampled flows ispermitted; this isrisky, but maybe appropriate ifthe slope is well defined from the sample data and ifthe extrapolation isnot over awide flow range. This option willhave no effect ifthe range ofsample flows equals or exceeds the range ofdailyflows, which isthe desired situation when data are derived from anideal sampling program. The setting turns on and offeach
2-24 Chapter 2 FLUXtime the Restrict procedure is selected. A screen message beneath the menu indicates the current setting. TheUtilities/Set/Method 6procedure toggles the option to conduct error analysis calculations using Method 6:

Method 6 **Toggle Option**  **for Error**  **Analysis** Using Calc Method 6 IfMethod 6 setting ison (default), error estimates are calculated forMethod 6. Depending upon thenumbers ofsample and dailyflow records, these calculations canbetime-consuming because the concentration/flow regression is applied separately to each dailyflow. IftheMethod 6 setting isoff, error analyses are not conducted andthe CV oftheMethod 6load estimate is setto 0.0. The setting turns on and offeachtime the procedure is selected.
Help procedure Supplementary help screens canbe 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 tohelp screens that are organized inseven categories, as summarized below:
HELP TOPICS INTROOUCTORY SCREENS PROGRAH tlECHAN ICS GLOSSARY DATA FILE FORMATS CALCULAT ION METHODS OUTPUT FORHATS GENERALGUIDANCE Ahelp category isselected bymoving the cursor and pressing <Enter>. A list ofthehelp screens available inthe selected category ispresented. Contextsensitive help screens can also be accessed during execution ofother procedures bypressing the <F1>fiction key. The general Help menu can also be accessed from anyData-Entry screen bypressing <F9>.

Chapter 2 FLUX 2-25Quit 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 canbegenerated using formats described below (see Data File Formats). The user directs the flow ofthe program through the fourleveltree menu screen described inthe previous section. ADocumented Session showing steps involved inatypical application isprovided atthe end of this chapter. The program starts byreading inthe concentration and flow data and using the data files and date ranges specified bythe user. Data stratification can be definedhedefined atanytime, based upon flow, date, and/or season ranges, The analysis is subsequently directed from the main menu, which includes categories ofprocedures. After executing agiven procedure, the program returns to the main menu for another selection. Because each loading estimation problem isunique, itisimpossible to speci~ a“universal” pathway forthe analysis. In some cases, afew iterations (mainly involving alternative strata definitions) would berequired before arriving atan acceptable loading estimate. Generally, however, atypical program application sequence isoutlined inTable 2.4. Further steps would involve, but not be limited to, refinement ofthe stratification scheme, testing ofalternative models, deletion ofoutliers, andtesting fortrends. The selection ofthe “best” loading estimate to beused insubsequent modelingefforts isup to the user, based upon the following criteria:

a. Calculation method and stratification scheme yielding minimum estimated variance inthe mean loading estimate. b. Sensitivity ofthe loading estimate to alternative calculation methods, stratification schemes, and individual samples.
c. Residuals analysis results.

2-26 The selection can bebased primarily upon minimum estimated variance, provided that the following conditions are met (corresponding FLUX procedures are listed inparentheses):
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/Flow/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 

# I Plot/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 isrepresentative; 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 ofdate, season, andflow. (Plot/Residuals/Date,Month,Flow).

Chapter 2 FLUX 2-27d Residuals are serially independent. (P1ot/Residuals/Autocorr).
e. Sampling events are independent; for intensive data sets only. (Utilities/Set/Events). Ifthe above conditions are marginally satisfied orcannot be met because of existing data limitations, factors other than minimum variance (sensitivity and residuals analyses) should begiven greater weight. Further sampling may be indicated, particularly ifthetributary accounts for amajor portion ofthetotal reservoir loading. Differences among the various calculation methods should be interpreted in relation to the estimated variances. For example, arange of45 to 50 kg/year in the mean loading estimate isoflittle significance ifthe estimated coefficients of variation are onthe order of0.1 orgreater. Provided that flow regimes are adequately sampled, limited variation among calculation methods suggests robust results. Calculation Methods 2or 3 aregenerally the most robust and should be used (typically with flow stratification into two groups with the boundary setnear the mean flow) ifload estimates must begenerated from limited data not conforming rigidlyto the above criteria. A general approach isto refine the stratification scheme so that estimates for six calculation methods converge to acommon result. This occurs when the mean estimates forMethods 1-6 are not significantly different from each other. The uncertainty ofthe estimates (CVS)may differ substantially, however. In most cases, the Method 2 estimate willhave the lowest uncertainty and should be used ifconvergence isreached. Aregression estimate (usually Method 6) mayhave the lowest uncertainty ifstratification alone does not capture essential features ofthe flow/concentration relationship, especially ifflow and concentration are strongly correlated within thehighest flow stratum. Inapplications to small, flashy streams orstorm sewers, special consideration must be given to the specification ofsample flows. Inflashy streams, the variance and extremes ofinstantaneous sample flows will be considerably higher than the variance and extremes ofdailymean flows. This can cause severe bias inthe load estimates when (a) concentration varies with flow, and (b) either the data are stratified based upon flow oraregression method (4-6) is used. To avoid this bias, thetime scale (averaging period) ofthe sample flows should be equivalent to thetime scale ofthe dailyflows. This canbe accomplished inone oftwo ways:
a. Preprocess the instantaneous flows and sample concentrations so that each sample record read byFLUX represents adaily mean flow and dailyflow-weighted mean concentration.

2-28 b. Read the instantaneous flows and sample concentrations into FLUX. Run the “Data/Composite” procedure to calculate a dailyflow-weighted mean concentration for each sample day.
**Chapter 2**  **FLUX**Then run the “Data/FlowSub” procedure to substitute dailymean flows for sample mean flows. Then proceed with load calculations. This type ofproblem isgenerally indicated when the mean sample flow in thehighest flow stratum is significantly higher than the mean dailyflow (Calculate/Compare orCalculate/Loads procedures). Itisalso revealed by plotting sample flows against dailymean flows (Plot/Flow/Both procedure). If the sample flow rates generally exceed the dailyflow rates (particularly inthe high-flow range), one ofthe preprocessing steps outlined above should be taken. Inany application where instantaneous samples are used, itisgenerally agood idea to test whether substitution ofdailymean flows has an effect onthe load estimates. Ifsuch an effect isindicated, estimates based upon daily mean flows are less likelyto be biased. Inareservoir eutrophication study, FLUX can beused to estimate annual (October-September) and seasonal (May-September) loadings oftotal phosphorus, ortho-phosphorus, total nitrogen, inorganic nitrogen, and aconservative 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 inpredicting growing-season water quality inthe reservoir pool. Unless flow/concentration/seasonal dynamics differ markedly among thenutrient components, itisagood ideato usethe same stratification scheme for each component. The stratification scheme can be optimized for calculating total phosphorus loading (usually the most important) and subsequently used incalculating other component loadings. 

### Procedure Following is 

### Outline

alistofallFLUX procedures. Names are listed onthe left. Indentation reflects Menu level (Lines 1-4). Abriefdescription ofeach procedure isgiven onthe right. **Data Read**  **Reset Keep**  **Samples Index**  **Stratify** F1OH 2 Strata 3 Strata 4 Strata **Other General**  **Reset List**  **Delete Excluded**  **Coq30site F** **1**ousub **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** SampleAllot **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 orDattiStrati@ procedures. The help screens areaccessedby hitting <Fl>. Additional help screens containing more detailed information on specific fields maybe obtained bymoving 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**  2-31HELP 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 CONC **or 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:**  MAXIMUM **FLOU: 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**  2-33HELP 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 areprovided to facilitate this task. Five data-file formats aresupported forsample andflowdata records. One format is supported fortheoptional station index file. Briefdescriptions, naming conventions, and filenames are given inTable 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 isprovided (*.WK1), most other spreadsheet programs (including Windows versions) can export files inthe
**Chapter 2**  **FLUX**.WK1 format. Lotus WK3 and WK4 (Windows) fileformats are not equivalentto the WKl format. IfaWindows version ofLotus isbeing used, allofthe data must be stored onthe firstpage ofthe worksheet, and the .WK1 extension must be specified insaving the file. Iftheuser’s spreadsheet program cannot save orconvert files to the .WK1format, data canbeprinted to adisk as an ASCII file and edited to comply with one ofthe ASCII formats described below. The following general rules apply to allfileformats (except where noted):
a.

b.

c.
d.
e. $
/3

h.
i. j. ADate field must be included, labeled atthetop ofthe fileas 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 inwhich dates are always assumed to be inYYMMDD 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 atfirstblank row). Entries beyond the firstblank row inaspreadsheet are ignored. Sample files can be sorted inanyorder. Daily flow files should be sorted bydate. Missing values are identified using the missing value codes specified at thetop ofthe file (ASCII formats). Blank fields inspreadsheets are assumed missing. Ifablank field is intended, make sure that itistruly blank and not acharacter fieldfilled with spaces; the latter willbe interpreted as zero (not necessarily missing). For concentrations, blank, negative, zero values, or character strings are assumed missing. For dailyflows, negative orzero values (other than the specified missing value code) orcharacter strings are interpreted aszeroes (no flow). With the exception ofthe optional station field inthe first column of sample worksheets, allspreadsheet entries should benumeric values or blank. Character constants are interpreted aszeroes. Computed fields inspreadsheets (numeric values assigned byformulas) are acceptable for allfields except the optional station field (character string).

**Chapter 2**  **FLUX** 2-35k. In speci&ing filenames, variable labels, and station codes, case isnot significant (i.e., “stal” = “STA 1”= “StA1”). 1. A maximum of64 fields (columns) canbe contained inthe sample or flow data sets. FLX format files can contain upto seven fields. Each fileformat isdescribed indetail below. Examples areprovided onthe program diskette.

* .FLX Format for Sample & Flow Data This format isindicated bythe .FLX fileextension. This fixed-format file contains both sample data and dailyflow data. The filecontains 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 = 8characters) CF = Factor to convert data units to program units Program Units = MILLION M3NR (hm3/yr)forflow Program Units = MG/M3 =PPB for concentration NOTES:

a. Conversion factors contained inthe input filewill override those specified onthe input screen. b. Ifthe flow lookup option isused (sample flows retrieved from daily flows), the appropriate flow conversion factor must be specified onthe FLUX data-ent~ screen.
c. The order ofvariable labels must correspond to that specified inData Group 3 (columns). d The lastrecord ofData Group 2must 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 inYYMMDD 6-character format (e.g., 840126) or YYYYMMDD 8-character format (e.g., 19840126) Data value (include decimal points orright-justi~ infield; entries that are blank, zero, ornegative are assumed to be missing). Atleast one ofthese should refer to sample concentration. The sample flow field is optional ifthe ‘Lookup’ option is specified when retrieving data. Number ofvariable indexes defined inGroup 2

a. The lastrecord ofData Group 3 must be

- “000000”. b. Include one record for each sample (maximum samples= 500).
c. Use blanks, zeros, ornegative values for missing concentrations or sample flows. Group 4: F1OW Distribution Records

-DATE, FLOW FORMAT (F6.0,2x,F8.0) DATE = Date inYYMMDD 6-character format orYYYYMMDD 8- character format Use aconsistent format within eachfile. 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 inthe same units asthe sample flows specified in Group 3. Include decimal point orright-justi$ infield. Zero ornegative entries arevalid. Blank values are interpreted aszeros (omit the entire record ifflow ismissing for a given date). NOTES:
a. The 

### lastrecord ofData Group 4 must be

-“000000”. b. Include one record foreach mean dailyflow (maximum flow records = 7000).

**Chapter 2**  **FLUX** 2-37The file ‘CADDO.FLX’ isan example ofthe 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** 

Thefile ‘CADD02K.FLX’ isanexampleofthe 8-character dateformat.
*.DATASCII FormatforSample orFlowData This format is specified bythe ’.DAT’ file extension. format ASCII file. Column locations arenot significant. by spaces orcommas. The layout is asfollows: Line 1 Title This isafreeEntries are separated

Line 2 Number ofVariables= M (columns indatabase) Line 3 Missing Value Code (Typicallyzeroor negative) Line 4to 3+M Variable Labels (Max 8 Characters PerLabel) Line3+M...n DataRecords (AnyNumber, Max500 used atonetime) Variable labels must include adate field labeled as: YYMMDD for dates inYYMMDD Format, or DATE for dates inLotus Format (#Days from Jan 1, 1900) For compatibility after 1999, sample orflow 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 IfYY<50 It isrecommended that the alternative DATEformat (Sequence @om 1900/1/1) be used inspreadsheet~les (“.WKI). Ifthe *.WK1format isused, DATE or YX!l.4MDD values must bestored in the spreadsheet as numerical values (not labels or characters!~. Variable labels may include sample flows, concentrations, screening variables, orother record identifiers. Columns must be contiguous (no blank columns). Rows (data records) must also be contiguous. Sample records can be sorted inanyorder. Units conversion factors arenot included inthe file. These must be specified ontheFLUX Input Screen orinthe station index file(see below). The file ‘CADDO_S.DAT’ isan example ofthis 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>** Thefile ‘CADDO_Q.DAT’ isanexampleofthis formatfordailyflowrecords: **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 beused (instead of *.DAT format) forfiles containing data formore than one station. The file layout isas follows:

**Chapter 2**  **FLUX** 2-39Line 

### 1 ‘Title’ (enclosed insingle quotes) Line 2 Number ofFields (columns) =Nfields Line 3 Missing Value Code Lines 4 thru 3+Nfields ‘Field Labels’ (enclosed insingle quotes) Lines 4+Nfields etc Sample Records, free-format Each sample record contains station code, date, andnumeric fields. Allcharacter entries inthis filemust be enclosed in ‘single quotes’. This includes the title line, field labels, and station labels. Fields are delimited by spaces orcommas. The first data field (column) isused to speci& 8-character station codes, enclosed in ‘single quotes’. The file ‘CADDO_S2.ASC’ isanexample ofthis format for sample records: ‘degray inflow, flows inm3/sec

-dates inyymmdd 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 onlyone station, records from other stations can be included inthe file; the program will select the appropriate records based upon the sample station code specified onthe FLUX Input Screen. Ifthe specified sample station code isblank, allrecords are selected.

* .FLO ASCII Format for Daily Flow Data

2-40 This ASCII format for dailyflow records isindicated bythe ‘.FLO’ extension. This isafree-format file containing one record per month:

**Chapter 2**  **FLUX**Line 1 Title (station descriptor, etc.) Line 2 Missing Value Code (must be anegative number) Line 3.n DailyFlows (one record per month) YY MM Q1 Q2 Q3 Q4 Q5
.... Qn, or YYYY MM Q1 Q2 Q3 Q4 Q5
.... Qn, wheren=# days inmonth Data records are fi-eeformat, delimited bycommas or spaces (one line/month). The program willread the appropriate number ofdays per line, depending upon specified year and month. IfLine 2 (missing value code) isomitted, allnegative values inthe flow file are interpreted as missing. Theyear canbe in2-character ~) or4-character (YYYY) format (e.g., 80 or 1984). Years between Oand 49 are interpreted as2000 to 2049. The file ‘CADDO.FLO’ isanexample ofthis format for dailyflow 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 isindicated bythe .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) canbeused to select data from a specific station. Ifincluded, STATION codes must be stored as character constants in COLUMN A ofthe worksheet. Ifthe STATION column isexcluded, FLUX will read alldata from the file. One field may refer to sample flows, others to concentrations (Example: VAR1 = flow, VAR1 = total p, VAR2 = ortho p, etc.) orto sample identifiers. The Date label (Cell B2 inthis example) must be DATE ifdates are stored inLotus format (days fkomJanuary 1, 1990). The Date label must be WMMDD ifdates are stored inYYMMDD format (numeric values only). The file ‘CADDO_S. WK1’ isanexample ofthis format with the optional station field included and dates stored inLotus 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’ isanexample ofthis 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’ isanexample ofthis 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 beused 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 dailyflow data from different stations. (e.g., STA1 = flow data from station 1,STA2 = data from station 2) Ifflow data are missing, omit the entire row orleave fieldblank.

2-42 DATE orFLOW fields can be formulas ornumeric constants.

**Chapter2 FLUX** The file ‘CADDO_Q.WKl’ isanexample ofthis format for dailyflow 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 ofstation codes canbe maintained on diskto facilitate reading ofsample andflow data. The default extension of’ *.IDX’ is suggested to identi~ astation index file. Amaximum of63 stations canbe indexed ina given file. An index fileisaccessed through theData/Read/ Index procedure. The format is asfollows: Line 1 Title (for user reference) Line 2 Flow Scale Factor (default, canbe modified when read) Line 3 Concentration Scale Factor (“”) Lines 4+ Station Record, fields enclosed in ‘quotes’ Station Record Format: Field Description

1 station identifier (<= 8characters) 2 sample station code (reference values insample file) 3 sample filename 4 sample flow variable (’lookup’ to retrieve from dailyflow data) 5 flow station code (for .WK1 or .DAT data filetypes) 6 daily flow file 7 flow sign (+1 or -1) not enclosed inquotes This is afree-format filewith fields delimited byspaces or commas. All character strings must be enclosed insingle quotes. Itisusefhl to create aseparate index for each reservoir orgroup ofstations inacommon application. The file ‘CADDO.IDX’ isanexample: ‘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 fileiscreated, theneed to speci& sample and flow data files ondata-entry screens iseliminated. 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 inexactly the same data byaccessing files with different formats. hactudapplications, each station would referto adifferent location or data set. Examples ofother *.IDX files are included onthe program diskette.


### FLUX Documented Session This section demonstrates atypical FLUX session. As atraining exercise, the user should be able to recreate this session byrunning FLUX and accessing the data files for Caddo River supplied withthe program. Notes tothe user are provided initalics below. Selected menu options are underlined. To begin, enter ‘flux’ atthe 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 briefdescriptionsof theprogram and summarize any newfeatures not documented in this manual. Tobypass these screens, press KESC>and theprogram 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 1** owsub **Title List**  

# I **Reset Keep**  **Samples -1** **nde~** 

## 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 thestation indexJle ‘caddo.idx’andlists theindexed stations. As discussed intheData File Formats section, this example index file illustrates a variety ofdata setcon~gurations allaccessing thesame data. I.npractice, users can create separate indexJles tofacilitate access todatafor dl~erent stations within agivenprojector reservoir. Caddol isselected 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 theselected station are opened. i%eprogram reads thejile headers and asks the user toselect the variable tobeanalyzed (totalp) @om a list ofall~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 ofdaily~ows ispresented, including date range, missing values, and zero values. Anyflow records out ofsequence 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** **1 ousub**  **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 theDatalListlS 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** **1 owsub**  **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. [Jsethekeypad arrows toforwardor backward through thejle. Zhelisting canbesavedon disk bypressing 

### <F8>. Press <Esc> tocontinue.
**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**  2-47Caddol 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 ofsample collection (squares). Note that relativelyfew high--ow samples were collected during the high-runoflperiod in late 1978 to early 1979. Thesquare symbols indicate thedailyfiows on thedates of sample collection (not the sampleflows). 7ke CaIculatelCompare procedure provides amore quantitative comparison ofsample and totalflow distributions.



# v;”’[’tvER’;’:’”’’ “lP ‘“i’ **Compare Sample**  **and Total**  **Flow Distributions**  **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**  **=** 6406.68**hfi/yr Maximum**  **Total Flow**  **Rate =**  9305.78**hm3/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 thehigh-flow regimes are not represented very well in this case. Xhisis consistent with impressions derived abovefrom the dailyflow plot. Plotting concentration against~ow isgenerally 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 0MTD C 

## 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 isselected, thepredicted concentration isconstant. Regression methoak attempt to represent concentration variations with~ow within each stratum. i%iscan be demonstrated by selecting Method 

### 6and 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** 2-49Caddol NET~D : 6 REC-3

c o N c

o **L, 1**  ***** **, , I**  **, , lm**  **lme s**  **FLon**

When Method 6 isselected, thepredicted concentration varies withflow. Some nonlinearity isevident. Concentrations are underpredicted athigh jlows. This suggests thatmoreflow strata are needed tocapture the~ow/ concentration relationship. I’_he following sequence demonstrates the ejiects ofstratlfiing the data on the load estimates. Loads arejirst calculated without stratljication. Method 

### 2isreselected.

**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 CCMfPAR** **I 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) QMTDC 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** **1 owsub**  **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 islisted: 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-1eSTll~r-2
. ES IlWT~

Thepredicted concentrations usingMethod 2 now have two levels, onefor eachflow stratum. Loaak can be recalculated using the current stratljication scheme: 

# PLu’lO’_ 

# “’’’’”T Calculate **Loads Using**  **Each Method** 
**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 thePMIBarchart 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 

# +E 400

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 tosee whetherprecision can be improved.

— — **FLUX**

**- VERSION**  **5.0 Calculate**  **Method Plot**  **List Utilities**  **Help Quit**  **Read**
**~ Delete**  **Coaposite F** **1 owsub**  **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 CaddoRiver 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 strataprovides a betterfit oftheflow/concentration relationship.



# FLU””; “’’’5tCalculate **Loads Using**  **Each Method**  Caddo **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 168100.0 413.588 405.163

**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** **1 owsub**  **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**  2-57i%ehighestflow stratum (4)now contains only three samples. Zhis isnot 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 toresultsfor 3flow strata. 7hissuggests thatthesampling intensi~is notsuf~cient tosupport 4strata.
**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 ofload estimates as the number of strata increases isadesired result. The following table summarizes the eflect ofincreasing the number ofjlow strata on the estimatedflow-weighted mean concentration for Method 2: Number ofStrata Flow- Weighted-Mean Cv 1 76.7 .169 2 76.5 .139 3 77.8 .118 4 77.6 .138 i%emean estimates did not change signljicantly, and the error W was lowest for 3strata. The increase in error at 4strata reJects data limitations (only

three samples injlow interval 4). This causes instability, particularly in the regression methods (4-6), when 4strata are used. Based upon these results, the load estimate based upon 3JOWstrata andMethod 2 isselected. This could befirther re~ned byadjusting thejlow strata boundaries (using the DaWStratify/FJowl Other procedure) toobtain a better C/Q~t and reduce the CVestimate. Wecan 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** **1 owsub**  **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 CaddoRiver METHOD: 2 ClMTDC

-. 4

-11 , , , 7H 79 86 81 DfiTE

❑ STRflT-1 o STRRT-2 o STRRT-3
. REGRESS I’_hisplotca nbeusedto testfor trend, i.e., increasingordecreasing concentrations, adjustedfor variations inflow. Generah’y,severalyears ofmonitoringdda collected overawide range offlowregimes are requiredin orderto make areliable testfor trend. Stratljicationbasedupondute maybe appropriatel~signljicanttrendorstep change isapparent. An alternative approach wouldbe toestimate loads separatelyfor different timeperiods byspeclfiing appropriate date ranges in theDatalIlead 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

Thisplot can be used to test for seasonality. Ifsignljlcant seasonal patterns in the residuals are evident, stratl~cation based upon season maybe appropriate. This isaccomplished by using the Ik.itd Stratify/General procedure. Now examine the load breakdown byflow stratum.



# vL’Lu’’’ick::K5;ti’ieses “lP ‘“i’ **List Load**  **& Flow**  **Breakdowns by**  **Stratun; Optimal**  SampleAl10C.
**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 thedistributionof sampling effort,flow days,jlow volume, mass, anderrorvariance, each expressedaspercentage ofthe total. i%ebottompart ofthe table estimates thepotential bene$t ofoptimizing the sample allocation across stratato obtain the lowest error variancefora]xednumber ofsamplingeven ts.

**Chapter2 FLUX**  2-61NE% =percent oftotal sample events instratum NEOPT?? =optimalpercent oftotal sample events instratum i%ereduction in error CVattributed toshlftingfiom 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, 98.3percent ofthe variance in the load estimate isattributed to the Stratum 3. This received only 8.3percent ofthesampling effort WE%). An optimal sampling design would devote 75.5percent ofthe 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 isaninteractive program designed to assist inthe analysis and reduction ofpool water quality measurements. The user supplies adata file containing basic information onthe morphometry ofthe reservoir, monitoring station locations, surface elevation record, andwater quality monitoring data referenced bystation, date, and depth. The program’s fbnctions are inthree general areas:
a. Display ofconcentrations as afhnction ofelevation, location, and/or date. b. Calculation ofmixed-layer summary statistics and standard errors.
c. Calculation ofhypolimnetic and metalimnetic oxygen depletion rates from temperature and oxygen profiles. These applications are introduced inthe following paragraphs. Details are given insubsequent sections. Several display formats support exploratory analysis ofreservoir water quality data. These elucidate important spatial and temporal variance components. Reviewing these displays canhelp the user inevaluating data adequacy, designing future monitoring programs, and specifying appropriate segmentation schemes for modeling. The various display formats and options are described indetail inthe Program Operation section and demonstrated inthe Documented Session section ofthis chapter. Mixed-layer water quality data canbe summarized inatwo-way table format that depicts variations as afunction ofspace (station orreservoir segment) and time (sampling date) over date, depth, and station ranges specified bythe user. Inthe two-way analysis, filtering andweighing algorithms are used to generate robust sumnuuy statistics (median, mean, and coefficient ofvariation ofthe mean) for characterization ofreservoir trophic status, evaluations of data

**Chapter 3**  **PROFILE** 3-1adequacy, and application ofBATHTUB (Chapter 4) orother empirical models. Hypolimnetic oxygen depletion rates are important symptoms ofeutrophication instratified reservoirs. Using input oxygen andtemperature profiles, the program applies interpolation and area-weighing procedures to calculate depletion rates. Graphic andtabular outputs assistthe user inselecting appropriate sampling dates and thermocline boundaries foroxygen depletion calculations. The following sections ofthis chapter describe:
a. b.
c. d
e. $ Input data requirements. Application procedures. Program operation. Input data fileformat. Data-entry screens. Documented session. 

### Input Data Requirements PROFILE requires aninput filecontaining data inthe following groups: Group 1: Title Group 2: Parameters and UnitConversion 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) Allofthis information can be specified inasingle, fixed-format ASCII file, as described inthe section entitled Input Data File Format. As an option, water quality measurements (Group 7) canalso beread 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 bythe program (square kilometers for area and meters for elevation and depth). Missing concentration values are flagged with a speckl code specified inGroup 2. The “date blocking factor” isused to combine data for summary purposes. Inlarge reservoirs, itmaybe difficult to
**Chapter 3**  **PROFILE**sample allpool monitoring stations in 1day. Ifablocking factor of2 isspecified, for example, sample dates differing by<=2 days willbe associated with the same sampling round for data-summary purposes. Group 3 contains an elevation versus surface area table for the reservoir. This information isused onlyincomputing arealhypolimnetic oxygen depletion rates. Group 4 defines water quality components and concentrations interval for contour plotting. Ineutrophication studies, the input filewould normally contain measurements ofoxygen, temperature, total phosphorus, ortho phosphorus, inorganic nitrogen, organic nitrogen, total nitrogen, chlorophyll a, and Secchi depth. Output isformatted to provide one place to the right ofthe decimal point; thus, input units should be milligrams per cubic meter (orparts 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. Amaximum of 10water quality components can be read from diskfiles and analyzed inagiven session. Integers (range 01- 15)are used to identi~ sampling stations and are cross- -referencedto user-defined station codes and descriptions inGroup 5. To facilitate interpretation of data displays andtables, station numbers should be assigned inalogical order (e.g., upstream ordownstream order within each tributary arm). The optional “river kilometer” input for each station would normally represent the distance along thethalweg from the reservoir inflow; since the river kilometer index isused onlyfor spatial display purposes, any frame ofreference can beused. In computing summary statistics, “segment numbers” specified inGroup 5 canbe used to combine data from specific stations based upon their relative proximities, major tributary arms, horizontal mixing characteristics, etc. For example, ifthe filecontains two adjacent stations (ortwo stations with similar observed water quality), data from these stations canbegrouped by assigning them the same segment number. Segment numbers canrefer directly to the spatial segments used inreservoir modeling (see BATHTUB). Ifoxygen depletion calculations are not desired, itisalso possible to use segment numbers to refer to stations indifferent reservoirs. “Areal weights” specified inGroup 5 areused incalculating area-weighted summ~ statistics over the entire reservoir and should reflect the approximate surface area represented byeach station. These canbe estimated byplotting stations on areservoir map and allocating agiven area to each station, based upon relative station locations andbisecting lines between adjacent stations. Since they are resealed incalculations, the weighing factors do nothave to sum to 1.0. Group 6contains daily measurements ofreservoir surface elevation overthe period ofwater quality measurements. The program uses this information in
**Chapter 3**  **PROFILE** 3-3generating concentration versus elevation plots and incalculating hypolimnetic oxygen depletion rates. Onlythe 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 canhandle problems with the following maximum dimensions: Elevation/Area pairs = 29 Number ofstations = 50 Number ofsamples = 2,500 Number ofwater quality components = 10 Number ofsample dates = 250 Number ofmeasurements = 12,000 Water quality records must speci& the station, date, and depth, inaddition to measurements. Ifthe depth field ismissing, asample depth ofOisassumed. Note that limitations on sample numbers and number ofwater quality components apply onlyto data read into the computer memory atthe time ofprogram execution, notto the data fileitself. Since the user isprompted forthe ranges ofstation numbers, sample years, and water quality components to be considered inagiven run, the data file canbe much largerthan indicated above (except for the maximum number ofstations). Users should check the online documentation file (accessed through the HELP menu) for maximum problem dimensions orother program changes inupdated versions ofPROFILE (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 inatwo-way table format. These steps are described below.

3-4 The data window defines the ranges ofstations, dates, and depths to be included indisplays and statistical summaries. For characterization ofreservoir trophic status, the window would normally be setto include allstations, dates

**Chapter 3**  **PROFILE**inthe growing season (e.g., April-October), and depths inthemixed layer. In model development research, amixed-layer depth of 15ft(4.6 m) was used for data summary purposes; this value should be adjusted inspecific applications, based on areview ofmidsummer temperature profile data. Because the data-summary procedure does not apply weighting factors with depth, use outside ofthe mixed layer (or innonhomogeneous depth layers) isnot recommended. The data-summary procedure organizes the data inatwo-way table depicting spatial (columns) andtemporal (rows) variations. This isillustrated in Figure 3.1 using Beaver Reservoir data. Spatial groups canbe defined by station orreservoir segment. Temporal groups are defined bysampling round, which is determined bysample date and date blocking factor specified inthe input file. The purpose of date blocking isdiscussed below, Asummary value (mean or median) iscomputed for each cell (row/column combination). For each row (sampling date), summary values areweighted bysurface area and averaged across cohmms (stations or segments) to compute areservoir mean concentration. Values are subsequently analyzed vertically to estimate a median, mean, coefficient ofvariation (CV, standard deviation/mean), and coefficient ofvariation ofthe 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** 3-5The distinction between the lasttwo statistics (CV and CV(MEAN)) is important. CV isameasure oftemporal variability inconditions atagiven station (standard deviation expressed as afraction ofthe mean). CV(MEAN) is ameasure ofpotential error inthe estimate ofthe MEAN value. From classical sampling theory (Snedecor and Cochran 1979), CV(MEAN) iscalculated from the CV divided bythe square root ofthenumber ofnonmissing rows (sample dates). This assumes thatthe rows are statistically independent. The calculation ofCV(MEANS) forthe entire reservoir (last column inFigure 3.1) considers onlytemporal and random variance components and assumes that the stations are distributed throughout representative areas ofthe reservoir. Estimates of“mean” conditions aregenerally required fortrophic state assessment and empirical modeling (Chapter 4). Direct calculation ofarithmetic mean concentrations from allmixed-layer data would be one way ofcomputing desired summary statistics. However, this approach maybe undesirable fortwo reasons:
a. Lack ofrobustness (a single errant value canhave amajor impact on the computed mean). b. Nonrandomness insamples (multiple samples taken within the mixed layeronthe same date would tend to behighly correlated). The PROFILE data summary algorithm has been designed toprovide more robust estimates ofthe mean and coefficient ofvariation than would be derived from simple averaging. “Robustness” can be introduced byusing medians to compute summ~ values within each cell. Cells may contain more than one observation as a result ofthe following:
a. Replicate sampling atagiven 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 (ifsegments areused to define columns). d Blocking of adjacent sampling dates (speci&ing date-blocking factors greater than 1inthe input file). IntheBeaver Reservoir example (Figure 3.1),cells contain between two and four observations as aresult ofsampling with depth. Use ofthe median in computing asummary value provides some protection against “errant” observations andyields summary statistics (across stations and across dates) that are less sensitive to outliers. For example, acellcontaining five observations (10, 20, 15, 12, 100) would be summarizedbyameanof31 and amedian of 15. The median isless dramatically influenced bythe singlehigh value.
3-6 **Chapter 3**  **PROFILE**Medians provide “filtering” ofoutliers only incells containing atleastthree observations, which may be achieved byreplicate sampling, sampling with depth, including more than one station perreservoir segment and/or blocking of adjacent dates. Generally, date blocking should not beused unless the sampling frequency isatleastbiweekly and the resulting number ofrows isat leastthree. In such cases, date blocking may also improve the CV and CV(MEAN) estimates byreducing serial dependence inthe rows. While the calculation procedure accounts for missing values inthe two-way table, the usefulness and reliability ofthe surface water quality summary are enhanced bycomplete sampling designs (i.e., each station sampled on each date). Based upon review ofbox plots and two-way tables, monitoring programs can be refined byreducing excessive redundancy across stations, improving characterization ofspatial gradients, and modi&ing temporal sampling frequency to achieve the desired precision insumm~ statistics. Figure 3.2 illustrates the use ofaBox Plotto summarize spatial variations in mixed-layer total phosphorus concentrations. Ingenerating Box Plots, data can begrouped bystation, segment, month, round, year, or depth interval. An accompanying table (not shown) summarizes the distribution ofmeasurements 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** 3-7illustrated inthe Documented Session section ofthis chapter. Calculations are applied to vertical oxygen profiles atagiven station; simultaneous measurements oftemperature are also required to characterize thermal stratification. Empirical models have been developed forrelating near-dam oxygen depletion rates to surface-layer chlorophyll a concentrations (Walker 1985). Accord**hgly, the**  procedure would normally be applied to data from near-dam stations. For the present purposes, the arealhypolimnetic oxygen depletion rate (HOD~ mg/m2-day) is defined astherate ofdecrease ofdissolved oxygen mass (mg/day) inthe reservoir hypolimnion divided bythe surface area ofthehypolimnion (m*). The rate isalso expressed on avolumetric basis (HODV, mg/m3-day), which isessentially the rate ofdecrease ofthe volume-weightedaverage dissolved oxygen concentration inthehypolimnion between two dates, orHODa divided bythe mean depth ofthehypolimnion (m). These rates are symptoms ofeutrophication because theypartially reflect the decay oforganic loadings resulting from surface algalgrowth and sedimentation. The initial oxygen concentration atthe onset ofstratification (usually onthe order of 10to 12g/m3)and HODVdetermine the days ofoxygen supply. Subtracting the days ofoxygen supply from the length ofthe stratified period (typically 120to 200 days) provides anestimate ofthe duration ofanaerobic conditions. While HODVisofmore immediate concern for water quality management purposes, HODa isamore direct measure ofsurface productivity because itisrelatively independent ofreservoir morphometric characteristics. For agiven surface productivity andHOD% HODVisinversely related to mean hypolimnetic depth. Thus, the morphometry ofthereservoir has amajor impact onthe severity ofhypolimnetic oxygen depletion atagiven surface water quality condition. In a given stratified season, the areal and volumetric depletion rates are calculated between two monitored dates, the selection ofwhich isimportant. The following criteria are suggested for selection ofappropriate dates:

a. Reasonable top-to-bottom distribution ofoxygen andtemperature measurements. b. Vertically stratified conditions, defined astop-to-bottom temperature difference ofatleast4 ‘C.
c. Mean hypolimnetic oxygen concentrations inexcess of2g/m3.

3-8 The first criterion provides adequate data for characterizing thermal stratification and volume-weighting (estimation oftotal oxygen mass and volumeweighted concentration) within thehypolimnion on each sampling date. The second criterion isbased upon the concept that HODa isvalid as ameasure of productivity only inwater bodies thathave stable vertical stratification. The calculation ismeaningless inunstratified or intermittently stratified reservoirs
**Chapter 3**  **PROFILE**because ofoxygen transport into bottom waters. The 4 ‘C temperature difference is an operational criterion employed indeveloping data sets for model calibration and testing (Walker 1985). Special consideration must be given to water bodies with density stratification that isnot related to temperature. The third criterion isdesigned to minimize negative biases caused by calculating HODa values under oxygen-limited conditions. The underlying model assumes thatthe depletion rate islimited bythe organic supply, notthe oxygen supply. The first date generally corresponds to the first profile taken after the onset ofstratification. The last date corresponds to the lastprofile taken before the end ofAugust, the loss ofstratification, orthe loss ofhypolimnetic dissolved oxygen (mean <2g/m3), whichever occurs first. Due to existing data limitations, itis sometimes difficult to cotiorm to allofthe above criteria inselecting dates. Small deviations maybe acceptable, but should be noted and considered ininterpreting subsequent modeling results. To permit calculation ofhypolimnetic and metalimnetic depletion rates between two dates, fixed thermocline boundaries (top andbottom) must be specified. Temperature profile displays can assist inthe selection ofappropriate boundaries. The bottom ofthethermocline (metalimnetic/hypolimnetic boundary) is setatthe intersection ofone linetangent to theregion ofmaximum temperature gradient and another linetangent to the bottom ofthe profile. The top ofthe thermocline (epilimnetic/metalimnetic boundary) isset atthe intersection ofone linetangent to the region ofmaximum temperature gradient and another linetangent to thetop ofthe profile. Ifsignificant thermocline migration has occurred between thetwo sampling dates, calculations should be based upon the thermocline levels atthe last sampling date. Adegree ofsubjective judgment must be exercised ininterpreting temperature profiles and setting thermocline boundaries, Program output provides perspective onthe sensitivity ofthe calculated depletion rates to the dates andthermocline boundaries employed. Inresponse 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 atthe specified elevation increment from the bottom ofthe reservoir to the top ofthe water column. Atelevations below the deepest sampling point, concentrations and temperatures are set equal to those measured atthe 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 isinthe form ofseveral tables and plots that are useful for tracking the calculations and evaluating sensitivity to sampling date and thermocline selections. Interpolated profiles andthe summary table for Beaver Reservoir are displayed inthe Documented Session section. The summary table canbe considered the “bottom line” inthe calculations. The Beaver
**Chapter 3**  **PROFILE** 3-9Reservoir example illustrates apronounced metalimnetic oxygen depletion, which is often found inrelatively deep reservoirs. 

### Program Operation
Introduction This section describes thePROFILE menu structure and operation procedures. When the program isrun (from the DOS prompt), a series ofhelp screens summarizing model features isfirstencountered. Iferror messages appear, itgenerally means that one ofthe PROFILE program fileshas been corrupted orthatyour computer does nothave enough available memory. Try reinstalling the program. Try unloading anymemo~-resident sofbwi.re. Ifyou aretrying to run the program from Windows, tryexiting Windows and running directly from DOS. The program permits selection of ‘user mode’ at startup, after the introductory screens. The selection of user mode isfollowed bya menu that provides interactive access to eighttypes ofprocedures 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** Aprocedure category isselected bymoving the cursor (using arrow keys) orby pressing the first letter ofthe procedure name. Selected procedures inthe menu box arehighlighted onthe screen and underlined inthe 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 bypressing <Fl>. Afler each procedure iscompleted, control returns to the above menu screen.
Data procedures Data procedures control input and listing ofsample 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 liststhe sample data inone oftwo 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 areusedto 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 ineffect until another data fileisread or one ofthe 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 ofwater quality data inseveral 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**  3-11I **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 isgenerated 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 anyofeight 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 canbe 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 foroptions controlling the calculationof mixed-layer summaries:



# mpRkR-vER’’l’”es ‘e’p Quit
**Length Set**  **Output Format:**  **Short or**  **Long (default)**  **co 1** **l.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 onlythe 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 setsthemethod used for summarizing multiple observations inagiven cell ofthe 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 anydiskfile: canbe selected toroute output to adiskfile orto 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, orga**PRO 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 ofdata. The specified formats, descriptions, and limitations ofeach group are given indetail 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 inthe 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 bythe 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 ofthe 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 ofData Group 3 must be

- “00”. Group 4: Component Key

- IC, LABEL, V1, .. .. V6 FORMAT (12,1X,A8,6F5.0) IC = Component sequence number inData 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 ofData 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 ofreservoir bottom atthe 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 = 16characters)

a. Include one record for each station in Data Group 7 (maximum = 50) b. Include the decimal point inELEV, 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 ofData 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 whichformat isused, based upon the~rst record in each group. Useone orthe other (donotmix). DATE = Sample date inYYMMDD format (e.g., 840126) or YYYYMMDD format (e.g., 19840126) If6-character dates are 

### used,theyare interpreted asfollows: Y Y M MD D Year Month Day 990113 1999 01 13 000113 2000 01 13 Rule: YY0113 19YY01 13ifYY>=50 YY0113 20YY01 13 ifYY<50 SELEV = Surface elevation ofthereservoir atthe dam onthe sample date NOTES:

**Chapter 3**  **PROFILE** 3-17a. b.

c.
d.

e. Include one record for each sample date in Date Group 7. Dates must beinchronological order (maximum = 100dates). Input units must be consistent with the conversion factors specified in Data Group 2. Group must contain at leasttwo records; ifan elevation record is not specified for agiven sample date, itis estimated by interpolation from adjacent elevation records. The last record ofData 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 inData Group 5 Sample date inYYMMDD orYYYYMMDD format, indexed inData 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 inDEPTH 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 ofData Group 7 must be

- “00”. Inclusion of data inGroup 7 is optional. The file name(s) ofspread3-18 sheet or free-format ASCII data files containing sample data may be substituted. Any number offile names may be specified (one per line). The component labels inGroup 4 should correspond with the field labels inthe data files (not necessarily a 1-to-1 correspondence). PROFILE will read data from any components contained inboth Group 4 and the data file. Station codes inthe data files should correspond to the Station codes (8-character

**Chapter 3**  **PROFILE**alphanumeric) specified inGroup 5. The following file formats are supported: *o~ I - LOWS-123worksheet
*.ASC - ASCII File formats and conventions are described inChapter 2 (FLUX

- Data File Formats). 

### Asampleinputdata>le, BM VER.PRF(6-characterdates), islistedbelow: 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. 02oxygen 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



### BEAVER2K.PRFisanexampleofan8-characterddefile.
Chapter3 PROFILE 3-19NOTE: Spreadsheet filenames forfree-format ASCII filenames may be substituted for sample records. See example file ‘BEAVER2.PRF’ (6-character date) orBEAVER2K.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**  3-21DATA-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 sameplot 

### 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 asthe program isrun. Notes to the user areinitalics below. Selected menu items are underlined. To begin, enter ‘profile’ atthe 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. Toby~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 selectedprocedure appears atthe bottom ofthe menu box. Characteristics ofthe currentdata setandprogram option settings are listedon the bottom halfofthe scrcen. ,S’ince no data set has beenloa~ed, the above valuesarezeroes orblank. SelectIhtalRead toreadin adata 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 tobeusedin thiswindow. 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 theabove listofall variables contained in the dilta~le. Hit <Enter> tocontinue.
**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?iztacanbe 

### listeu!usingtheDataJListllSortprocedure:



# 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** TheDaWList12Sort procedure generates similar output, but sorted inadl~ 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 thenumber 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**  

### TheI)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>** 
Windowparameters are initially set to include the entire range ofvalues 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) tobeplotted(o~gen). HotlLinell generates verticalpro@les using dl~ferentsymbols 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 todisplay a longitudinal pro~le (y =elevation, x = distance along thalweg (i.e., oldriver channel)). I%is format 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** 3-29Beauer Resexwoir MTE : 740630 SwlmL: C(MC UfiR: total **p**
**34e /**  **........ .. ...... ..a”_-y** 
**.................... ...!....**  **1. ~..---..~**  **. . t**  l-i:

.................... ........................................ 

# $,~F~:: ..:%-.+-> . ... . ...... : ~ ‘ .. ............ ...+

.......

............................................................ ......... ..7
...........1
............ ~

26el -y I I I I I e 26 40 60 80 166 120 RKM ● 213~4fl =68=168=326
Dl~ferentcolors are used to represent contour intervals (notdiscernible here). Select PiotlGeneral todefine your ownplotformat. Remember that allplots usea!htain 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** Thisscreenprovides ahigh degree of~exibility for de~ning plots. In this example, aphosphorus contourplot (elevation versus rkm) isspecljied. The plot is repeatedfor each sampling &te (only one isshown 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 todisplay 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** 

### 3-31E 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 beset 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 tobeplottedon log scales (open appropriate for nutrient and chlorophyll data, notappropriate-for oxygen ortemperature).

**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 todisplay t.hta summaries byde$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**  

### 3-33t 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 tostratljiedreservoirs 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 theabovehelpscreen, 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**  3-35Calculations begin. Hit <I%nter > toselect thedefault depth intervalfor 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 verticalpro~les oftemperature, oxygen, areal oxygen depletion rate and total oxygen demand @elow each elevation incremen~, andvolumetric oxygen depletion rates, Viewthejirstplot (temperature) toselect 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: .....................................~
V 288 .. ............................................ 2681 I B 2 ........................

....................... ,................l...
........... .............;

. . . . . .......

........... ................. /

0 1

■ 740405 x 740838 ‘RESS R to Resca le , D to Dump

**Chapter 3**  **PROFILE** 3-37Beaver 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 upperplot shows the total oxygen demand (@#day)below each elevation. Thismay be usefilfor sizing hypolimnetic aerators. The lowerplot shows volumetric oxygen depletion rate ateach elevation and themean depletion rate below each elevation. Thermocline boundaries are dejined in thefollowing 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**  7hefollowing 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** Thefollowing plot shows the time series ofvolume-weighted mean oxygen concentrations in the hypolimnion and metalimnion. Xheslopes ofthese lines areproportional to the volume-weighted mean oxygen depletion rates.

Beauem Remervo ir - STfl 1 UOLUME-NEIHITED CCWWENTRRT IONSle6 - ..........................
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

ViewCalculation **File ? n**  **I** Hit y to view details ofoxygen depletion calculations. program menu. Hitn to return to Following isademonstration ofthe 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**  MOVECURSOR& 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**  3-41total 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 endsession:



# rpRO’a’c’L’’’vER’:L ‘e”

# w II **End Profile**  **Session 1**  **MOVE CURSOR&HIT**  **<Enter>OR <First**  **Letter> TO**  **RUN ROUTINE,**  **<FI, F7>**  **HELP**

3-42 **Chapter3 PROFILE** 

# 4 BATHTUB

BATHTUB Overview BATHTUB isdesigned to facilitate application ofempirical eutrophication models to morphometrically complex reservoirs. The program performs water andnutrient balance calculations inasteady-state, spatially segmented hydraulicnetwork that accounts for advective transport, diffusive transport, and nutrient sedimentation. Eutrophication-related water quality conditions (expressed interms oftotal phosphorus, total nitrogen, chlorophyll a, transparency, organic nitrogen, nonortho-phosphorus, andhypolimnetic oxygen depletion rate) are predicted using empirical relationships previously developed andtested 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 ornetworks ofreservoirs. As described inChapter 1,applications ofthe program would normally follow use ofthe FLUX program forreducing tributary monitoring data anduse ofthePROFILE program for reducing pool monitoring dat~ although use ofthe data reduction programs isoptional if independent estimates oftributary loadings and/or average pool water quality conditions are used. The fhnctions ofthe program can be broadly classified as diagnostic or predictive. Typical applications would include thefollowing:
a. Diagnostic. (1) (2) (3) Formulation ofwater andnutrient balances, including identification and ranking ofpotential error sources. Ranking oftrophic state indicators inrelation touser-defined reservoir groups and/or the CE reservoir database. Identification offactors controlling algalproduction. b. Predictive.

**Chapter 4**  **BATHTUB** 4-1(1) (2) (3) Assessing impacts of changes inwater and/ornutrientloadings. Assessing impacts of changes in mean pool level. Estimating nutrientloadings 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 afirst-order error analysis scheme thatincorporates 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 thefollowing topics isgiven inthe 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 theprogram maybe examined by reviewing the example data sets supplied attheend of this chapter and by viewing help screens supplied with the program. 

### Theory
Introduction Aflow diagram for BATHTUB calculations isgiven inFigure 4.1. This section describes calculations performed inthemodel 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**  4-3Using afirst-order error analysis procedure (Walker 1982), the model core is executed repeatedly inorder to estimate output sensitivity to each input variable and submodel andto develop variance estimates and confidence limits for each output variable. The remainder oftheprogram consists ofgraphic and tabular output routines designed to summarize results. Control pathways forpredicting nutrient levels and eutrophication response ina given model segment are illustrated inFigure 4.2. Predictions arebased upon empirical models which have been calibrated andtested forreservoir 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 inTable 4.2, several options are provided for modeling nutrient sedimentation, chlorophyll a, and transparency. Ineach case, Models 1and 2 arethe most general formulations, based upon model testing results. Alternative models are included to permit sensitivity analyses and application ofthe program under various data constraints (see Table 4.2). Table 4.3 specifies submodels forpredicting supplementmy response variables (organic nitrogen, particulate phosphorus, principal components, oxygen depletion rates, trophic state indices, algalnuisance frequencies). Error statistics for applications ofthe model network to predict spatially averaged conditions are summarized in Table 4.4. The following sections describe underlying theory. The development and testing ofthe network equations (Walker 1985) should bereviewed prior to using the program. Segmentation Through appropriate configuration of model segments, BATHTUB can be applied to awide range ofreservoir morphometries and management problems. Figure 4.3 depicts segmentation schemes in sixgeneral 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 ofreservoirs, spatially averaged.

4-4 J Network ofreservoirs, spatially averaged.
**Chapter 4**  **BATHTUB z** 

**s**

**~** UJ **o**

**Chapter 4**  **BATHTUB** 4-5Table 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 BATHTUBTable 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 4-7Table 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 A1 ~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 4-9Table 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 (1976) 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 (1985) [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 BATHTUBTable 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 (Sheet4 of 4)

Chapter 4 BATHTUB 4-11Table 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 BATHTUBTable 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 orlinked inanetwork. Each segment isdefined interms ofitsmorphometry (are% mean depth, length, mixed layer depth, hypolimnetic depth) and observed water quality (optional). Morphometric features referto average conditions during the period being simulated. Segment linkage isdefined byassigning each segment anIDnumber (from 1to 39) and speci@ing the IDnumber ofthe segment that isimmediately downstream ofeach segment. Multiple external sources and/or withdrawals can be specified for each segment. With certain limitations, combinations ofthe above schemes are also possible. Characteristics and applications ofeach segmentation scheme are discussed below.

Chapter 4 BATHTUB 4-13Table 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 BATHTUBTable 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 4-15Table 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) isthe simplest configuration. Itisapplicable to reservoirs inwhich spatial variations innutrient concentrations and related trophic state indicators arerelatively unimportant. Itcan also be applied to predict area-weighted mean conditions inreservoirs with significant spatial variations. This isthe simplest type ofapplication, primarily because transport characteristics within the reservoir (particularly, longitudinal dispersion) are not considered. The development ofsubmodels fornutrient sedimentation and eutrophication response has been based primarily upon application ofthis segmentation scheme to spatially averaged data from 41 CEreservoirs (Walker

4-16 1985).

Chapter 4 BATHTUBSCHEME 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 thereservoir into anetwork ofsegments for predicting spatial variations inwater quality. Segments represent different areas ofthe reservoir (e.g., upper pool, midpool, near dam). Longitudinal nutrient profiles are predicted based upon simulations ofadvective transport, diffusive transport, andnutrient sedimentation. Reversed arrows inFigure 4.3 reflect simulation oflongitudinal dispersion. Branches inthe segmentation scheme reflect major tributary arms orembayments. Multiple and higher order branches are also permitted. Segment boundaries canbe defined based upon consideration ofthe following:
a. Reservoir morphometry. b. Locations ofmajor inflows andnutrient sources.
c. Observed spatial variations inwater quality. d Locations ofcritical reservoir use areas.
e. Numeric dispersion potential (calculated bytheprogram).

Chapter 4 BATHTUB 4-17Ifpool monitoring data are available, spatial displays generated by PROFILE can beuseful for identi&ing appropriate model segmentation. A degree ofsubjectivejudgment isnormally involved inspeci~g segment boundaries, and sensitivity to alternative segmentation schemes should be investigated. Sensitivity to assumed segmentation should be low iflongitudinal transport characteristics are adequately represented. Experience with the program indicates that segment lengths onthe order ofs to 20 km aregenerally appropriate. Segmentation should be done conservatively (i.e., usethe minimum number required for each application). Scheme 3 illustrates the use ofBATHTUB for modeling partial reservoirs or embayments. This is similar to Scheme 2, except the entire reservoir isnot being simulated and the downstream water quality boundary condition isfixed. DiiTusiveexchange withthe downstream water body isrepresented bythe bidirectional arrows attached to the last (most downstream) segment. An independent estimate ofdiffusive exchange with the downstream water body is required forthis type ofapplication. Scheme 4 involves modeling multiple loading scenarios for asingle reservoir inaspatially averaged mode. Each “segment” represents the same reservoir, but under adifferent “condition,” as defined byexternal nutrient loading, reservoir morphometry, or other input variables. This scheme isuseful primarilyinapredictive mode for evaluation and rapid comparison ofalternative management plans orloading scenarios. For example, Segment 1might reflect existing conditions; Segment 2 might reflect projected future loadings as a result ofland development; and Segment 3 might reflect projected future loadings with specific control options. Bydefining segments to reflect awide range ofloading conditions, loadings consistent with specific water quality objectives (expressed interms ofmean phosphorus concentration, chlorophyll a, and/or transparency) can be identified. One limitation ofScheme 4 isthat certain input variables, namely precipitation, evaporation, and change instorage, are assumed to be constant for each segment. Ifyear-to-year variations inthese factors are significant, aseparate input fileshould be constructed for eachyear. Scheme 5 involves modeling acollection ofreservoirs inaspatially averaged mode. Each segment represents adifferent reservoir. This isuseful for regional assessments ofreservoir conditions (i.e., rankings) and evaluations of model performance. Using this scheme, asingle filecan be setup to include input conditions (water andnutrient loadings, morphometry, etc.) and observed water quality conditions for each reservoir inagiven region (e.g., state, ecoregion). As for Scheme 4, aseparate input filemust be constructed for each reservoir ifthere are significant differences inprecipitation, evaporation, or change in storage across reservoirs.

4-18 Scheme 6represents anetwork ofreservoirs inwhich flow and nutrients can be routed from one impoundment to another. Each reservoir ismodeled ina spatially averaged mode, For example, this scheme could be used to represent anetwork oftributmy and main stem impoundments. This type of
Chapter 4 BATHTUBapplication is feasible intheory buthas been less extensively tested thanthose described above. One limitation is thatnutrientlosses instreams linking the reservoirs are not directly represented. Such losses may be important insome systems, depending upon such factors asstream segment length and time of travel. In practice, losses in transport could be approximately handled by defining “stream segments,” provided thatfield data are available for calibration of sedimentation coefficients (particularly inthe case of nitrogen). Networking of reservoirs is most reliable for mass balances formulated on a seasonal basis and for reservoirs thatare unstratified or have surface outlets. As illustrated inFigure 4.3, ahigh degree offlexibility isavailable for speci- &ing model segments. Combinations ofschemes are also possible within one input file. While each segment ismodeled as vertically mixed, BATHTUB is applicable to stratified systems because the formulations have been empirically calibrated to data from awide variety ofreservoir types, including well-mixed and vertically stratified systems. Effects ofvertical variations are incorporated inthe model parameter estimates and error terms. Segment groups As indicated inTable 4.2, nutrient sedimentation coefficients may depend upon morphometric andhydrologic characteristics. To provide consistency with the data sets used inmodel calibration, segments must be aggregated for the purpose ofcomputing effective sedimentation rate coefficients (Al and B1 inTable 4.2). A“Segment Group Number” isdefined forthis purpose. Ratecoefflcient computations are based upon the following variables summarized bysegment group:
a. Surface overflow rate. b. Flushing rate (orresidence time).
c. Total external nutrient load. d Tributary total nutrient load.
e. Tributary ortho or inorganic nutrient load. Flushing rate is also used inchlorophyll aModels 1and 2. Area-weighted mean chlorophyll a values are computed foreach segment group and used in the computation ofhypolimnetic oxygen depletion rates (see Table 4.3). Group numbers are integers ranging from 1 up to thetotal number of segments defined forthe current case. Generally, ifacase involves simulation ofa single reservoir with multiple segments, allsegments should be assigned the same group number (1). Ifthe segments represent reservoir regions (tributary arms) with distinctly different morphometric, hydrologic, and water quality
Chapter 4 BATHTUB 4-19characteristics, different group numbers can be assigned to each region. Ifthe case involves simulation ofmultiple reservoirs (Schemes 5 or6 inFigure 4.3), different group numbers are assigned to each reservoir.

Tributaries Multiple ofexternal inflows (’Tributaries’) canbe specified for anymodel segment. Tributaries are identified byname and asequence number between 1and 99. Each tributary isassigned to aspecific segment number and classified using the following ‘Type Codes’: 1 Monitored Inflow 2 Nonpoint Inflow 3 Point-Source Inflow 4 Outflow orWithdrawal 5 Internal Load 6 Diffusive Source Type 1 describes tributaries with monitored inflows and concentrations. Type 2 describes tributaries orwatershed areas that are not monitored; inflow volumes and concentrations are estimated from user-defined land-use categories and export coefficients. Inorder to invoke this tributary type, the user must supply independent estimates ofexport 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 orwithdrawals; these are optional, sincethe model predicts outflow from the last segment based upon water-balance calculations. Specification ofoutflow streams isusefbl for checking water-balance calculations (bycomparing observed and predicted outflow volumes). Type 5 can beused to define internalnutrient loading rates (recycling from bottom sediments); this option would be invoked inrare circumstances where independent estimates ofsediment nutrient fluxes are available. Type 6defines diffusive exchange with downstream water bodies insimulating embayments (e.g., Scheme 3 inFigure 4.3).
Transport channels Innormal segmentation schemes, outflow from each segment discharges to thenext downstream segment or outofthe system. An option for specifying additional advective and/or diffusive transport between anypair ofsegments is also provided. Amaximum of 10 ‘Transport Channels’ can be defined forthis purpose. Independent measurements or estimates ofadvective and/or diffusive flow are required to invoke this option. Definition oftransport channels isnot required for simulating typical one-dimensional branched networks inwhich each segment discharges onlyto one downstream segment.
4-20 Chapter 4 BATHTUBMass balances The mass-balance concept isfimdamental to reservoir eutrophication modeling. BATHTUB formulates water andnutrient balances byestablishinga control volume around each segment and evaluating thefollowing 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 bythe user inthe 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 onlyto problems involving simulation ofspatial variations within reservoirs. They reflect eddy diffusion (as driven byrandom currents and wind mixing) and are represented bybulk exchange flows between adjacent segment pairs. Chapra andReckhow(1983) present examples oflake/embayment models that consider diffusive transport. As outlined inTable 4.2, five methods are available forestimating diffusive transport rates. Each leads to the calculation ofbulk exchange flows which occur inboth directions ateach segment interface. Dispersion coefficients, calculated from the Fischer etal. (1979) equation (Model 1) orfrom afixed longitudinal dispersion coefficient (Model 2), are adjusted to account for effects ofnumeric dispersion (“artificial” dispersion ormixing that isaconsequence ofmodel segmentation). Model 3 can beused fordirect input ofbulk exchange flows. Despite itsoriginal development based upon data from river systems, the applicability ofthe Fischer etal. equation forestimating longitudinal dispersion rates inreservoirs has been demonstrated previously (Walker 1985). For a given segment width, mean depth, and outflow, numeric dispersion isproportional to segment length. Byselecting segment lengths tokeep numeric dispersion rates less than the estimated values, the effects ofnumeric dispersion on the calculations can be approximately controlled. Based upon Fischer’s dispersion equation, the numeric dispersion rate willbe lessthanthe calculated dispersion rate ifthe following condition holds: L< 200w2Z-084° where L= segment length, km
Chapter 4 BATHTUB 4-21W = 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 forthe appropriate segment length. Inmost cases, simulated nutrient profiles arerelatively insensitive to longitudinal dispersion rates. Fine-tuning ofexchange flows canbe achieved via the use ofsegmentspecific calibration factors. While, intheory, the increase-in-storage term should reflect both changes in pool volume and concentration, only thevolume change is considered in massbalance calculations, and concentrations are assumed to be atsteady 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 awater balance orconservative substance balance, the net sedimentation term iszero. Nutrient retention submodels areused to estimate net sedimentation ofphosphorus ornitrogen ineach segment according to the equations specified inTable 4.2. Based upon research results, asecond-order decay model isthe most generally applicable formulation forrepresenting phosphorus and nitrogen sedimentation inreservoirs: 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 intesting alternative models (see Table 4.2). The default model error coefficients supplied with the program, however, have been estimated from themodel 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-yearfor total phosphorus and 0.0032 m3/mg-yearfor total nitrogen, as specified under “Model 3“ inTable 4.2. With these coefficients, nutrient
Chapter 4 BATHTUBsedimentation models explain 83 and 84percent ofthe between-reservoir variance inaverage phosphorus andnitrogen concentrations, respectively. Residuals from these models are systematically related to inflow nutrient partitioning (dissolved versus particulate orinorganic versus organic) and to surface overflow rate overthe data setrange of4to 1,000 m/year. Effective rate coefficients tend to be lower insystems with high ortho-P/total P (and high inorganic N/total N) loading ratios orwith low overflow rates (4 to 10m/year). Refinements to the second-order formulations (Models 1and 2) are designed to account forthese dependencies (Walker 1985). As indicated inTable 4.2, Sedimentation Models 1 and 2use different schemes to account for effects ofinflow nutrient partitioning. Inthe case of phosphorus, Model 1performs mass balance calculations on “available P,” a weighted sum ofortho-P andnonortho-P which places aheavier emphasis on the ortho-P (more biologically available) component. Model 2uses total phosphorus concentrations but represents the effective sedimentation rate as inversely related to thetributary ortho-P/total Pratio, sothat predicted sedimentation rates arehigher insystems dominated bynonortho (particulate or organic) Ploadings and lower insystems dominated byortho-P ordissolved 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 1accounts for inflow nutrient partitioning byadjusting 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 1has advantages inreservoirs with complex loading patterns because afixed sedimentation coefficient can beused and effects ofinflow 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 betested for applicability to aparticular case. Inmost situations, predictions willberelatively insensitive to the particular sedimentation model employed, especially ifthe ortho-P/total P loading ratio isinamoderate range (roughly 0.25 to 0.60). Additional model application experiences suggest that Method 2mayhave an edge over Model 1 in systems with relatively longhydraulic residence times (roughly, exceeding 1year), although further testing isneeded. Because the coefficients are concentration- or load-dependent andbecause themodels do not predict nutrient partitioning inreservoir outflows, Sedimentation Models 2 and4 cannot be applied to simulations ofreservoir networks (Scheme 6 inFigure 4.3). Based upon error analysis calculations, themodels discussed above provide estimates ofsecond-order sedimentation coefllcients which are generally accurate to within afactor of2forphosphorus and afactor of3 fornitrogen. Inmany applications, especially reservoirs with lowhydraulic residence times, this level ofaccuracy isadequate because thenutrient balances are dominated byother terms (especially, inflow and outflow). Inapplications to existing
Chapter 4 BATHTUB 4-234-24 reservoirs, sedimentation coefficients estimated from the above models can be adjusted within certain ranges (roughly afactor of2for P, factor of3 forN) to improve agreement between observed and predicted nutrient concentrations. Such “tuning” ofsedimentation coefficients should be approached cautiously because differences between observed and predicted nutrient levels maybe attributed to factors other than errors inthe estimated sedimentation rates, particularly ifexternal loadings and pool concentrations arenot atsteady state. Figure 4.4 shows the relationship between hydraulic residence time and mean depth inthe reservoirs used inmodel development. Predictions ofnutrient sedimentation rates are less reliable inreservoirs lyingoutside the data set range. This applies primarily to reservoirs with residence times exceeding 2years, mean depths greater than 30 m, or overflow rates less than 4 m./year. Tests based upon independent data sets indicate thatthe sedimentation models areunbiased under these conditions buthavehigher error variances. Insuch situations, the modeling exercise should include asensitivity analysis to model selection and, ifpossible, calibration ofsedimentation coefficients to match observed concentration data. Deviations atthe other extremes (reservoirs with lower residence times orhigher overflow rates than those represented inthe model development data set) are ofless concern because the sedimentation term isgenerally aninsignificant portion ofthetotal nutrient budget insuch systems (i.e., predicted pool concentrations arehighly insensitive to estimated sedimentation rate). Because the sedimentation models have been empirically calibrated, effects of“internal loading” orphosphorus recycling from bottom sediments are inherently reflected inthemodel parameter values and error statistics. Generally, internal recycling potential isenhanced inreservoirs with the following characteristics:
a.

b.

c.

d. High concentrations ofortho-phosphorus (orhigh ortho-P/totalP ratios) innonpoint-source tributary drainage (indicative ofnatural sediments that arephosphorus-rich andhave high equilibrium phosphorus concentrations). Low summer sufiace overflow rates, typically <10 m/year (indicative of low dilution potential for internal loadings generated on amass per unit areabasis and low external sediment loadings). Intermittent periods ofstratification and anoxic conditions atthe sedimentiwater interface (contribute to periodic releases ofsoluble phosphorus from bottom sediments and transport into the mixed layer). Low iron/phosphorus ratios (typically <3 on amass basis) insediment interstitial waters or anaerobic bottom waters (permits migration of phosphorus into aerobic zones without iron phosphate precipitation). The above conditions are often found inrelatively shallow prairie reservoirs; Lake Ashtabula (U.S. Army Engineer District, St. Paul) isanexample
Chapter 4 BATHTUB1.8

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 inthe CEreservoir data set. Insuch situations, empirical sedimentation models willunderpredict reservoir phosphorus concentrations. Depending upon the efficiency ofthe internal recycling process, steady-state phosphorus responses can be approximately simulated byreducing the effective sedimentation coefficient (e.g., roughly to O.inthe case ofAshtabula). An option for direct specification ofinternal loading rates isalso provided foruse insituations where independent measurements orestimates are available.

Nutrient residence time and turnover ratio The “averaging period” isdefined asthe period oftime over which water and mass balance calculations are petiormed. The selection ofanappropriate averaging period isanimportant step inapplying this type ofmodel to reservoirs. Two variables must beconsidered inthis 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 4-25The estimates ofreservoir nutrient mass and external loading correspond to the averaging period. The turnover ratio approximates thenumber oftimes that thenutrient mass inthe reservoir isdisplaced during the averaging period. Ideally, theturnover ratio should exceed 2.0. Ifthe ratio istoo low, then pool and outflow water quality measurements would increasingly reflect loading conditions experienced prior tothe start ofthe averaging period, which would be especially problematical ifthere were substantial year-to-year variations in loadings. At extremely high turnover ratios and low nutrient residence times (s2 weeks), the variability ofloading conditions within the averaging period (as attributed to storm events, etc.) would be increasingly reflected inthe pool and outflow water quality measurements. Insuch cases, pool measurement variabilitymay berelatively high, andthe biological response (e.g., chlorophyll a production) maynot be inequilibrium with ambient nutrient levels, particularly immediately following storm events. Figure 4.5 shows that thehydraulic residence time isanimportant factor in determining phosphorus and nitrogen residence times, based upon annual mass balances from 40 CEreservoirs used inmodel development. For aconservative substance, the mass andhydraulic residence times would be equal atsteady state. The envelopes inFigure 4.5 show thatthe spread ofnutrient residence times increases withhydraulic residence time; this reflects the increasing importance ofsedimentation as acomponent ofthe overall nutrient balance. At lowhydraulic residence times, there isrelatively little opportunity for nutrient sedimentation, and pool nutrient concentrations and residence times can be predicted relatively easilyfrom inflow concentrations. Athighhydraulic residence times, predicted pool nutrient concentrations and residence times become increasingly dependent upon the empirical formulations used torepresentnutrient sedimentation. This behavior isreflected inthe sensitivity curves discussed inChapter 1. Normally, the appropriate averaging period forwater and mass balance calculations would be 1year forreservoirs with relatively long nutrient residence times or seasonal (May-September) for reservoirs with relatively short nutrient residence times. As shown inFigure 4.5, most ofthe reservoirs inthe model development data sethad phosphorus residence times lessthan 0.2year, which corresponds roughly to anutrient turnover ratio of2for a5-month seasonal averaging period. Thus, assuming thatthe reservoirs used inmodel development are representative, seasonal balances would be appropriate for most CE reservoir studies. BATHTUB calculates mass residence times and turnover ratios using observed orpredicted pool concentration data. Results can be used to select anappropriate averaging period foreach application.

4-26 Chapter 4 BATHTUB0.5
0.0

-- z “2.0
-2.5 t

“2*!5 -2.0 -1.5 -1.0 -0.s 0.0 0.5 LOG 14 YDf3AULlC 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 4-27Solution algorithms The water balances areexpressed as asystem ofsimultaneous linear equations that are solved viamatrix inversion to estimate the advective out-flow from each model segment. The mass balances are expressed as asystem of simultaneous nonlinear equations which are solved iteratively viaNewton’s Method (Burden, Fakes, and Reynolds 1981). Mass-balance solutions canbe 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 ineach 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 orpredicted pool nutrient levels to measures ofalgal density and related water quality conditions. Table 4.5 lists diagnostic variables included inBATHTUB output and guidelines fortheir interpretation. They maybe categorized asfollows:
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 andMetalimnetic Oxygen Depletion Rates. Principal components ofnetwork variables: firstand second principal components. Indicators ofnitrogen versus phosphorus limitation (Total N- 150)/Total P, and Inorganic N/P ratios. Indicators oflightlimitation. (1) Nonalgal turbidity, mixed depth xturbidity. (2) Mixed depth/Secchi depth, and chlorophyll ax Secchi Depth. Chlorophyll a response tophosphorus: chlorophyll a/total P. AlgalNuisance Frequencies. Carlson Trophic State Indices. 4-28 Chapter 4 BATHTUBStatistical summaries derived from the CE model development data setprovide one frame ofreference. Low andhigh ranges given for specific variables provide approximate bases for assessing controlling processes andfactors, includinggrowth limitation bylight, nitrogen, and phosphorus. The ranges ofconditions under which the empirical models have been developed should be considered ineach application. Figure 4.6 depicts relationships among three keyvariables determining eutrophication responses (total phosphorus, total nitrogen, and nonalgal turbidity) inthe CE model development data set. Figure 4.7 depicts relationships among phosphorus, chlorophyll a, and transparency. Plotting data from agiven application on each ofthese figures permits comparative assessment ofreservoir conditions and evaluations ofmodel applicability. Ifreservoir data falloutside the clusters inFigure 4.5, 4.6, or4.7, potential model errors aregreater than indicated bythe statistics in Table 4.4. The prediction ofmean chlorophyll a from observed orpredicted nutrient concentrations can bebased on one ofthe five models listed inTable 4.2. Error analyses indicate that itisgenerally more difficult to predict chlorophyll a from nutrient concentrations and other controlling factors than to predict nutnentconcentrations from external loadings and morphometry. This partially reflects greater inherent variability ofchlorophyll 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 aregiven inTable 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 ofconditions under which simple phosphorus/ chlorophyll relationships are appropriate andto develop more elaborate models (Models 1-3)which explicitly account for additional controlling factors (nitrogen, light, flushing rate). While model refinements have been successful inreducing error variance associated with simple phosphorus/chlorophyll relationships by approximately 58 percent, a“penalty” ispaid interms ofincreased data requirements (e.g., nonalgal turbidity, mixed-layer depths, nitrogen, and flushing rate). For existingreservoirs, 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 ofturbidity, 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 BATHTUB1.0
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* ● 

# ‘s



# .*e: ● & ● ● 

### ‘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 4-31depth are summarized inTable 4.6. These should beused onlyinthe absence ofsite-specific measurements. Since mechanistic models forpredicting nonalgal turbidity levels as afunction ofdeterministic factors (e.g., suspended-solids loadings and the sedimentation process) have not been developed, itispossible to predict chlorophyll a responses to changes innutrient loading inlight-limited reservoirs onlyunder stable turbidity conditions. Projections ofchlorophyll a concentrations should include asensitivity analysis over areasonable range ofturbidity levels. Estimates ofnonalgal turbidity ineach segment (minimum= 0.08 m-l) are required for chlorophyll a Models 1and 2, Secchi Model 1 (Table 4.2), and Nutrient Partitioning Models (Table 4.3). Ideally, turbidity iscalculated from observed Secchi and chlorophyll a data ineach segment. Iftheturbidity input field isleflblank, the program calculates turbidity values automatically from observed chlorophyll a and Secchi values (ifspecified). An error message is printed, and program execution isterminated ifallofthe following conditions hold:
a. Turbidity value missing orzero. b. Observed Chlorophyll a or Secchi missing orzero.
c. Chlorophyll a Models 1,2 or Secchi Model 1used. Inthe absence ofdirect turbidity measurements, the multivariate regression equation specified inTable 4.6 canbeused (outside ofthe program) to estimate areservoir-average value. Such estimates canbe modified to based upon regional databases. Model calibration and testing have been based primarily upon data sets describing reservoir-average conditions (Walker 1985). Ofthe above options, Model 4 (linear phosphorus/chlorophyll a relationship) has been most extensivelytested foruse inpredicting spatial variations within reservoirs. The chlorophyll/phosphorus ratio issystematically related to measures oflight limitation, including the chlorophyll a andtransparency product, and the product ofmixed-layer depth and turbidity. Ifnitrogen isnot limiting, then lightlimitation effects maybe approximately considered bycalibrating the chlorophyll/phosphorus ratio to field data; this isanalternative to using the direct models (i.e., Models 1and 2) that require estimates ofturbidity and mixed-layer depth ineach segment. The relationships depicted inFigure 4.8 may beused to obtain approximate estimates ofreservoir-average calibration coefficients for use inModel 4based upon observed monitoring data orindependent estimates ofturbidity and mixed-layer depth (Table 4.6). Models 1and 3 attempt to account forthe effects ofnitrogen limitation on chlorophyll a levels. nitrogen budget and Nitrogen concentrations arepredicted from the external donot account forpotential fixation ofatmospheric 4-32 Chapter 4 BATHTUBTable 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 Ofor 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 bybluegreen algae. Nitrogen fixation maybe important insome impoundments, as indicatedbythepresenceofalgaltypesknowntofix nitrogen, lowN/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 acausal factor related directly to external nitrogen loads. Use ofModels 1 and 3 may be inappropriate inthese cases; modeling ofnitrogen budgets would beusefil for descriptive purposes, but notuseful (or necessary) for predicting chlorophyll a levels. Chapter 4 BATHTUB 4-330.6 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

# r 0.4

-

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**Ifthe reservoir is stratified and oxygen depletion calculations are desired, temperature profile data taken from the period ofdepletion measurements (typically late spring to early summer) areused to estimate the mean depth of thehypolimnion. Ifmean hypolimnetic depth isnot specified (=0.0), the reservoir is assumed to beunstratified and oxygen depletion calculations are bypassed. The oxygen depletion models arebased upon data from near-dam stations. Accordingly, mean hypolimnetic depths should be specified only for near-dam segments, based upon the morphometry ofthe entire reservoir (not the individual segment). Inmodeling collections ornetworks ofreservoirs (Schemes 5 and 6 inFigure 4.3), amean hypolimnetic depth can be specified separately for each segment (i.e., each reservoir). Table 4.6 gives anempirical relationship that can beused to estimate mean hypolimnetic depth inthe absence ofdirect measurements.

Calibration factors The empirical models implemented inBATHTUB aregeneralizations about reservoir behavior. When applied to data from aparticular reservoir, observations may differ from predictions byafactor oftwo or more. Such differences reflect data limitations (measurement orestimation errors inthe average inflow and outflow concentrations), aswell asunique features ofthe particular reservoir. Afacility to calibrate the model to match observed reservoir conditions is provided inBATHTUB. This isaccomplished byapplication of ‘Calibration Factors’, which modi~ reservoir responses predicted bythe 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 inreservoir conditions likelyto result from specific management scenarios under the assumption thatthe calibration factors remain constant. For convenience, calibration factors canbe applied on two spatial scales: global (applying to allsegments) and individual (applying to each segment). The product ofthe global and individual calibration factors ismultiplied bythe reservoir response predicted bythe empirical model to produce the “calibrated” prediction. All calibration factors have adefault value of 1.0. Separate sets of calibration factors can be applied to anyor allthe 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 4-35inassessing whether calibration isappropriate. General guidance ispresented inasubsequent section (see Application Steps).

Error analysis The first-order error analysis procedure implemented byBATHTUB can be used to estimate the uncertainty inmodel predictions derived from uncertainty inmodel inputs and uncertainty inherent inthe empirical models. To express uncertainty ininputs, key input variables are specified using two quantities: Mean = Best Estimate

CV = Standard Error ofMean/Mean The CV reflects the uncertainty inthe input value, expressed as afraction ofthe mean orbest estimate. CV values carIbe 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 canbeused to estimate Mean and CV values for inflow and reservoir concentrations, respectively. Model uncertainty isconsidered by specifing aCV value foreach global calibration factor; default CV values derived from CE reservoir data sets are supplied (see Table 4.4). Erroranalysis calculations provide onlyrough indications ofoutput uncertainty. Four error analysis options areprovided: None Inputs (Consider input uncertainty only) Model (Consider model uncertainty only) All (Consider input and model uncertainty) Specified CV values are not used inthe calculations iferror analyses arenot requested. 

### Program Operation
Introduction

4-36 This section summarizes procedures for running the BATHTUB program. When the program isrun (from the DOS prompt), aseries ofhelp screens summarizing model features isfirst encountered. These arefollowed bya menu that provides interactive access to seven types ofprocedures 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**  Aprocedurecategory is selected bymoving the cursor(usingarrow keys) orby pressing the first letter oftheprocedure name. Assistance innavigating around themenu can reobtained bypressing the<F7> function key. Generally, Case, Run, List, and Plot procedures would be implemented sequentially inagiven session. Program control returns to thetop ofthe menu after executing aprocedure. AHelp screen describing the selected procedure can be viewed by pressing <Fl>.

Case procedures Case procedures are invoked to define, edit, save, retrieve, orlistinput values. Once Case is selected, themenu expands byone lineto 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 isaccomplished byselecting Edit, which provides access to data-entry screens inthe 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: 4-37Once the case input values have been entered, the Case/Models procedure canbe used to define model options inthe 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 userto setmodel options inany ofthe above categories. Option settings are documented inTable 4.2. For most options, asetting ofzero willbypass the corresponding calculations. Conservative substance (e.g., chloride) balances maybe useful for veri@ng water balances and calibrating diffusive transport coefficients. Forthe phosphorus, nitrogen, and chlorophyll models, settings of 1or2 correspond to the most general formulations identified inmodel testing. Ifthe conservative substance, phosphorus, ornitrogen sedimentation model is setto O,corresponding mass balance calculations are bypassed, and predicted concentrations are setequal to observed values ineach segment. This feature isuseful for assessing pool nutrientfchlorophyll relationships and controlling factors inthe absence of nutrient loading information. The Case/Read procedure isused to read existing data sets andhas 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 insubsequent sessions (Case/Retrieve). Case files should be named with anextension of’. BIN’ to facilitate future identification and retrieval. The Case/Save procedure saves the current data set. The Case/New procedure resets alldata and model coefficients to their default values and begins anew data set. The Case/List procedure lists allinput values forthe current case. The Case/Morpho option lists abrief summary of segment morphometric features.

4-38 **Chapter 4**  **BATHTUB**Run procedures Once acomplete set ofinput 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 isencou.ntered, execution stops and control isreturned 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, acopy ofthe error messages is saved inadiskfilewhich can be accessed using the Utilities/Error procedure. Ifno input errors are detected, the program attempts to solve the massbalance equations. Inrare cases, solutions cannot be reached and anerror message appears. This type ofproblem may occur when the segmentation scheme isnot defined correctly (outflow segment numbers are not correctly specified) orwhen the solution ofthe water-balance equation indicates that there isno net outflow from the reservoir (evaporation and/or withdrawals exceed inflows). Steady-state solutions cannot bereached insuch situations. Ifasolution isreached, control isreturned to the main menu. The message ‘MODEL EXECUTED’ appears inthe lower righthand comer ofthe screen. This indicates that List and Plot procedures can be accessed to review output. Ifinput values are subsequently edited oranew data fileisread, the model must be executed again before output can be viewed. As indicated above, the Run/Model procedures can be implemented withfour levels oferror 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 ofpredicted nutrient concentrations ineach segment to variations innutrient sedimentation rate and inlongitudinal 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 areprovided tosummarize andhighlight various aspects ofthe model output. These are accessed byselecting Listfrom the main menu:

**Hydrau 1**  **Balances/**

**Gross By**  **Segment Smnary**  **Compar D** **i agnos**  **Profiles F** **1 ownet**  **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 diskfile. When output iscomplete, autility isexecuted to permit interactive viewing ofthe 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 ofobserved 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 ofthese procedures, plotformats 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 Iferror analysis calculations have been petiormed, Format 1 shows predicted concentrations + 1standard error. Similarly, observed concentrations are shown * 1standard error for observed variables with specified CV values. The lastmodel segment displayed inFormats 1and 3 shows results forthe areaweighted mean across allcase segments; for example, ifthe case contains 4 segments, area-weighted means willbe shown above segment number 5. Samples ofeach plot format aregiven inthe ‘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 adiskfile. IfUtilities/Output/ File is selected, alloutput listings willberouted to auser-specified diskfile; no screen output will occur until Utilities/Output./Screen is selected. This utility isusefid for creating permanent log files ofprogram output forfuture reference orfor inclusion inreports. The Utilities/Restrict procedure can beused to restrict program output (listing and plots) to specific segments. As discussed above, the Utilities/Error procedure permits viewing ofanyerror messages from the last execution ofthemodel. This isuseful for debugging input files.
Help procedure Supplementary help screens canbe viewed from the program menu by selecting the Help:
***B A**  **T H**  **T U B** 
**- VERSION**  **5.4**
This provides access tohelp screens that are organized inthe 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 isthe user’sintention. The current casefileshould besaved before quitting. 

### Application Steps This section describes basic steps involved inapplying BATHTUB to a reservoir. Three application scenarios canbe defined, based upon reservoir status and data availability: Data Avtib ilitv Water/Nutrient Pool Water

~ Reservoir Balance Datz @al ityData A Existing Yes Yes B Existing No Yes 

## c Existing or Proposed Yes No Scenario Anormally applies to anexisting reservoir with nutrient balance data and pool water quality data. Under Scenario B, nutrient balance (loading) information islacking; inthis case, the program canbe used for diagnostic purposes (e.g., assessing pool nutrientichlorophyll relationships and regional ranking). Scenario C isdistinguished bylack ofpool water quality dat~ which would otherwise be used forpreliminary testing and calibration. For each scenario, application procedures can be summarized interms 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 ofprevious steps iscommon intypical modeling projects. As described below, not all modeling steps are applicable to each scenario. The procedures are intended to provide general indications offactors to be considered during the modeling process. They are not intended as arigid framework for applying the model. Userjudgment must be exercised to account forunique aspects ofeach application. The Theory section ofthis chapter describes model formulations, options, and other background information required to support applications. Before considering each scenario, afew general aspects ofdeveloping model applications are discussed. Itisimportant to define purpose and scope prior to undertaking the modeling effort. This includes speci~ing management issues to be evaluated and types ofmodel output required to support the evaluations. Intypical applications, most ofthe effort and cost is devoted to data collection and data reduction. In situations where modeling isundertaken after the monitoring data have been acquired, model results maybe severely limited bydata. This situation canbe avoided byinitiating modeling before designing and undertaking additional monitoring. Modeling canbe conducted intwo phases. The first phase isbased upon historical data andhelps to define data gaps that can be filled in subsequent monitoring. The second phase isbased upon more complete data. Chapter 1contains guidance fordesigning monitoring programs to support model applications. In defining study scope, the user must decide which components willbe modeled. Inthe most general case, amodel application involves specification oftributary loads (flows and concentrations) for aconservative tracer, total phosphorus, ortho phosphorus, total nitrogen, and inorganic nitrogen. Ofthese, onlytotal phosphorus is absolutely necessary. Based upon the CEreservoir data setused indeveloping the phosphorus sedimentation models, additional consideration ofortho phosphorus loads reduces the standard error ofpredicted reservoir-mean phosphorus concentrations by 16to 32 percent, depending upon model formulation. Considering total phosphorus loads only willprovide unbiased predictions ofreservoir response, however, ifthe ratio oftributary ortho phosphorus load to tributay total phosphorus load isinthe range of 15to 50 percent. Considering nitrogen loads provides additional descriptive information, but may not contribute significantly to predicting the trophic response ofthe reservoir, asmeasured bychlorophyll a because nitrogen may not be limiting algal growth orbecause external nitrogen loads maybe supplemented byfixation ofatmospheric nitrogen (see Eutrophication response models). Modeling aconservative tracer, such as chloride orconductivity, provides a
**Chapter 4**  **BATHTUB** 4-43means for calibrating and testing diffusive transport terms andfortesting overall water balances. BATHTUB provides afacility for calibrating the empirical models to account for site-specific conditions (see Calibration fwtors). Calibration should be attempted onlybyexperienced users working with intensive monitoring data sets. Apotential need for site-specific calibration isindicated 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 ofcoefficients within reasonable ranges). Differences between observed and predicted concentrations result from two basic sources: data errors and model errors. Random data errors always occur inthe specification ofmodel input values (tributary loads, observed reservoir water quality, flows, morphometry, etc.). Omission of important nutrient sources informulating the reservoir nutrient balance is another type ofrandom error. These are essentially artifacts ofstudy design, data collection, and data reduction. Model errors reflecttrue differences between model predictions and reservoir response. Calibration to account for model errors may bejustified, but calibration to account for data errors is generally notjustified. One possible exception to this rule occurs when data errors are not random, but are biases attributed to differences inmeasurement methods; for example, calibration ofthe chlorophyll a model maybe appropriate to account for differences inmeasurement technique. BATHTUB error analyses canhelp to distinguish between model and data errors. Calibration is generally notnecessary when there isconsiderable overlap between observed and predicted distributions (Plot procedures). Each application should start with construction ofaschematic diagram showing major reservoir regions, inflow streams, point sources, outflow streams, and monitoring stations. Examples ofschematic diagrams aregiven in the Documented Session and Instructional Cases sections atthe end ofthis chapter. The diagram can be overlaid on areservoir map. Initial definitions of model segments should be shown; these mayberevised based upon subsequent review and summary ofmonitoring data. Segments andtributaries should be labeled and numbered. The diagram provides auseful frame ofreference for subsequent data reduction and modeling steps.

Scenario A
- Existing reservoir with loading and pool water quality data Step 1involves reduction ofwatershed data used inmodeling. Formulation ofadrainage area “balance” isanimportant first step insummarizing watershed characteristics. The FLUX program (Chapter 2) can beused for estimating seasonal and/or annual loadings forgauged tributaries, point sources, and discharges. An averaging period forcalculating tributary inflows must be selected. This istypically 1year for reservoirs with relatively longhydraulic 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 andturnover ratio). Sensitivity to choice ofaveraging period can betested bycreating separate input files for different averaging periods. Ungauged inflows and stream concentrations can be estimated bydrainagearea proportioning using data from other regional watersheds with similar land uses. Alternatively, ungauged inflows and concentrations can be estimated by calibrating and applying thenonpoint source model provided with BATHTUB (TYPE=2 tributaries). Calibration requires specification oftypicaJrunoff rates and concentrations as afiction ofland use (Case/Edit/Non-Point Procedure). Step 2involves reduction ofreservoir morphometric and water quality data. Morphometric inilormation canbe estimated from contour maps and/or sediment accumulation surveys. PROFILE (Chapter 3) canbe used to summarize observed water quality conditions bysegment and calculate oxygen depletion rates in stratified reservoirs. Segment boundaries depicted onthe schematic diagram may berevised based upon review ofpool monitoring data. Generally, itisappropriate to aggregate adjacent reservoir areas with similar water quality into asingle segment. Box plots summarizing water quality data bystation can beusefid forthis purpose (see PROFILE, Chapter 3). Even ifsignificant spatial variations inwater quality are apparent, division ofthe reservoir into multiple segments isnotnecessary for modeling. Modeling the entire reservoir with one segment provides predictions ofarea-weighted mean concentrations, which may be adequate to support management decisions. Insuch situations, it willbe particularly important to apply spatial weighting factors when averaging observed water quality data. Defining multiple segments may berequired to support management decisions. Simulating spatial variations within the reservoir can provide evidence ofmodel applicability and reliability that isnot available in single-segment applications. In Step 3, aninput data fileiscreated byrunning 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). Ifortho phosphorus and/or inorganic nitrogen concentrations for all stream inflows are not supplied, availability factors should not be used incalculating nutrient balances. This isachieved bysetting the ‘Availability Factor’ option to Ousing the Case/Models procedure. Water balances are checked and adjusted inStep 4using the List/Balances/ Gross procedure. Measured flows for allmajor inflow and outflow streams must be specified inorder to check the water balance. Itmaybe appropriate to adjust certain inflow, outflow, and/or increase-in-storage terms until balances are established. The appropriate terms to adjust varyfrom case to case, depending upon watershed characteristics andflow monitoring networks. Based upon familiarity with the flow data sources, the user should assess the
**Chapter 4**  **BATHTUB** 4-45most likely source(s) ofwater balance error and adjust the appropriate value(s) inthe CASE file. Flow-balance errors are often attributed to ungauged surface orgroundwater inflows. Ifawater balance cannot be established with reasonable adjustments, additional monitoring with refinements to flow gauging networks may be required. Nutrient turnover ratios are checked inStep 5 using theList/Balances/ Gross procedure. As discussed above (seeNutrient residence time andturnover ratio), the appropriate averaging period for mass-balance calculations is determined bythe observed turnover ratio ofthe limiting nutrient (usually phosphorus). A seasonal averaging period (April/May through September) is usually appropriate ifitresults inaturnover ratio exceeding 2.0. An annual averaging period may beused otherwise. The turnover ratio criterion isan approximate guideline, which maybe adjusted from case to case. Other considerations (such as comparisons ofobserved and predicted nutrient levels) can also beused as abasis for selecting anappropriate averaging period, particularlyifthe turnover ratio isnear 2.0. Note that ifthe reservoir isvertically stratified and significant hypolimnetic accumulations ofphosphorus occur, seasonal phosphorus turnover ratios calculated from mixed-layer concentrations will be overestimated. Inthis situation, mixed-layer nutrient levels during the growing season mayreflect 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 betested inthis situation. Depending upon results ofStep 5, itmaybe necessary to repeat the calculation oftributary loadings (Step 1)using adifferent averaging period. Step 6 involves checking and possible calibration ofdiffusive transport terms using the List/Hydrau procedure. Ifnumeric dispersion exceeds the estimated dispersion inagiven segment, the user should consider revising the segmentation scheme (e.g., increasing segment numbers and thus decreasing segment lengths) until this criterion is satisfied. Insome cases, this may be difficult to achieve with areasonable number ofsegments, particularly in upper-pool segments, where advective velocities tend to be greater. The criterion maybe waived ifthe sensitivity ofpredicted nutrient profiles to alternativesegmentation schemes is shown to be minimal. Conservative tracer data (typically chloride orconductivity), maybe used to calibrate diffusive transport terms inproblems 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 ofpredicted tracer concentrations to fourfold variations indispersion rates. Where possible, adjustments should be made onlyto theglobal calibration factor (keeping segment calibration factors attheir default setting of 1.0); this is amore 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 inthe range of0.25 to 4.0, the approximate 95-percent confidence limit for dispersion estimated fi-omFischer’s equation. Ifadjustment outside this range isrequired, other dispersion models and/or alternative segmentation schemes should be investigated. Ifthere isalong wind fetch and segments are aligned along predominant wind directions, upward adjustment ofthe dispersion factors may be necessary. Conversely, downward adjustment may benecess~ inreservoirs orreservoir areas that are sheltered from winds. The segment calibration fmtor for dispersion can be adjusted downward to reflect local restrictions caused byweirs, bridges, etc. Calibration ofdispersion rates based upon tracer data isfeasible only ifsignificant tracer gradients are detected inthe reservoir as aresult ofthe 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 isalso feasible, provided that tracer data are not available inStep 6. As discussed above, differences between observed and predicted nutrient profiles mayreflect random errors inthe data, as well astrue differences between the model predictions and reservoir responses. As discussed above, aconservative approach to calibration is recommended. The List/Compar procedure provides statistical comparisons ofobserved and predicted concentrations. These are computed using three alternative measures oferror: observed error only, T(1); error iypical ofmodel development data set, T(2); and observed and predicted error, T(3). Tests ofmodel applicability arenormally based upon T(2) andT(3). Iftheir absolute values exceed 2forthe comparison ofarea-weighted mean concentrations, there isless than a 5-percent chance thatnutrient sedimentation dynamics inthe reservoir are typical ofthose inthe model development data set, assuming that input conditions have been specified inanunbiased manner. The applicability ofthe models would be questionable inthis case. Ifthe discrepancy cannot be attributed to possible errors inthe input data file (particularly, inflow concentrations), other options for modeling nutrient sedimentation should be investigated. Lack offitmay also result from unsteady-state loading conditions, particularlyifthe nutrient turnover ratio isless than 2based upon annual loadings. In such cases, averaging periods longer than ayear may berequired to establish a valid loadhesponse relationship. This situation ismore likelyto 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 beused as a basis for deciding whether calibration isappropriate. Ifthe absolute value of T(1) exceeds 2, then there islessthan a5-percent chance that the observed and
**Chapter 4**  **BATHTUB** 4-47predicted means are equal, given the error inthe observed mean. Inthis situation, itmaybe desirable to calibrate the model so that observed and predicted nutrient concentrations match. As outlined inTable 4.2, two calibration methods areprovided for phosphorus andnitrogen: Method O

-calibrate decay rates and Method 1- calibrate concentrations. Inthe first case, the segment-specific calibration factors are applied to estimated sedimentation rates incomputing nutrient balances. Inthe second case, the factors are applied to estimated concentrations. InMethod O (default), itis assumed that the error isattributed primarily to the sedimentation model. InMethod 1,the error source isunspecified (some combination of input error, dispersion error, and sedimentation model error). The latter may be used when predicted nutrient profiles are insensitive to errors inpredicted sedimentation rate because the mass balance is dominated byinflow and outflow terms (low hydraulic residence times, seeFigures 1.3 and 1.4). Regardless of the selected calibration option, global calibration factors forphosphorus and nitrogen (specified onthe Case/Edit/Mcoef screen) are always applied to the nutrient sedimentation rates. Nutrient Sedimentation Models 1and 2have been empirically calibrated and tested for predicting reservoir-mean conditions. Error analysis calculations indicate that sedimentation rates predicted bythese models aregenerally accurate to within afactor of2forphosphorus and afactor of3 fornitrogen (Walker 1985). To account forthis error, nutrient calibration factors (Case/ Edit/Mcoefs screen) can be adjusted within the nominal ranges of0.5 to 2.0 and 0.33 to 3 for phosphorus andnitrogen, respectively. IrIsome cases, nutrient retention coefficients forphosphorus ornitrogen may benegative. Even after setting thenutrient calibration coefficient to zero (essentially treating thenutrient as aconservative substance), the model will underpredict the observed nutrient concentration inthe reservoir. This may reflect net nutrient releases from bottom sediments (phosphorus ornitrogen) or fixation ofatmospheric nitrogen bybluegreen algae. These “internal sources” can be represented inthe model using tributaries withTYPE CODE=5. Apparent negative retention coefficients mayreflect use ofanimproper averagingperiod orunderestimation ofsignificant external loads. Independent evidence and estimates ofsediment nutrient sources should be obtained before speci&ing internal sources inthemodel. As discussed intheTheory section of this chapter, reservoirs with negative nutrient retention coefficients were rarely encountered inthe supporting research (Walker 1985). Ifinternal sources are specified, estimates ofmodel error derived from the supporting research are invalid. While itisusually possible to “tune” the model predictions using the internal source terms, this does notprovide away ofpredicting how the internal sources will change inresponse to changes inexternal loads orother management strategies evaluated inStep 11. Once nutrient balances have been established, eutrophication responses (as measured bychlorophyll a, transparency, andhypolimnetic oxygen depletion
**Chapter 4**  **BATHTUB**rate) are developed inStep 8.This involves model selection, testing, and possible calibration. As outlined inTables 4.2 and 4.3, several options are available for predicting chlorophyll a concentrations and Secchi depths as afunction of nutrient levels and other controlling factors. Ifnitrogen balances are considered inaddition to phosphorus, chlorophyll aModels 1or3 can beused; otherwise, chlorophyll a Model 2 (default) isthe most general for application to reservoirs. Secchi Model 1(default) requires an estimate ofnonalgal turbidity for each model segment (see Theory). The interpretation and use oft-statistics (List/Compar procedure) intesting and calibrating the chlorophyll a and Secchi submodels follow the above discussion for nutrients (Step 7). With the completion ofStep 8, the model has been setup and possibly calibrated using pool and tributary data from aparticular year orgrowing season. Step 9involves testing ofthe model based upon anindependent data set derived from adifferent monitoring period. Model options and calibration factors areheld constant, and performance isjudged based upon acomparison ofobserved and predicted nutrient, chlorophyll a, andtransparency profiles. This procedure isespecially recommended insystems with significant year-toyear variations inhydrology, loading, and pool water quality conditions orin cases where extensive calibration isnecessary. Generally, multiyear reservoir studies are necessary inorder to obtain adequate perspectives onwater quality variations driven byvariations inclimate orflow. Aseparate model input file can be created for each studyyear; each fileuses the same segmentation scheme, model options, and calibration coefficients. Successful simulation of year-to-year variations isimportant evidence ofmodel validity. Reiteration of previous modeling steps mayberequired to improve model performance over the range ofmonitored conditions. Step 10involves application ofthe 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 ofphosphorus, nitrogen, and light as factors controlling algal productivity. Results are reviewed to ensure that controlling factors are consistent with the chlorophyll a andtransparency submodels employed. The model isapplied topredict the impacts ofalternative loading scenarios ormanagement strategies inStep 11. Typically, aseparate input fileiscreated for each management strategy andhydrologic condition (e.g., wetyear, average year, dryyear). Effects ofmanagement strategies under different hydrologic conditions can be evaluated bycomparing model predictions. Model output from multiple runs can berouted to diskfiles and subsequently read into a spreadsheet fortabulation, comparison, and display. Insimple cases, multiple loading scenarios can be specified within asingle file (see Scheme 4 inFigure 4.3 or Instructional Cases atthe end ofthis chapter). Sensitivity to critical assumptions made inthe modeling process can be evaluated byrepeating Steps 1-11 using alternative assumptions and comparing
**Chapter 4**  **BATHTUB** 4-49results. Iftie~plication hwkvolved substitid calibration hSteps 6-8, management scenarios should also be evaluated using model runs with the uncalibrated model (allcalibration coefficients setto 1.0). Inmany cases, the relative impacts ofalternative management strategies (expressed aspercentage differences inpredicted mean chlorophyll a, for example) willbe insensitive to whether they are based upon the calibrated orthe uncalibrated model. Error analyses canbe runto quanti~ uncertainty ineach predicted response variable for each scenario andhydrologic condition. Uncertainty isexpressed interms ofthe mean coefficient ofvariation (CV). The error analysis will overpredict this uncertainty incases where the model has been calibrated and tested based upon site-specific conditions. Inallcases, the uncertainty associated with relative predictions (e.g., expressed aspercent change inchlorophyll a resulting from different management strategies) willbe substantially lower than that associated with absolute predictions (expressed inppb). Inapplying the model to predict future conditions, diagnostic variables are checked to ensure that controlling factors are consistent with the chlorophyll a andtransparency submodels. For example, ifaphosphorus-limited chlorophyll a submodel (e.g., 4 or5 inTable 4.2) isapplied to existing conditions inStep 8, model predictions willbe invalid for afuture loading condition, which causes aswitch from phosphorus- to nitrogen-limited conditions. Similarly, ifthe phosphorus sedimentation model does not account for inflow phosphorus availability, predictions offuture conditions involving asignificant 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 rankwater quality conditions and to evaluate controlling factors insegments 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 ofanalysis can be applied inthe absence ofnutrient loading and water balance information. Itisessentially descriptive ordiagnostic in nature and does not provide apredictive basis. Because water-balance and nutrient-balance calculations arenot involved, Steps 4-7 and 11 arenot petiormed.

Scenario C

- Reservoir with loading data only

4-50 BATHTUB can beused to predict water quality conditions inafuture reservoir orinan existing reservoir lacking observed water quality data. Lack of observed water quality data precludes calibration andtesting ofdiffusive transport, nutrient sedimentation, and eutrophication-response models. Ifthe application isto anexisting reservoir, amonitoring program should be
**Chapter 4**  **BATHTUB**implemented to obtain data for calibration andtesting before using the model to evaluate management strategies. Ifthe application isto aproposed reservoir, the accuracy and credibility ofmodel projections would be enhanced byfirst applying itsuccessfidly to an existing reservoir inthe same region and, ifpossible, with similar morphometry andwatershed characteristics. Model predictions for afiture reservoir referto steady-state conditions and do not apply to the initial “reservoir aging” period, during which significant “internal” loadings may occur as aresult ofnutrient releases from inundated soils and vegetation. The reservoir aging period isinherently dynamic and not suited for direct simulation via the steady-state algorithms used inBATHTUB. Approximate estimates ofconditions during the reservoir aging period maybe derived by speci@ing additional internal nutrient sources ofappropriate magnitudes to reflect sediment releases during this period, based upon literature reviews and/or field data. 

### Procedure Outline Following isalistofallBATHTUB procedures. Names are listed onthe left. Indentation reflects Menu level (Lines 1-4). Abriefdescription ofeach procedure isgiven onthe 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 1** **antes 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**  **Observed &**  **Predicted Variables**  **Plot 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 isalisting ofeach data-entry screen inBATHTUB and itsassociated 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 bymoving the cursor to the field andhitting <F8>; this works onlywhen the message ‘<F8>=HELP FIELD’ appears inthe lower right comer ofthe 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**  4-53DATA-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**  4-55HELP 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**  **DEFAULT MEAN** 

**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**  4-57HELP 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 ofeach output format using data from Keystone Reservoir (located onthe Arkansas and Cimarron rivers in Oklahoma). Data from this reservoir are analyzed extensively inthe supporting research document (Walker 1985). Model segmentation for Keystone is illustrated inFigure 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** 4-59Pool and tributary water quality data were derived from measurements made in 1974 and 1975 bytheEPA National Eutrophication Survey (NES) (U.S.’Environmental Protection Agency) (USEPA 1975). The Keystone pool was sampled bytheNES atnine stations fourtimes between April and October 1975. The role oflightlimitation inKeystone has been previously discussed (Walker 1985). Because oftherelatively low summer hydraulic residence time ofthe reservoir (0.08 year), seasonal nutrient turnover ratios arehigh, and water and mass balance calculations are based onMay through September conditions during the pool monitoring year. Point sources include three sets of municipal sewage effluents which have been aggregated byreservoir segment. Since theNES estimated nutrient loadings but not flows forthese ellluents, a flow of 1hm3/yearhas been assumed foreach source (insignificant inrelation to reservoir water balance) and thenutrient concentrations have been adjusted to correspond with thereported loadings. The input data file ‘KEYSTONE.BIN’ file (found onthe distribution diskette and copied to thehard drive during installation) isused 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 insequence, while referring to comments and instructions below, willhelp users to become familiar with program operation and output formats.

4-60 Start the program from theDOS prompt byentering:

**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 toreada BATHTUBd’ata set (selected choices are underlined below butare highlighted on thescreen). Choices aremade inone oftwo ways: (a) bypressing thefirst letter ofthedesired command, orfi)by using the cursor keys. Aone-line description ofthe 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**  4-61The next screen asks the user tospeclfi theDOSpath to the directory where BATHTUB data sets are stored. Ifahta sets are kept in the same directory as theBATHTUB program (asisrecommended 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) toclearthecurrent 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%elower halfof the screen summarizes thedimensions and selected model optionsfor the current case. Input values can be listed byselecting 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 LOUEiv**  **4 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’helisting ofinput values can be used tocheck and70rdocument the input casejile. l’helisting should be checked against original data sources to identlfi any dda-entry errors. l%elisting iscopied toa temporary diskfile and ajile viewing utility is loaded. Function keys are identljied atthe bottom ofthe screen. The user can scrollforward orbackward through the output listing by using the keypad arrows. Xhe ~130meL’key moves to the top ofthejle. The c~33nd ~,key moves to the bottom ofthe$le. A Help screen related to the current output listing can be viewed bypressing <~1’1~~. i’%elisting can be saved inapermanent disk$le bypressing <3?8:’>.Pressing <l%sc>returns to the main menu. A short summary ofsegment 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**

7hisprocedure summarizes input morphometric datafor each segment. Average segment width iscalculated as the ratio ofsurface area tosegment length. Total surface area, volume, and mean depth are also listed. Themodel can be executed with afill error analysis byselecting 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** 4-65Ifinput &ta errors are encountered or themass-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

‘ModelEkecuted’ message appears in the lower right-hand corner ofthe screen. l%is indicates that the execution was successji.dand theList and Plot routines can be accessed to review results. Output screens and commentsfor 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 exchangeflows. A40delsegmentation shouldbe designed so that estimated dispersion exceeds numeric dispersion in each segment. Numeric dispersion rates can be reduced bydecreasing segment lengths. The exchange rate represents thedlyusive exchange-between each segment (SEG) and itsdownstream 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**  **COE F**  **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 beforeproceedingto 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**  4-67fiture data collection efiorts bykeying on the major sources oferror (e.g., by increasing samplingfrequencies). 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 inselecting an appropriate averagingperiodfor water and mass balance calculations. In the case oftheKeystone phosphorus balance, the turnover ratio is 13.4, which means thatphosphorus stored in thewater column was displaced approximately 13.4 times during the 5-month balance period based upon observedpool phosphorus concentrations. 7his isa relativelyfavorable ratio for mass balance modeling because itindicates thatpool nutrient levels are not likely to reflect loading conditions experienced prior to the mass balance period. As discussed above, a turnover ratio of2 ormore isdesirablefor modeling purposes.
**Procedure: List**  **/ Balances**  **/ Detai**  **led**

**SEGMENT BALANCE**  **BASED UPON**  **EST I**  **MATED CONCENTRATE** **IONS 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**  **M FL~**  **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** ***EvApmAT 10N **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. Thesummary terms inch.de internal transfers (attributed toadvection andexchange with neighboring segments) aswell as external inputs,
**Chapter4 BATHTUB** outflows, and retention. i%eadvective outflow termfor 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 ofthewater andmass balances bysegment. S’ummary terms arepresentedin tabIesthatdepict 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**  4-69retention, and net exchange with adjacent (upstream and downstream) segments. In the mass balances, the netexchange term is formulated as an input (i.e., itwill bepositive ornegative), depending upon whether dispersion causes net transport ofmass into oroutofthesegment, respectively. Note that the advective outjlowfiom each segment iscalculatedfiom the water balance. Ifthe computed advective outflowfiom any segment (except those segments that discharge out ofthesystem) isless than zero, the water and balances are satis+ed by backjlowfiom downstream segments (i.e., the direction ofthe advectiveflow at the corresponding segment interface is reversed). 7his might occur,for example,for asegment inwhich the evaporation rate exceeds the sum ofexternal in.ow andprecipitation. The program handles this condition by reversing the~ow direction. Solutions towaterbalance and mass-balance equations cannot be obtained lj’thenetwater injlowfor the entire reservoir (sum ofinjlows +precipitation

- evaporation) is negative. In the last (near-dam) segment, theadvective outjlow term ofthe water balance table represents the cumulative water balance errorfthe reservoir discharge rate isspecljled. In theKeystone example, a residual water balance error of-O.2 hm3/year is indicated. Since this issmall relative to the gauged outjlow (10,556 hm3/year), the impact on thewater and nutrient balance calculations isnegligible. l%iswater balance has been achieved byadjusting 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 isnotsignl~cantly dl~ferentfiom thepredictedmean at the 95-percentcon@ence level, given theprecision in the observed mean value, which reflects variabilityin themonitoring data andsamplingprogram design. b. Zhesecondtest(supplementarytothe third) compares theerrorwith thestandarderror estimatedfiom themodeldevelopment 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**  4-71values. In calculating the CVsfor area-weighted mean observed conditions, theprogram attributes themajor source oferror to temporal variance and assumes that the errors are correlated across stations. Note that comparisons ofarea-weighted mean conditions are tobeaccurate only ifsampling stations are distributed throughout the reservoir. Ifdata sets do notprovide 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 mthegeometricmeanandgeometric standarddeviation ofareaweightedmean observed values in the modeldevelopmen tdata setassuming a log-normal distribution. Ehevariable listinchdesthebasicnet workvariables plus nine composite variables thatare 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 asFigure 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**  Userselects variables tobe includedfrom a listofallpredicted 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-v **MG/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 thesensitivityanalysis 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 innear-dam segments, as comparedwith upper-pool segments. Plotprocedures compare observedandpredicted concentrationsin each modelsegment. ZhePlotiSomeprocedureis 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‘. Fordemonstrationpurposes, 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%efirstformat isselectedfor demonstration. i%iscompares observed and predicted concentrations bymodel segment. Solid symbols are mean values.

Vertical lines are mean &1standard error. Plots thatfollow are in the same order as theselected variable list. TOTAL P N(WI3 HEAN+/- 1 SThNl)f’iRD ERROR
**40[**

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**Chapter 4**  **BATHTUB** 

### 4-77CHL-A **H(YN3**

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Select Quit toend the session.
**BATHTUB**
**- VERSION**  **5.4 List**  **Plot Utilities**  **Help w** 



### 4-78 **Chapter4 BATHTUB** Input@les should besaved before quitting. Type ‘Y’or ‘y’to endsession. Ty~ any other key to return tomenu. 

### Instructional Cases

**The** following hypothetical cases illustrate BATHTUB applications to predict among-reservoir orwithin-reservoir (spatial ortemporal) variations in trophic-state indicators. Each case isdescribed by (a) abasic data sheet showing the segmentation scheme and essential input data and (b) alisting 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 ofreservoirs, spatially averaged
These simple cases can beused fortraining purposes or astemplates for creatingreal applications. An input filefor each case is supplied with the program. The following procedure issuggested:
a. b.
c. d.
e. f. g. Select application ofinterest from listings below. Review basic data sheet. Review listing ofBATHTUB 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 ofinterest.

**Chapter 4**  **BATHTUB** 

### 4-79Basic 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&C**  **A 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 1980CONDITIONS 

### Bc 

# 1 A 1985CONDITIONS
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 km** 

2 -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**  4-87liLU6AL 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 oftotal nitrogen inlakes and reservoirs.” Restoration oflakes and inland waters; Proceedings ofan international symposium on inland waters and lake restoration. Portkmd, Maine, U.S. Environmental Protection Agency, OffIceofWater Regulations and Standards, EPA-440/5-8 1-010, Washington, DC, 320-324. Beale, E. M. L. (1962). “Some uses ofcomputers inoperational research,” Industrielle Organization31, 51-52. Benjamin, J. R., and Cornell, C. A. (1970). Probability, statistics, and u!ecisionfor civil engineers. McGraw-Hill, New York. Bodo, B., and Umy, T. B. (1983). “Sampling strategies for mass-discharge estimation,” Journal oftheEngineering Division, American Society of Civil Engineers 198(4), 812-829.

. (1984). “Errata: Sampling strategies for mass-discharge estimation,” Journal oftheEnvironmental 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 oftotal phosphorus concentrations, chlorophyll-~ and Secchi depths innatural and artificial hikes,” Canadian Journalfor Fisheries andAquatic ,$’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 approachesfor 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 handbookforpilot watershed studies. International Reference Group on Great Lakes Pollution forLand Use Activities, Windsor, Ontario, Canada. Jones, J. R., and Bachman, R. W. (1976), “Prediction ofphosphorus and chlorophyll levels inlakes,”J. WaterPollution Control Federation 48, 2176-2182. Mosteller, F., and Tukey, J. W. (1978). Data analysis and regression -A second course instatistics. 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 oftheEnvironmental Engineering Division, American Society of CivilEngineers 106(EE3),591 -608. Vollenweider, R. A. (1976). “Advances indefting critical loading levels for phosphorus inlake eutrophication,” A4em.Ist. Ital. Idrobiol 33,53-83. Walker, W. W. (1980). “Analysis ofwater quality variations inreservoirs: Implications for monitoring and modelling efforts.” Proceedings ofthe symposium on surface water impoundments. Minneapolis, MN., H. G. Stefan, cd., American Society ofCivilEngineers, New York, 472-481.

. (198 1). “Empirical methods forpredicting 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 forpredicting 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 forthe Lake Morey314 diagnostic study,” prepared forVermont Agency ofEnvironmental Conservation, Department ofWater Resources, Lakes Program, Montpelier, VT.

. (1984). “Empirical prediction ofchlorophyll inreservoirs,” Lake and reservoir management. U.S. Environmental Protection Agency, Ofice ofWater 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 forpredicting 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 oftechniques 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 oftwo Colorado reservoirs.” Proceedings ofthe symposium on surface water impoundments. Minneapolis, MN, H. G. Stefan, ed., American Society ofCivilEngineers, 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: Anationwide study,” EPA-600/3 -77-l 05, Corvallis Environmental Research Laboratory, U.S,Environmental Protection Agency. Organization forEconomic Cooperation and Development. (1982). Eutrophication ofwaters -Monitoring, assessment, and control. Synthesis Report ofthe OECD Cooperative Programme onEutrophication, 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 ofthe WaterPollution 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: Amanual and compilation ofexport coefhcients,” U.S. Environmental Protection Agency, Clean Lakes Section. Reckhow, K. H., and Chapr~ S. C. (1983). Engineering approachesfor 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 ofphosphorus inputs to lakes,”Journal ofEnvironmental Quality 11(4), 555-562.
**Bibliography B-1** StaufEer,R E. (1981). “Sampling strategies for estimating the magnitude and importance ofinternal phosphorus supplies inlakes,” 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 oflakes 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 inlimnology,” Schweitz. Z. Hydrol. 37, 53-84. Walker, W. W. (1982a). “An empirical analysis ofphosphorus, 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,” WaterResources Bulletin 18(1), 53-61. Winter, T. C. (1981). “Uncertainties inestimating the water balance oflakes,” WaterResearch Bulletin 17, 82-115.

B-2 **Bibliography**

# Appendix A Installation

The programs require anIBM-compatible PC with atleast a286 processor, amath co-processor, and 3 megabytes ofdisk storage. Atleast 530 kilobytes ofconventional memory must be available forthe programs to run. Installation isinitiated byinserting the distribution diskette inan appropriate floppy drive and entering the following command: >inst~l C: Note that drives other than c: maybe substituted and that aparent directo~ can be established (e.g., c:lmodels). The installation program creates destination directories for each set ofprogram files and installs files to appropriate directories. For instance, after issuing the command install c:, the following occurs: FLUX files are installed indirectory c:\flux PROFILE files areinstalled indirectory c:\profile BATHTUB files are installed indirectory c:\bathtub Assistance inthe acquisition and implementation ofthe software is available bycontacting: 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 onthe 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.