U.S. ENVIRONMENTAL PROTECTION AGENCY
Annapolis Field Office
Annapolis Science Center
Annapolis, Maryland 21401
TECHNICAL PAPERS
Volume 20
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Table of Contents
Volume 20
A Digital Technique for Calculating and Plotting
Dissolved Oxygen Deficits
A River-Mile Indexing System for Computer Application
in Storing and Retrieving Data (unavailable)
Oxygen Relationships in Streams, Methodology to be
Applied when Determining the Capacity of a Stream
to Assimilate Organic Wastes - October 1964
Estimating Diffusion Characteristics of Tidal Waters
May 1965
Use of Rhodamine B Dye as a Tracer in Streams of the
Susquehanna River Basin - April 1965
6 An In-Situ Benthic Respirometer - December 1965
7 A Study of Tidal Dispersion in the Potomac River -
February 1966
8 A Mathematical Model for the Potomac River - What it
has done and what it can do - December 1966
A Discussion and Tabulation of Diffusion Coefficients
for Tidal Waters Computed as a Function of Velocity -
February 1967
10 Evaluation of Coliform Contribution by Pleasure Boats
July 1966
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PUBLICATIONS
U.S. ENVIRONMENTAL PROTECTION AGENCY
REGION III
ANNAPOLIS FIELD OFFICE*
VOLUME 1
Technical Reports
5 A Technical Assessment of Current Water Quality
Conditions and Factors Affecting Water Quality in
the Upper Potomac Estuary
6 Sanitary Bacteriology of the Upper Potomac Estuary
7 The Potomac Estuary Mathematical Model
9 Nutrients in the Potomac River Basin
11 Optimal Release Sequences for Water Quality Control
in Multiple Reservoir Systems
VOLUME 2
Technical Reports
13 Mine Drainage in the North Branch Potomac River Basin
15 Nutrients in the Upper Potomac River Basin
17 Upper Potomac River Basin Water Quality Assessment
VOLUME 3
Technical Reports
19 Potomac-Piscataway Dye Release and Wastewater
Assimilation Studies
21 LNEPLT
23 XYPLOT
25 PLOT3D
* Formerly CB-SRBP, U.S. Department of Health, Education,
and Welfare; CFS-FWPCA, and CTSL-FWQA, Middle Atlantic
Region, U.S. Department of the Interior
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VOLUME 3 (continued)
Technical Reports
27 Water Quality and Wastewater Loadings - Upper Potomac
Estuary during 1969
VOLUME 4
Technical Reports
29 Step Backward Regression
31 Relative Contributions of Nutrients to the Potomac
River Basin from Various Sources
33 Mathematical Model Studies of Water Quality in the
Potomac Estuary
35 Water Resource - Water Supply Study of the Potomac
Estuary
VOLUME 5
Technical Reports
37 Nutrient Transport and Dissolved Oxygen Budget
Studies in the Potomac Estuary
39 Preliminary Analyses of the Wastewater and Assimilation
Capacities of the Anacostia Tidal River System
41 Current Water Quality Conditions and Investigations
in the Upper Potomac River Tidal System
43 Physical Data of the Potomac River Tidal System
Including Mathematical Model Segmentation
45 Nutrient Management in the Potomac Estuary
VOLUME 6
Technical Reports
47 Chesapeake Bay Nutrient Input Study
49 Heavy Metals Analyses of Bottom Sediment in the
Potomac River Estuary
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VOLUME 6 (continued)
Technical Reports
51 A System of Mathematical Models for Water Quality
Management
52 Numerical Method for Groundwater Hydraulics
53 Upper Potomac Estuary Eutrophication Control
Requirements
54 AUT0-QUAL Modelling System
Supplement AUT0-QUAL Modelling System: Modification for
to 54 Non-Point Source Loadings
VOLUME 7
Technical Reports
55 Water Quality Conditions in the Chesapeake Bay System
56 Nutrient Enrichment and Control Requirements in the
Upper Chesapeake Bay
57 The Potomac River Estuary in the Washington
Metropolitan Area - A History of its Water Quality
Problems and their Solution
VOLUME 8
Technical Reports
58 Application of AUT0-QUAL Modelling System to the
Patuxent River Basin
59 Distribution of Metals in Baltimore Harbor Sediments
60 Summary and Conclusions - Nutrient Transport and
Accountability in the Lower Susquehanna River Basin
VOLUME 9
Data Reports
Water Quality Survey, James River and Selected
Tributaries - October 1969
Water Quality Survey in the North Branch Potomac River
between Cumberland and Luke, Maryland - August 1967
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VOLUME 9 (continued)
Data Reports
Investigation of Water Quality in Chesapeake Bay and
Tributaries at Aberdeen Proving Ground, Department
of the Army, Aberdeen, Maryland - October-December 1967
Biological Survey of the Upper Potomac River and
Selected Tributaries - 1966-1968
Water Quality Survey of the Eastern Shore Chesapeake
Bay, Wicomico River, Pocomoke River, Nanticoke River,
Marshall Creek, Bunting Branch, and Chincoteague Bay -
Summer 1967
Head of Bay Study - Water Quality Survey of Northeast
River, Elk River, C & D Canal, Bohemia River, Sassafras
River and Upper Chesapeake Bay - Summer 1968 - Head ot
Bay Tributaries
Water Quality Survey of the Potomac Estuary - 1967
Water Quality Survey of the Potomac Estuary - 1968
Wastewater Treatment Plant Nutrient Survey - 1966-1967
Cooperative Bacteriological Study - Upper Chesapeake Bay
Dredging Spoil Disposal - Cruise Report Mo. 11
VOLUME 10
Data Reports
9 Water Quality Survey of the Potomac Estuary - 1965-1966
10 Water Quality Survey of the Annapolis Metro Area - 1967
11 Nutrient Data on Sediment Samples of the Potomac Estuary
1966-1968
12 1969 Head of the Bay Tributaries
13 Water Quality Survey of the Chesapeake Bay in the
Vicinity of Sandy Point - 1968
14 Water Quality Survey of the Chesapeake Bay in the
Vicinity of Sandy Point - 1969
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VOLUME 10(continued)
Data Reports
15 Water Quality Survey of the Patuxent River - 1967
16 Water Quality Survey of the Patuxent River - 1968
17 Water Quality Survey of the Patuxent River - 1969
18 Water Quality of the Potomac Estuary Transects,
Intensive and Southeast Water Laboratory Cooperative
Study - 1969
19 Water Quality Survey of the Potomac Estuary Phosphate
Tracer Study - 1969
VOLUME 11
Data Reports
20 Water Quality of the Potomac Estuary Transport Study
1969-1970
21 Water Quality Survey of the Piscataway Creek Watershed
1968-1970
22 Water Quality Survey of the Chesapeake Bay in the
Vicinity of Sandy Point - 1970
23 Water Quality Survey of the Head of the Chesapeake Bay
Maryland Tributaries - 1970-1971
24 Water Quality Survey of the Upper Chesapeake Bay
1969-1971
25 Water Quality of the Potomac Estuary Consolidated
Survey - 1970
26 Water Quality of the Potomac Estuary Dissolved Oxygen
Budget Studies - 1970
27 Potomac Estuary Wastewater Treatment Plants Survey
1970
28 Water Quality Survey of the Potomac Estuary Embayments
and Transects - 1970
29 Water Quality of the Upper Potomac Estuary Enforcement
Survey - 1970
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30
31
32
33
34
Appendix
to 1
Appendix
to 2
3
4
VOLUME 11 (continued)
Data Reports
Water Quality of the Potomac Estuary - Gilbert Swamp
and Allen's Fresh and Gunston Cove - 1970
Survey Results of the Chesapeake Bay Input Study -
1969-1970
Upper Chesapeake Bay Water Quality Studies - Bush River,
Spesutie Narrows and Swan Creek, C & D Canal, Chester
River, Severn River, Gunpowder, Middle and Bird Rivers -
1968-1971
Special Water Quality Surveys of the Potomac River Basin
Anacostia Estuary, Wicomico.River, St. Clement and
Breton Bays, Occoquan Bay - 1970-1971
Water Quality Survey of the Patuxent River - 1970
VOLUME 12
Working Documents
Biological Survey of the Susquehanna River and its
Tributaries between Danville, Pennsylvania and
Conowingo, Maryland
Tabulation of Bottom Organisms Observed at Sampling
Stations during the Biological Survey between Danville,
Pennsylvania and Conowingo, Maryland - November 1966
Biological Survey of the Susquehanna River and its
Tributaries between Cooperstown, New York and
Northumberland, Pennsylvnaia - January 1967
Tabulation of Bottom Organisms Observed at Sampling
Stations during the Biological Survey between Cooperstown,
New York and Northumberland, Pennsylvania - November 1966
VOLUME 13
Working Documents
Water Quality and Pollution Control Study, Mine Drainage
Chesapeake Bay-Delaware River Basins - July 1967
Biological Survey of Rock Creek (from Rockville, Maryland
to the Potomac River) October 1966
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VOLUME 13 (continued)
Working Documents
5 Summary of Water Quality and Waste Outfalls, Rock Creek
in Montgomery County, Maryland and the District of
Columbia - December 1966
6 Water Pollution Survey - Back River 1965 - February 1967
7 Efficiency Study of the District of Columbia Water
Pollution Control Plant - February 1967
VOLUME 14
Working Documents
8 Water Quality and Pollution Control Study - Susquehanna
River Basin from Northumberland to West Pittson
(Including the Lackawanna River Basin) March 1967
9 Water Quality and Pollution Control Study, Juniata
River Basin - March 1967
10 Water Quality and Pollution Control Study, Rappahannock
River Basin - March 1967
11 Water Quality and Pollution Control Study, Susquehanna
River Basin from Lake Otsego, New York, to Lake Lackawanna
River Confluence, Pennsylvania - April 1967
VOLUME 15
Working Documents
12 Water Quality and Pollution Control Study, York River
Basin - April 1967
13 Water Quality and Pollution Control Study, West Branch,
Susquehanna River Basin - April 1967
14 Water Quality and Pollution Control Study, James River
Basin - June 1967 .
15 Water Quality and Pollution Control Study, Patuxent River
Basin - May 1967
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VOLUME 16
Working Documents
16 Water Quality and Pollution Control Study, Susquehanna
River Basin from Northumberland, Pennsylvania, to
Havre de Grace, Maryland - July 1967
17 Water Quality and Pollution Control Study, Potomac
River Basin - June 1967
18 Immediate Water Pollution Control Needs, Central Western
Shore of Chesapeake Bay Area (Magothy, Severn, South, and
West River Drainage Areas) July 1967
19 Immediate Water Pollution Control Needs, Northwest
Chesapeake Bay Area (Patapsco to Susquehanna Drainage
Basins in Maryland) August 1967
20 Immediate Water Pollution Control Needs - The Eastern
Shore of Delaware, Maryland and Virginia - September 1967
VOLUME 17
Working Documents
21 Biological Surveys of the Upper James River Basin
Covington, Clifton Forge, Big Island, Lynchburg, and
Piney River Areas - January 1968
22 Biological Survey of Antietam Creek and some of its
Tributaries from Waynesboro, Pennsylvania to Antietam,
Maryland - Potomac River Basin - February 1968
23 Biological Survey of the Monocacy River and Tributaries
from Gettysburg, Pennsylvania, to Maryland Rt. 28 Bridge
Potomac River Basin - January 1968
24 Water Quality Survey of Chesapeake Bay in the Vicinity of
Annapolis, Maryland - Summer 1967
25 Mine Drainage Pollution of the North Branch of Potomac
River - Interim Report - August 1968
26 Water Quality Survey in the Shenandoah River of the
Potomac River Basin - June 1967
27 Water Quality Survey in the James and Maury Rivers
Glasgow, Virginia - September 1967
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VOLUME 17 (continued)
Working Documents
28 Selected Biological Surveys in the James River Basin,
Gillie Creek in the Richmond Area, Appomattox River
in the Petersburg Area, Bailey Creek from Fort Lee
to Hopewell - April 1968
VOLUME 18
Working Documents
29 Biological Survey of the Upper and Middle Patuxent
River and some of its Tributaries - from Maryland
Route 97 Bridge near Roxbury Mills to the Maryland
Route 4 Bridge near Wayson's Corner, Maryland -
Chesapeake Drainage Basin - June 1968
30 Rock Creek Watershed - A Water Quality Study Report
March 1969
31 The Patuxent River - Water Quality Management -
Technical Evaluation - September 1969
VOLUME 19
Working Documents
Tabulation, Community and Source Facility Water Data
Maryland Portion, Chesapeake Drainage Area - October 1964
Waste Disposal Practices at Federal Installations
Patuxent River Basin - October 1964
Waste Disposal Practices at Federal Installations
Potomac River Basin below Washington, D.C.- November 1964
Waste Disposal Practices at Federal Installations
Chesapeake Bay Area of Maryland Excluding Potomac
and Patuxent River Basins - January 1965
The Potomac Estuary - Statistics and Projections -
February 1968
Patuxent River - Cross Sections and Mass Travel
Velocities - July 1968
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VOLUME 19 (continued)
Working Documents
Wastewater Inventory - Potomac River Basin -
December 1968
Wastewater Inventory - Upper Potomac River Basin -
October 1968
VOLUME 20
Technical Papers-
1 A Digital Technique for Calculating and Plotting
Dissolved Oxygen Deficits
2 A River-Mile Indexing System for Computer Application
in Storing and Retrieving Data (unavailable)
3 Oxygen Relationships in Streams, Methodology to be
Applied when Determining the Capacity of a Stream to
Assimilate Organic Wastes - October 1964
4 Estimating Diffusion Characteristics of Tidal Waters -
May 1965
5 Use of Rhodamine B Dye as a Tracer in Streams of the
Susquehanna River Basin - April 1965
6 An In-Situ Benthic Respirometer - December 1965
7 A Study of Tidal Dispersion in the Potomac River
February 1966
8 A Mathematical Model for the Potomac River - what it
has done and what it can do - December 1966
9 A Discussion and Tabulation of Diffusion Coefficients
for Tidal Waters Computed as a Function of Velocity
February 1967
10 Evaluation of Coliform Contribution by Pleasure Boats
July 1966
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VOLUME 21
Technical Papers
11 A Steady State Segmented Estuary Model
12 Simulation of Chloride Concentrations in the
Potomac Estuary - March 1968
13 Optimal Release Sequences for Water Quality
Control in Multiple-Reservoir Systems - 1968
VOLUME 22
Technical Papers
Summary Report - Pollution of Back River - January 1964
Summary of Water Quality - Potomac River Basin in
Maryland - October 1965
The Role of Mathematical Models in the Potomac River
Basin Water Quality Management Program - December 1967
Use of Mathematical Models as Aids to Decision Making
in Water Quality Control - February 1968
Piscataway Creek Watershed - A Water Quality Study
Report - August 1968
VOLUME 23
Ocean Dumping Surveys
Environmental Survey of an Interim Ocean Dumpsite,
Middle Atlantic Bight - September 1973
Environmental Survey of Two Interim Dumpsites,
Middle Atlantic Bight - January 1974
Environmental Survey of Two Interim Dumpsites
Middle Atlantic Bight - Supplemental Report -
October 1974
Effects of Ocean Disposal Activities on Mid-
continental Shelf Environment off Delaware
and Maryland - January 1975
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VOLUME 24
1976 Annual
Technical
Report 61
Technical
Report 62
Current Nutrient Assessment - Upper Potomac Estuary
Current Assessment Paper No. 1
Evaluation of Western Branch Wastewater Treatment
Plant Expansion - Phases I and II
Situation Report - Potomac River
Sediment Studies in Back River Estuary, Baltimore,
Maryland
Distribution of Metals in Elizabeth River Sediments
A Water Quality Modelling Study of the Delaware
Estuary
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TABLE OF CONTENTS
Page
List of Figures
I. Introduction 1
II. Oxygen Sag Equation 1
III. Main Program and Subroutines . 2
IV. Preparation of Data 5
V. Data Output . . 8
VI. Cost Data . 9
VII. Conclusions ...... 10
VIII. Acknowledgments 10
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LIST OF FIGURES
Figure 1 Simplified flow chart showing operations
performed by the program
Figure 2 Main program for the oxygen sag equation
Figure 3 Subroutine MAP - used by the main program
Figure 4 Subroutine WRTTTEM - used by subroutine MAP
Figure 5 Data package format for Set No. 1
Figure 6 Data output and graph for Set No. 1
Figure 7 Data output and graph for Set No. 2
Figure 8 Data output and graph for Set No. 3
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I .
A package program for vise on the IBM 7090 computer is
presented for obtaining a numerical solution of the classical
Street er-Phelps oxygen sag equation. Oxygen deficits are com-
puted for each desired time and plotted as a function of time.
In general, no knowledge on the reader's part is assumed
with regard to computers or the program presented. Certain
terminology having general use will be discussed in order to
clarify the presentation; however, the step-by-step instructions
should enable engineers and scientists to obtain correct results
without a thorough knowledge of computer terminology.
II. Oxygen Sag Equation
In 1925 Streeter-Phelps^ ' formulated the oxygen sag
equation which describes the changes in dissolved oxygen content
of a stream following the introduction of an oxygen demanding
organic waste. The mathematical formulation describes the net
rate of change in the oxygen deficit (D) at any time (t) and is
expressed as a first order differential equation:
= %L - K2D Equation (l)
dt
where K,L represents the increase in the deficit at a rate which
is assumed to be proportional to the oxygen demand of the waste.
The second term of the equation, namely -^D, represents the
rate of reaeration expressed in terms of the oxygen saturation
deficit .
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On integrating Equation (l) the dissolved oxygen content
of the water may be obtained as the deficit below saturation at
any time. The integrated form is then:
Jf T K t K +
D = !_S (e~ 1 - e" 2 ) + Dae "*" Equation (2)
K2 ~ Kl
where: Da = Initial dissolved oxygen saturation deficit (mg/l)
D = Oxygen deficit, after time (t) (mg/l)
La = Ultimate biochemical oxygen demand (mg/l)
KI = Empirical deoxygenation rate constant
Kฃ = Empirical reaeration rate constant
t = Elapsed time in days
e = Base of naperian or natural logarithms and is equal
to 2.71828
The numerical solution to the above form requires that
knowledge of the reaeration and deoxygenation rate constants
together with the ultimate biochemical oxygen demand and initial
oxygen deficit be known. Once these values are in hand, we may
solve for the oxygen deficits at any desired time.
o Main Program and Subroutines
In order to visualize the flow of data and functions of
the program, Figure 1 is presented showing a simplified flow
chart of the various operations performed The input informa-
tion is seen to consist, of K^, Kฃ, La, Da, and T-j_ values where
i = 1 to N. The program computes the corresponding D^ value
jSSfc
or each tฑ value for a given K^, Kg, La, and D&. The computed
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START
i
READ IN ! K|,K2
L,Q,Da and Tj
values i = ! to N
COMPUTES :
(e~kiti-e"k2tซ)-l-Da
i = I to N
i
PRINTS
Dj,t; values
i s I to N
GRAPHS
DJ as a function of t;
i= I to N
SIMPLIFIED FLOW CHART SHOWING OPERATIONS
PERFORMED BY THE PROGRAM
FIGURE I
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tj[ and DJ> values for each set of input data are printed and
graphed. After the first set of data has been computed, control
returns to the beginning of the program and new values for %,
K2, La, Da, and t^'s are read in. This process continues until
the last set of data has been computed and printed.
The program presented here has been written in what is
termed FORTRAN. Every type of computer is designed to respond
to a special code, called a "machine language." The instructions
telling the computer what steps to perform to solve a problem
must be given to the computer in its own language. The FORTRAN
program makes it unnecessary for the programer to learn the more
complicated machine language. The word FORTRAN, derived from
formula translation, is a method of programing using language
similar to familiar usage. The FORTRAN program is then assembled
by the computer in proper form for machine interpretation.
The main program for calculating dissolved oxygen deficits
and plotting the deficits as a function of time is shown in Figure
2.. In all, there are eighteen FORTRAN statements, exclusive of
the XEQ, LABEL, and END card. Each statement is punched on a
separate IBM card. At times it may be necessary to change three
cards in the main program depending on the data input, plus the
input and output tape unit numbers. In order to obtain an under-
standing of when these changes should be made, a sample case
will be discussed here. First, let us consider Card No. 3; the
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FORTRAN statement appears as DIMENSION TIME (25), FIVE (25).
This instructs the computer to assign 25 storage locations for
each variable TIME and FIVE, The FIVE written here is actual
storage assigned for the D^ values. If more than 25 TIME values
are to be used in calculating the dissolved oxygen deficits, it
will be necessary to change both TIME (25) and FIVE (25) to read
the number of TIME values desired. Let N represent the number
of TIME values; then the statement in general form may be written
DIMENSION TIME (N), FIVE (N). If the number N of desired TIME
values is less than or equal to 25, no change to the statement
is necessary.
Card No. 4 and Card No. 5 in the main program specify
the input and output tape unit numbers used by the computing
center. In preparing these cards, it is necessary to request
the input and output tape unit numbers from the center where
the program will be run. In general, the computing center will
usually obtain the tape unit numbers; however, it is advisable
to instruct them of the input-output numbers.
Card No, 4> appearing with the statement IT = 5, specifies
that the input data tape unit number is 5. Similarly, KT = 6
on Card No. 5 specifies that the output tape unit number is 6.
Figure "ฑ shows one of the three subroutines used by the
main program. Again, each statement appearing is punched on a
separate IBM card. This subroutine is designed to aid in the
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plotting of dissolved oxygen deficits as a function of time and
is called into use by the main, program by the statement appear-
ing on Card No0 19= Figure 4 is the second subroutine that is
used by the first to write out the computed data. The other sub-
routine is not shown here because of its existence on tape or
card deck at the computing center. This type of subroutine is
termed a library routine and is designed to perform calculations
on the exponential function,,
In punching the main program and subroutine on IBM cards,
it is advisable to punch the main program on cards of a different
color than the subroutine cards. This practice insures rapid
identification when changes are to be made to the main program.
Prior to actually running the program, a request to the keypunch
operator for verification of the information punched on the cards
is desirable.
IV Preparation of Data
A sample case is shown in Table I of the input data.
Here it is desired to compute and plot the dissolved oxygen
deficits for three sets of data, each with a different initial
oxygen deficit (Da) and ultimate biochemical oxygen demand (La).
It is assumed that % = 0,12, and K/> - 0,25 for each set. This
is done here for reasons of simplicity; actually, K]_ and Kg nay
take on different values for each set of data0 Again, for sim-
plicity, the desired deficits here are computed for each day
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from 1 to 20 days for each set,, The time values may be given in
tenths or hundredths of a day, if desired; however, the interval
between values should remain constant In addition, for all
practical purposes the program is designed to accept an unlimited
and variable length number of time values from set to set. Refer
to Figure ฃ for the data setup.
Table I
Da
Set Initial Ultimate
Number Oxygen Deficit BOD
1 0.00 5.00
2 1.00 10.00
3 2.00 15.00
To begin, the first data card will contain:
! Number of time values N (In this case N = 20 for
each set)
20 Set Number (Set No. 1)
3. Values for K]_ (deoxygenation rate constant)
4. Value for K2 (reaeration rate constant)
5. Value of initial oxygen deficit (Da)
6. Value of ultimate biochemical oxygen demand (La)
The second card will contain ten values of the time,
starting with 1,00 and ending with 10.000 The third data card
will start with 11.00 and end with 20.00. This completes the
first set of data that the computer will work with,, The second
set of data will contain the six pieces of information contained
on the first data card, only using the values that pertain to
Set No, 2. Again, since our sample case specifies the same time
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-------
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values as the first set, the second and third cards of the second
set will be identical to the second and third cards of the first
set. Similarly, Set No. 3 will be punched in the order specified
above. The number of sets is unlimited, since each set is read
into memory prior to the calculations, and the second set of
data will not be read in until the completed plot of the calculat-
ed information from the first set is finished. After the last
set of data is worked on, the program halts.
In punching the data, the following format must be
rigidly adhered to:
1. The number of time values N should be punched from
right to left, beginning in Card Column 4; i.e., if
nine values of the time are to be used, a 9 punch
should appear in Column 4. If N = 20, as in our case
here, the 0 appears in Column 4, and the 2 appears
in Column 3.
2. The set number is to be punched in Column 10. Again,
if the set number exceeds 9, the last digit appears
in Column 10. Columns 5, 6, and 7 should contain
the word SET.
3. The deoxygenation rate constant K^ is punched in
Columns 19 and 20, with the decimal punch appearing
in Column 18. The decimal point must always appear
in Column 18, whether the number is an integer or
decimal.
4. The reaeration rate constant K2 is punched in Columns
29 and 30, with the decimal point punched in Column
28. Again, the same holds regarding the decimal
point punch as above,
5. Initial oxygen deficit is punched with the integer
value in Column 3V, decimal point in Column 38, and
tenths and hundredths in Columns 39 and 40, respec-
tively.
-------
-------
8
6,, The ultimate biochemical oxygen demand is punched
in Columns 46 through 50, with decimal punch in
Column 4#ป
The time values begin on the second data card of each
set, with the first appearing in Columns 1 through 7. The decimal
point punch appears in Column 5, Decimal points may be located
on each data card beginning with the second card by adding seven
columns successively; i.e., decimal point for the second time
value would be punched in Column 12, the third in Column 19,
etc., until the tenth decimal point appears in Column 68.
V. Data Output
Figures 6, 7_, and 8 show the output for our sample case
using three sets of input data. First, the run identification
number indicates the output data which follows is for a specific
set number. The input values for time are printed, together
with the computed oxygen deficits corresponding to a particular
time value. The printed data for each set is then plotted directly.
A graph of the oxygen sag appears with the time values
on the horizontal ordinate and oxygen deficit values along the
vertical ordinate. The time values along the horizontal ordinate
appear in floating point form where E 00 represents the exponent
to which 10 is raised. In conversion to decimal form, it is
necessary to multiply the number preceding the E by 10 to the
appropriate power.
-------
-------
I I I I I
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Set number
Number of time voluet
TIME (DAYS)
DATA OUTPUT AND GRAPH FOR SET NUMBER
FIGURE 6
-------
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TIME (DAYS)
DATA OUTPUT AND GRAPH FOR SET NUMBER 2
FIGURE 7
-------
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Set number
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TIME (DAYS)
DATA OUTPUT AND GRAPH FOR SET NUMBER
FIGURE 6
-------
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TIME (DAYS)
DATA OUTPUT AND GRAPH FOR SET NUMBER 2
FIGURE 7
-------
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-------
-------
The vertical ordinate is developed by taking the largest
value of the computed oxygen deficit and letting it be represented
by the alphabetic character K, with the smallest computed oxygen
deficit represented by the character A. The range of values for
the deficit then becomes K-A. The alphabetic characters from A
through K are assigned floating point values, as shown above
each graph.
ฅ1. Cost Data
For actual production runs, using the IBM 7090, the
machine rental rates vary from approximately $360 per hour to
$500 per hour. The rental time required to run the cases shown
in Figures 6_, 7_, and 8 amounted to less than one minute, or
approximately $6 for a minimum machine rental,, Since costs and
methods of charging vary from one computer installation to the
next, it is advisable to determine if a minimum rental charge
exists. In other words, certain installations may require a
minimum of five or ten minute charge regardless of actual machine
time. In this case, it would be advisable to run many sets of
data at one time or search for another installation. Since
computer rates vary, it is usually advisable to shop; however,
this should be justified by the rate differential, as the admin-
istrative time cost involved should not exceed the monies saved
by procuring a lower rate computer charge. In addition, the
procurement of a computer close to the technical personnel using
-------
-------
10
the machine will produce a savings far in excess of the differ-
ential between low and high computer rentals.
VII, Conclusions
The program package has been shown to consist of four
separate card decks, namely:
1. Main Program Deck
20 Subroutine Deck Map
3, Subroutine Deck Writtem
4, Data Input Deck
Assuming the program will be re-run at the same comput-
ing center, no changes need be made in the symbolic decks.
Hence, to conserve computing time, we may replace (l), (2), and
(3) by the corresponding binary decks, (These are machine
language programs which are compiled by the FQRTHAN program
during the first run)
VIII. Acknowledgments
The authors wish to express their appreciation to Mr0
Emanuel Mehr, Consulting Computer Mathematician, New York
University, and to Mr. P, O'Hara, Mathematician, National Bureau
of Standards, Washington, D. C., for their cooperation in develop-
ing this technique.
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-------
PURPOSE
This manual has been compiled to facilitate water resources
studies by providing a readily available source of information
covering methodology and some of the concepts used to estimate
oxygen relationships in a stream. There are many fine technical
writings, journals, and books covering oxygen relationships in
a stream; however, a need has developed to have some of the
methodology and analysis techniques available in a reference
manual. It is hoped this manual can fill the need.
ACKNOWLEDGMENTS
The preparation of this manual was greatly facilitated by the
use of information from the following sources and the assistance
of the following individuals:
T. A. Wastler - Public Health Service
R. L. O'Connell - Public Health Service
J. E. McLean - Public Health Service
Eckenfelder & O'Connor - "Biological Waste and
Treatment," Pergamon Press, 196l
Fair & Geyer - "Water Supply and Waste-Water
Disposal," Wiley & Sons, Inc., 195H
E. C. Tsivoglou - "Natural Self-Purification
of a Polluted Stream," (RATSEC Training
Course Manual), Public Health Service
Phelps - "Stream Sanitation," Wiley & Sons,
Inc.,
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TABLE OF CONTENTS
Page
I. Introduction .................... 1
II. Dissolved Oxygen Relationships in a Stream ..... 1
III. Biochemical Demand (BOD) .............. 3
IV. Deoxygenation Rate Constant (K, or k ) ....... 5
V. Determination of Deoxygenation Rate Constant
VII. Reaeration
8
VI . Determination of Stream K Rate .......... 11
VIII. Reaeration Coefficient - K (base e) or k?
(base 10) ....... ....... 7 ..... 15
IX. Oxygen Sag Equation ................ IT
X. Uses of Oxygen Sag Equation ............ 19
XI. Stream Assimilation Capacity ............ 22
TABLES
I. Expected Values for the Deoxygenation Rate (K, and
k ) for Streams vith Varying Degrees of Pollution 7
II. Typical Values of the Self -Purification Factor
"f" ....................... 19
FIGURES
1. Saturation D. 0. Concentrations vs. Temperature
and Pressure ................... 2k
2. BOD Exertion vs. Time ............... 25
3. Per Cent BOD Removed vs. Time and K (k ) ..... 26
/ rri^prj \
U. Temperature Correction Factor (l.OUT ~ ) for
K (k) and K (k) ............... 2?
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-------
TABLE OF CONTENTS (Continued)
FIGURES Page
5. Daily Difference Determination ........... 28
5a. BOD Exerted vs. Time ............. 28
5b. Log BOD Difference vs. Time .......... 29
6. Oxygen Balance Profile - Stream BOD (pounds) vs.
Stream Miles ................... 30
7. Stream Reaeration Reaction - D. 0. Concentration
vs. Time ..................... 31
8. Temperature Correction Factor (1.017 ) for
lOa. D = 1.0 mg/1
a
32
9. Graph of the Typical Oxygen Sag - D. 0. Concentra-
tion vs . Time .................. 33
10. Graphical Solution of the Oxygen Sag Equation ... 3^
lOb. D =2.0 mg/1 ................ 35
a
lOc. D = 3.0 mg/1 ................ 36
1
11. Log L (mg/l) vs. Temperature ........... 37
ฃL
12. Allowable Stream BOD Loading (pounds) vs.
Temperature and Flow ............... 38
EXAMPLES
I. Daily Difference Method .............. 8
II. Graphical Solution of the Assimilative Capacity
Problem by Method 2a ............... 20
III. Use of the Graphical Method to Determine Minimum
D. 0. Concentrations Following the Introduction
of a Waste Into a Stream ............. 20
IV. A Procedure for Developing Assimilative Capacity
Curves ...................... 22
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-------
I, Introduction
The availability of water of suitable quality has determined the
location of most past and present civilizations. Therefore, it
must be concluded that future population and economic growth will
rely heavily upon the availability of water.
To insure maximum utilization of water resources, many variables
must be considered, as maximum utilization requires water quality
to be suitable for multi-purpose uses- Multi-purpose uses include
water supply, recreation, support of fish and aquatic life, plus
waste assimilation and transport. To maintain water quality suit-
able for these beneficial uses requires development of specific
water quality objectives; and these objectives or criteria must
be basically concerned with the introduction, elimination, or
control of waste materials in the water.
A principal problem in the analysis or evaluation of water
resources is the coincidence of adverse natural stream conditions
with periods of maximum water use. Normally, summer and early
fall months are the most critical periods for water quality and
quantity, because of high temperatures, low flows, and maximum
water use. Prior to the formulation of specific water management
programs, it is necessary to have some knowledge of the physical,
chemical, and biological characteristics of available water
resources, especially surface waters.
This presentation will set forth some of the available methods
for analyzing and evaluating effects of biologically degradable
organic wastes on stream quality. The indicator of water quality
used throughout this manual is the dissolved oxygen content
(D.O.), while the measure used for expressing organic pollution
in the following discussions and calculations is the bio-chemical
oxygen demand (BOD). In presenting the following methodology,
it is assumed that there are multiple stream uses, including
waste assimilation and transport, and that a minimum quality
objective is to be maintained.
II. Dissolved Oxygen Relationships In A Stream
Aerobic stabilization of organic matter within a stream environ-
ment results in utilization of oxygen dissolved in the water.
Oxygen is generally available or becomes available from the
following five sources:
1. Dissolved oxygen within the stream,
-------
-------
2. Oxygen transfer to the water from the atmosphere
(stream aeration or reaeration),
3. Dissolved oxygen within the waste,
k. Oxygen produced by stream flora (algae),
5- Chemical reduction of compounds (e.g., nitrites and
nitrates, 2NO + 2N02 + Og
Where relatively high nutrient concentrations, long periods of
sunlight, and low turbidity exist, stream flora may cause con-
siderable fluctuations in dissolved oxygen and BOD levels. When
significant algal populations exist, oxygen concentrations
usually exhibit diurnal fluctuations; higher D.O. concentrations
during periods of sunlight and lower concentrations at night.
Stream flora utilize oxygen continuously in respiration; however,
at night, or on overcast days, a lack of sunlight may cause the
respiration rate (rate of oxygen use) to exceed the rate of
oxygen production from photosynthesis. When this condition
occurs, the flora can exert a considerable oxygen demand causing
the large diurnal fluctuations. Upon death, algae can be respon-
sible for a major BOD loading in the stream. Although nutrient
concentrations are becoming major problems in more and more areas,
the effects of nutrient balance and resulting flora on a stream's
oxygen balance are considered beyond the scope of this presenta-
tion; therefore, have been omitted.
The measurement of the D.O. concentration in a laboratory sample
is a reasonably accurate determination; however, it must be
recognized that a stream is a dynamic system. It is unrealistic
to consider a single D.O. measurement as representative of a
stream under all conditions, because of variations in flow,
temperature, waste load, and other independent variables.
The quantity of oxygen required to stabilize a given amount of
oxygen material is relatively constant. Approximately the same
number of pounds of oxygen are required to stabilize an organic
waste at 30ฐ as would be required at 5ฐC. However, because of
the effect of temperature on biological metabolic rates, the
time required for stabilization of a waste is greatly increased
when temperatures are lowered.
Oxygen, as it occurs in a stream, is measured as a concentration,
milligrams per liter (mg/l). To convert concentration to mass
flow rate (pounds/day) requires the following calculation:
Ibs oxygen/day = (mg/l D.O.) x (MGD stream flow) x (8.31* Ibs/gal)
or since 1 MGD =1.55 cfs
Ibs oxygen/day = (mg/l) x (cfs stream flow) x (5-38 Ibs/cfs)
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-------
This calculation gives the total mass flow rate of oxygen dis-
solved in the stream, for a particular location and time of
sampling. When a D.O. objective has been established for the
stream, the dissolved oxygen in the stream available for oxida-
tion of organic materials would be:
0 available (mg/l) = present stream D.O. (mg/l) - stream D.O.
objective (mg/l)
This calculation shows that in many cases only a portion of the
total D.O. in a stream may be utilized for oxidation, as the
stream D.O. objective (minimum allowable D.O.) may represent the
greater portion of the stream D.O.
Maximum dissolved oxygen concentrations in water (saturation D.
0's.) are dependent upon temperature, as illustrated by Figure
]L. Engineering calculations to determine stream waste assimila-
tion capacities-^- are dependent upon the amount of oxygen avail-
able and the rate of oxygen utilization. Both of these variables
are temperature dependent. Figure !_ gives oxygen solubility in
water in degrees Centigrade and degrees Fahrenheit for the usual
range of temperatures. Since less oxygen may be dissolved in a
stream at warm temperatures, the amount of D.O. available for
oxidation of wastes is also decreased. When periods of warm
stream temperatures and low stream discharges coincide, primarily
during the summer and fall, the critical conditions for waste
assimilative capacity occur.
III. Biochemical Demand (BOD)
BOD is a laboratory measurement of the amount of oxygen that is
required or utilized in the stabilization of an organic waste.
A graphical representation of a typical curve of BOD exertion vs
time is shown in Figure 2_. Figure 2_ shows that there are two
stages of BOD exertion; the first (carbonaceous) stage is satis-
fied in approximately 20 days; then the second (nitrogenous)
stage exerts its oxygen demand. In most engineering calculations,
the carbonaceous BOD is the measurement used; therefore, all
references to BOD in this report refer to the carbonaceous BOD.
It is significant to note that BOD results may show considerable
fluctuations, primarily because the BOD test is based upon the
functioning of a biological system which tends to be quite vari-
able. Averaging values over a period of time increases relia-
bility of the results; however, even the averaged values should
not be considered absolute, regardless of the type of sampling
and/or laboratory technique employed.
^- Assimilative Capacity - the ability of a system to absorb a
change (waste) without destroying the prior uses of the system.
-------
-------
BOD measurements to determine oxygen utilization are usually
carried out over a 5-day period at a temperature of 20ฐC; hence,
the reporting terminology "5-day BOD." Complete stabilization
of a waste normally requires a much longer period than 20 days;
hovever, the ultimate BOD (oxygen required to completely stabi-
lize the carbonaceous BOD) can be calculated from the 5-day value.
The deoxygenation of wastes (rate of BOD exertion) through the
first stage reaction is generally approximated by a first order
equation. The rate of reaction is directly proportional to the
amount of organic material present. This reaction is represented
mathematically by the differential equation:
Q- K r
dt - KLL
K = reaction rate constant
LI
L = amount of BOD remaining
= rate of BOD utilization
dt
On integration this becomes:
K i*
L = L e 1 and represents first stage curve, Figure 2.
ฃL """"
L = BOD remaining
L = ultimate BOD of the waste
a
K = deoxygenation rate constant (Base "e")^
t = elapsed time
~ T _ ft-T t T / -1 "1 "k \
Or: y = L - L e 1 = L (1-e 1)
a a a
y = amount of BOD utilized
L = ultimate BOD of the waste
a
K = deoxygenation rate constant (Base "e")
t = elapsed time
Reaction rates in the above equations are expressed in terms of
Base "e;" however, they may also be expressed to the Base "10."
-^- Convention indicates K be used for Base "e" notation and
k be used for Base "10" notation.
-------
-------
Considerable care must be exercised to insure the proper base
is being used. Base "e" figures may be converted to Base "10"
figures in the following manner:
Kx (Base "e") = kฑ (Base "10") (2.3)
To calculate the ultimate BOD value for a waste from the 5-day
BOD, the following relationships are used:
Tnt. n. RnT1 ,T } _ Y (5-day) 5-day BOD (100)
Ultimate J30D (L ) = * ^ t A\ =
a 1 - e 1O; # BOD satisfied in 5 days
The per cent BOD satisfied in 5 days is dependent upon tempera-
ture and the bio-degradability of the waste. Figure 3_ indicates
the proportion of BOD removed in a given time period with a
specified reaction rate constant. When laboratory data on a
given waste or stream are not available, 5-day BOD removal is
usually taken as 68 - 83 per cent which, from Figure _3_, indicates
K to be 2.3 - 3.^5- The above discussion was centered on 5-day
BOD values, but any time period can be taken to use in approxi-
mating the ultimate BOD; however, the 5-day values give more
consistent results than the BOD values for shorter time intervals.
In addition to providing more consistent values for the ultimate
BOD, the 5-day BOD is utilized to reduce the time lag between
the sample collection and laboratory results; to reduce incubator
space requirements in the laboratory; and to allow comparison of
results by the selection of standard conditions. These factors
are extremely important when volume sampling is being done.
IV. Deoxygenation Rate Constant (K, or k )
The deoxygenation rate constant is generally defined as the rate
of oxygen utilization by a waste material, within a particular
environment. Characteristics which influence the rate constant
are as follows:
a.. Turbulence - The speed of many chemical reactions
is increased by turbulence. The same effect is
expected on biochemical reactions because of the
greater opportunity that is afforded for contact
between the organic matter and the biological
population.
Eckenfelder and O'Connor, "Biological Waste Treatment,"
Pergamon Press, 196l.
-------
-------
t> Biological growth on the stream bed - A biological
population attached to the stream bed, particularly
in shallow, turbulent waters containing rocks, will
greatly increase the reaction rate. This biological
growth would be similar to that found in a trickling
filter at a waste treatment facility.
c. Immediate chemical demand - Some wastes contain chem-
ical substances or end products of anaerobic decompo-
sition which exert an immediate chemical demand. Upon
reaching a stream, these wastes have an almost instan-
taneous uptake of D.O. and reach stability by chemical
rather than biological processes.
NOTE: Significant amounts of immediate chemical
demand can be separated out when determining
the biological reaction rate constant. This
demand is measured as the BOD exerted in the
first few minutes; a period too short to
allow biological activity to become signifi-
cant, and is shown when plotting BOD exerted
vs time.
d. Nutrients - Nutrients (nitrogen, phosphorus, and per-
haps other substances) are necessary for the support
of stream flora and fauna (plant and animal life).
Lack of nutrients (fertilizer) restrains the growth
of biological organisms responsible for the oxida-
tion processes. If a waste of the receiving stream
is deficient in nutrients, oxidation will proceed
at a much slower rate than in a laboratory when a
standard BOD dilution water is used.
e. Lag in oxidation processes - If an insufficient bio-
logical population is present in a stream and/or
waste, some interval of time will pass before normal
oxidation occurs. The lag is the time required to
build up an adequate population.
f. Dilution or waste concentration - Large volumes of
water dilute waste discharges which, in turn, reduce
the opportunity for contact between the organic
material and the biological population. If waste
concentration is very low, the reaction rate will
be considerably reduced.
-------
-------
Other factors which must be considered when trying to establish
the deoxygenation rate in a stream include flocculation and
sedimentation, scour, and volatilization. Although these
factors do not affect the actual reaction rate, they can result
in the misinterpretation of field measurements. Flocculation
and sedimentation, as well as volatilization, give results
which indicate marked decreases in BOD. This would indicate
that the rate of removal of organic material in the stream is
much higher than actually exists. However, organic sediment
will exert its BOD at a later date. Scour can indicate a low
reaction rate, because sediments within the area may be brought
into suspension, indicating little BOD exertion, although con-
siderable oxidation may have taken place.
The deoxygenation rate varies significantly and directly with
temperature. The variation is a result of increased biological
activity at higher temperatures, and limited or reduced activity
at lower temperatures. The generally accepted relationship
between the reaction rate constant and temperature is as follows:
(T20)
K % any temperature T = K @ 20ฐC x 1.0^7
Where T = stream temperature in ฐC
(T20)
Figure h_ shows numerical values of the factor, 1.0^7 ,
plotted over the normal range of temperatures. The base temper-
ature of 20ฐC is used, since this agrees with the laboratory
incubation temperature at which the reaction rates are normally
evaluated.
Expected values for the deoxygenation rate constant are given in
the table below:
TABLE I
Stream Characteristics KI (base e) k (base 10)
Heavily polluted streams 0.23 -0.69 0.1 -0.3
generally O.Ul generally 0.17
Streams not subject to immediate
pollution 0.19 - 0.36 0.08 - 0.15
Streams with small pollution loads 0.12 - 0.23 0.05-0.10
Sludge deposits (does not consider
waste loads in the stream above
the sludge deposit) 0.023-0.19 0.01-0.08
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-------
V. Determination of Deoxygenation Rate Constant (K )
Given BOD-time series data from laboratory analyses, there are
several methods of obtaining the reaction rate of the incubated
sample. Each method gives approximately the same result; there-
fore, the simplest method has been selected for presentation
here. It must be realized that reaction rates calculated from
laboratory observations are not necessarily the same as those
in the stream. The biological environment of a dynamic system,
such as a stream, cannot be duplicated in the laboratory.
Example I
Daily Difference Method
The following results were obtained from a short-term
analysis of a sample by determining the BOD exerted each day
for a period of 7 days. It is not necessary to make the BOD
determinations at the time intervals indicated, but the time
of observation must be carefully noted and the data plotted
accordingly.
Step 1. Laboratory Results
t (days) y (BOD exerted) mg/1
0 0
1 0.7
2 l.U
3 1.6
4 1.7
5 1.9
6 2.2
7 2.3
Step 2. Graphic Plot
Plot the laboratory data on arithmetic graph paper as
shown in Figure 5a.
Step 3. Curve Fitting
Fit a smooth curve through the plotted points (Figure
5a). From this smooth curve, take BOD exerted values (y) for
the corresponding times (t). This procedure adjusts or averages
the BOD readings.
-------
-------
Adjusted Values
t (days) y (BOD exerted)
0 0
1 O.T2
2 1.25
3 1.55
h 1.80
5 2.00
6 2.20
7 2.35
Step k. Daily Differences
Using the adjusted BOD values, calculate the differences
over equal increments of time. A daily period is generally
satisfactory and most frequently used.
Time Interval BOD Difference Plotting Position
(days ) (mg/l) (used in Step 5)
0-1
1-2
2-3
3-U
M
5-6
6-7
0.72
0.53
0.30
0.25
0.20
0.20
0.15
1/2
1 1/2
2 1/2
3 1/2
It 1/2
5 1/2
6 1/2
Step 5.
Plot the incremental data on semi-log paper, with time
on the linear scale and the BOD differences on the log scale,
as shown in Figure 5b. Values are usually plotted at the mid-
point of the time interval.
Step 6.
Draw a line of best fit through the points, extending
the line to time zero. The plotted values may not exhibit a
straight line relationship beyond t = U, or t = 5, indicating
nitrification is beginning.
Step 7.
Using the incremental values of BOD at selected times
to get the maximum time interval having good correlation with
the curve, in this case t = 0 and t = U to eliminate the portion
affected by nitrification, make the following calculation:
-------
-------
10
BOD/day g t = h = 0.195 = n ?r
BOD/ day ง t = 0 0.75
This indicates that after ^ days, 26% of the BOD remains
to be oxidized, and that 7W of the ultimate (First Stage) BOD
has been stabilized.
Step 8.
From Figure 3_, using t = k, and y = 26$, the laboratory
K is determined to be approximately 0.32 @ 20ฐC (the laboratory
incubation temperature).
Figure J3 is an expedient over using the following equa-
tions to calculate the deoxygenation rate constant.
K = 1/t In r- NOTE: Ay figures are ordinates of
1 Ay Figure 5b.
bฐ Kl - - - - NOTE: Ay figures are ordinates
t or AO _ . ,-T
of Figure 5b_.
Step 9-
The ultimate BOD of this sample may be calculated as follows:
ง t = k, Jh% of the BOD has been oxidized; from Figure
5a, the BOD exerted @ t = k is 1.6 mg/1.
Therefore:
7W of the ultimate BOD (L ) = 1.6 mg/1
cL
0.72 L =1.6 mg/1
The ultimate BOD can also be calculated from the following
relationships :
a. L -
a , -K,t
1 - e 1
yt = BOD exerted after time t (from Figure 5a)
K = deoxygenation rate constant calculated above
t = elapsed time
-------
-------
b. L = yt
11
Ayo
a J Ayo - Ayt
yt = BOD exerted after time "t" (from Figure 5 a)
Ayo = ordinate @ time zero, Figure 5b_.
Ayt = ordinate ง time "t," Figure 5b.
VI. Determination of Stream K Rate
A combination of field measurements and the laboratory (bottle)
K rate is used to calculate the deoxygenation rate of a stream
reach. This determination requires stream BOD values for at
least two sampling stations downstream from a waste discharge.
The stations should be a reasonable time of flow apart, and
theremust not be another source of waste entering the reach.
The magnitude of the waste is determined by locating a sampling
point above as well as below the point of introduction of the
waste. Any tributaries entering between the sampling points must
be considered; however, sampling points should be selected to
avoid this situation when at all possible.
Derivation
1. It has previously been shown that the BOD-time curve
is logarithmic (Figure 2). The curve is expressed mathematically
as follows:
-K t -K t
L = L (e ) or L. = LQ (10 ^ )
U cl O cL
f
L = BOD (mg/l) remaining after time "t"
\j
K = deoxygenation rate, Base e
t = time interval (days)
L = ultimate first
fi.
2. By taking the In (log) of both sides of the equation,
it is possible to obtain a straight line relationship simplify-
ing the calculation of K .
-K t
Lt ' La
-------
-------
12
3. Assuming data is available for two sampling stations,
B and C, with flow time "t" "between stations; In La_ is the
natural logarithm of the ultimate BOD at point "B." Likewise,
In Lap is the natural logarithm of the ultimate BOD at point "C."
Therefore, given time zero at point B:
L = L
a aB
L = L
Sc ^
-K.t = In () (from Step 2)
X i_i
a
K. = in ) = in ()
It LaB t L&B
U. Using the ultimate BOD values at points A and B, plus
the time of flow between the points , K can be estimated a direct
calculation.
A graphical solution for the determination of the stream K
utilizes the same equation; however, the graph itself may indicate
many characteristics of the stream, waste, and environment. The
graphical approach is of greatest value when points of signifi-
cant waste discharge are known or suspected. The graph provides
a method for estimating waste strengths, reaches where sedimenta-
tion may be occurring, and the deoxygenation rate. This technique
is usually referred to as the Oxygen Balance Calculation.
Procedure for Constructing Figure 6:
Step 1.
Using K values computed from long-term BOD's in the
laboratory, adjust the stream 5-day BOD's (as determined in the
laboratory at 20ฐC) to ultimate BOD's.
Step 2.
Determine stream flows for the days of sampling.
Step 3.
Convert ultimate BOD's from mg/1 to pounds BOD/day in the
stream.
-------
-------
13
Step h.
Plot a BOD profile of the stream. The must useful plot
is log BOD pounds/day vs time of flow; however, this is only
practical when the flow rate is approximately uniform over the
stream reach during the sampling period. With variable flows,
a plot of log BOD vs stream mile is more practical. Figure j5
shows log, BOD's plotted against stream miles and points A, D, E,
H, I, L, and M represent measured values of stream BOD. Points
B1, C1, F', G', JT, and K' represent values or points located by
extrapolation.
Step 5-
Beginning with the first two plotted points downstream
from a waste discharge, use the following procedure:
a. Draw a straight line between the first two points
below the waste discharge, points D and E. For
more accurate results, there should not be any
significant waste or flow contribution between
points D and E.
b. Project the line fixed by points D and E to the
point of waste discharge, point C1 and downstream
to point F'.
c. Draw a line parallel to C'-D-E-F', through point A
and extending the line to point B1.
d. The number of pounds of BOD represented by the
distance between points C1 and B' indicates the
amount of waste contribution between points A and
D, probably contributed at point #1.
e. Continue for other points downstream.
The following conclusions may be reached after an analysis of
Figure 6_:
1. Slope of line D-E indicates the rate of BOD removal
for the reach of stream bounded by points C1 and F1.
2. The interval B'-C' indicates the amount of waste
contributed at point #1.
3. The interval F'-G1 indicates the waste contributed
at point #2. Slope of line H-I indicates the BOD
removal rate for the waste concentration below point
#2. The lesser slope indicates that the new waste
-------
-------
may be more difficult to oxidize biologically or
contains toxic substances which inhibit biological
activity.
k. The steep slope of line L-M indicates the waste
mixture below point #3 has a very rapid reduction
of BOD. The probable reasons for the rapid reduc-
tion would include:
a. The waste mixture below point #3 is easily bio-
degradable.
b. There is a chemical oxygen demand.
c. Sedimentation is occurring.
d. Shallow, rocky stream having heavy biological
growth on the rocks which perform like a trick-
ling filter.
Reaeration
Reaeration is the process of oxygen transfer from air into water
to bring the partial pressure of oxygen in the stream into equi-
librium with the partial pressure of oxygen in the atmosphere.
Absorption of oxygen in a stream occurs only at the surface layer
of water. The water surface is readily saturated; however, com-
plete oxygenation throughout the depth of the stream depends upon
turbulence to mix the saturated surface layer with the lower levels
and expose a new surface layer to the admosphere. Based on the
above, a swift, shallow, turbulent stream will have a much higher
oxygen uptake rate than a deep stream with laminar flow and uniform
channel characteristics.
Reaeration becomes operative when the oxygen content of water is
below the saturation level. Reaeration proceeds as a first
order reaction, as shown in Figure 7.. The mass transfer rate for
oxygen is proportional to the reaeration rate constant (K ) and
the oxygen deficit (D).
r = K2D
r = mass transfer rate for oxygen
K = reaeration rate constant
D = oxygen deficit = (saturation D.O. - stream D.O.)
-------
-------
15
Thus, higher oxygen deficits produce higher rates of oxygen trans-
fer (r) for a given reaeration rate constant. Temperature also
plays an important role in reaeration, since the dissolved oxygen
saturation values and the rate of oxygen transfer (K2) are
temperature dependent.
VIII. Reaeration Coefficient - K (base e) or k (base 10)
The reaeration coefficient is defined as the rate constant con-
trolling the process of reoxygenation, or rate of oxygen absorp-
tion in a stream under given physical conditions. Factors which
affect K values include: stream depth, velocity, turbulence
(physical characteristics of the stream bed), temperature, and
dissolved solids such as chlorides. Values of K? (base e)
usually range betveen 0.1 and 12.0 per day; the lover values
representative of deep, slow-moving rivers; and the higher
values for shallow and/or rapid streams.
After a stream K2 value has been determined for a particular
temperature condition, the value can, through the use of equa-
tions, be computed for any temperature condition. The two most
common empirical temperature equations are as follows:
1. K = K [l.OUT(t"20)]
T 20
This is identical to the temperature correction for K
shown in Figure h_.
2. K = K [1.01T(T"20)]
T 20
Use Figure 8_.
The amount of oxygen dissolved in a stream is readily determined
by laboratory analysis of stream samples; however, the amount of
dissolved oxygen added through reaeration must be calculated.
Several methods are available for calculating the reaeration
coefficient, but only two will be shown here. The first method
utilizes empirical relationships, such as those suggested by
O'Connor, Velz, Churchill, and others; while the second method
utilizes field observations to set up a "trial and error" solu-
tion of the oxygen sag equation.
0 ' Connor Method
1/2
(base e) = -^- x 2k hr/day
H
-------
-------
16
Where K = reaeration coefficient (day )
v = stream velocity (ft/hr)
H = average stream depth (ft)
D = molecular diffusivity of oxygen in water
(0.81 x 15'1* ft2/hr g 20ฐC)
Trial and Error Solution for K or (k?)
1. The field measurements of D.O., BOD, temperature,
and time of flow.
2. Compute K as discussed in Section VI.
3. Compute D.O. deficits at points A and B.
h. Assume values of K? and solve the oxygen sag equa-
tion for DB-
K L -Kt -K0t -K0t
DB icp\ ' - 10 1 + V10 '
Where D0 = oxygen deficit at point B
D
K = deoxygenation coefficient
K = reaeration coefficient
L = ultimate BOD @ point A
ฃ1
t = time of flow "between points A and B
D = oxygen deficit at point A.
/i
5. Plot the calculated values of D vs the assumed
K values.
6. Draw a smooth curve through the plotted points.
T. Using the actual (measured or observed) DB, read the
corresponding K value from the curve.
The "trial and error" solution seldom produces good results, "but
should be considered a reference or check calculation for empirical
solutions.
-------
-------
IT
. Oxygen Sag Equation
Introduction of an organic waste into a stream causes deoxygenation
then reaeration to be effected simultaneously. The resultant dis-
solved oxygen concentrations plotted vs time or stream mile define
the "dissolved oxygen sag." A plot of the D.O. profile of a stream
(D.O. vs time of flov) below a waste discharge gives a spoon-shaped
curve for which the mathematical relationships have been developed
by Streeter and Phelps. Modification of these relationships have
been proposed by Velz, Thomas, and many others.
When using the oxygen sag equation, it must be recognized that
complex biological processes, such as waste assimilation in a
stream, are extremely difficult to express mathematically. There-
fore, the sag equation can only approximate actual stream condi-
tions and limitations of the oxygen sag relationship must be
recognized and appreciated prior to any analysis.
The sag equation utilizes oxygen deficits to express stream D.O.
conditions. The equation is expressed as follows:
Base "e"
L K -K t -K_t -K_t
Dt = -Si [e I - e 2 ] + D e 2
K
Where D = D.O. deficit (mg/1 below saturation) after
t time "t"
L = ultimate BOD within the stream at point A
K = deoxygenation coefficient (days )
K = reaeration coefficient (days" )
t = elapsed time in days between point A and any
downstream point, point B
D = initial D.O. deficit at point A (mg/l)
3,
The equation may also be expressed in terms of Base "10"
La kl "V ~R2t -V
D = - - [10 X - 10 2 ] - D 10 2
t k2 1 a
In engineering practice, the maximum D.O. deficit (lowest D.O.
value, or worst D.O. condition to occur) is of major importance.
A typical oxygen sag is shown in Figure 9. which illustrates the
various terms involved. The critical time and critical deficit
indicated in Figure 9. give the relative location and magnitude
-------
-------
18
of the worst condition to be expected in the stream. These
values are used to determine the maximum waste load that can be
discharged to a stream and yet maintain beneficial water uses;
aid in the determination of allowable uses; and provide the basis
for programming waste and/or dilution water discharges to meet
the established dissolved oxygen quality objective.
The time to the critical point (tc) is determined by differentiat-
ing the oxygen sag equation and setting the first derivative equal
to zero.
_ K. L -K t -K.t -K t
uD 1 & r v 1 , v 2 i is T* 2 A
dt = K~^[-Kle + K2e ]-K2Dae =ฐ
The above equation simplifies to the following relationship
defining t :
ฐ K
2
*c = W? 10ge K7 [1 - Da
21 1 a 1
The basic differential equation expressing these processes is:
f V - V
At the sag point, the deoxygenation rate equals the rate of
oxygen transfer into the stream, giving rise to the following
relationships :
f = o = KIL - K2D
K,L = K0D
1 c 2 c
where D = critical deficit = D
c c
L = amount of ultimate BOD remaining after the
critical time t
c
-Knt
T T 1 C
since L = L e
C a -K.t
then K T) = K, L e
2 c la
K, -K.t
D =^Le I C
c Kg a
K2
When using the oxygen sag equation, it is convenient to let
K2 Kl
be represented by a factor "f" (f = ) . The parameter "f"
*1
occurs frequently and is known as the stream purification factor,
-------
-------
19
providing a means of defining the combined characteristics of
stream and waste. A stream with K = 0.3 and K_ = 1.2 has an
"f" value of k, as does a stream with K = 1.0 and K2 = U.O.
Higher "f" values indicate a greater capability of a stream to
assimilate organic wastes.
Temperature variations may or may not affect/the #alue of "f."
If the temperature correction factor (l.0l*7) is used for
both K and K values, temperature changes do not alter the / onฐr)
purification factor. If Kg is considered to vary by (1.017) ~ ,
temperature changes must be considered^ Many sanitary engineers feel
the refinement offered by the (1.017) factor is not warranted and
that the (1.0^7) factor gives more reliable results.
Typical values of the self-purification factor have been given by
Fair and Geyer in their text. Typical values of "f" for various
stream conditions are shown in Table II below:
TABLE II - TYPICAL VALUES OF THE SELF-PURIFICATION FACTOR "f"
"f" Value
Nature of Receiving Waters ง 20ฐC
Small ponds and backwaters 0.5 - 1.0
Sluggish streams, large lakes or impoundments 1.0 - 1.5
Large streams of low velocity 1.5 - 2.0
Large streams of moderate velocity 2.0 - 3.0
Swift streams 3.0 - 5.0
Rapids, waterfalls, etc. 5.0 and up
X. Uses of the Oxygen Sag Equation
The principal use of the sag equation is calculation of maximum
allowable organic loads that may be imposed upon a stream and
still maintain specified stream D.O. objectives. This technique
allows optimum location of points of waste discharge, to maximize
stream utilization and maintain maximum water quality. Three
methods are generally available for solving assimilative capacity
problems:
1. Manual solution of the sag equation (trial and
error not recommended because of time required).
2. Graphical solution (recommended).
-------
-------
20
a. Method published in course manual for "Water
Quality Studies," Sanitary Engineering Center,
Cincinnati, Ohio. (Discussed here)
b. Method proposed by T. A. Wastler, Public Health
Service, in Sewage and Industrial Wastes,
September 1958.
3. Computerized solution (large scale and repetitive
analyses).
Example II
Graphical Solution of the Assimilative Capacity Problem
by Method 2a;
f I'1, o c
f = A" iil, = 2.5
Given:
K = Q.ltU @ 20ฐC
K = 1.1 ง 20ฐC
Stream temperature = 28ฐC and C =7.92 mg/1
s
D = 1.0 mg/1
S.
Minimum acceptable D.O. = U.O mg/1
D = C - U.O = 7-92 - U.O = 3.92 mg/1
c s
Use Figure IQa for the solution, since D =1.0 mg/1. Figures
IQb and 10c may be used when D = 2.0 or 3.0 mg/1, respectively.
Although field measurements do not give D values of exactly
1.0, 2.0, or 3.0 mg/1, an interpolation of values obtained from
the tables will provide very close approximations.
Solving for the maximum allowable ultimate BOD concentration,
using Figure IQa, a value of about 17 mg/1 is obtained for L .
Example III
Use of the Graphical Method to Determine Minimum P.O.
Concentrations Following the Introduction of a Waste
Into a Stream:
Given:
5-day BOD of Waste = 100 mg/1
5-day BOD of Stream = 3 mg/1
-------
-------
21
Waste Flow =(^=60 mgd = 60 mgd x 1'^dcf- = 93 cfs
Stream Flow - Q = 1000 cfs
s
Temperature of Stream = 20ฐC and C =9-17 mg/1
S
D =1.5 mg/1
ฃL
l
K @ 20ฐC -
f - 0.69 _ . 0
1 ~ n ฐ^ ~ J
20ฐC = 0.69
5-day BOD of stream and waste mixture =
Q (BOD ) + Q (BOD )
C! Q \J TJ
5-day BOD mix = Q + Q
_ 1000 cfs (3 mg/1) + 93 cfs (100 mg/l)
1000 cfs + 93 cfs
= 11.25 mg/1
From Figure 3. the 5-day BOD for K = 0.23 represents 0.68 of L .
L of mixture = /-v^ = 19-^ mg/1
From Figure lOa with D =1.0 mg/1 and L = 19.^ mg/1
a a
D = k.O mg/1
From Figure IQb with D& = 2.0 mg/1 and L =19.^ mg/1
D = 1+.25 mg/1
c
Therefore, for D =1.5 mg/1, the critical D.O. deficit is
approximately:
U.25 mg/1 + U.O...mg/1 _
2
The stream D.O. concentration at the sag point (critical point)
equals the saturation D.O. minus the deficit.
D-ฐ'stream = ฐs " DC = 9>1T m/I " U'12 mg/1 = 5'ฐ5 mg/1
-------
-------
22
XI. Stream Assimilation Capacity
The most useful presentation for any reach of stream allovs
determination of allowable BOD loadings when temperature and
flow conditions vary. This is best achieved using a graphical
solution.
Example IV
A Procedure for Developing Assimilative Capacity Curves
Given: D =1.0 mg/1
a
K^ = 0.65
K2 = 3.9
3.9
f = "v"- = 6 and does not vary with temperature
fluctuations
Minimum acceptable D.O. = 5.0 mg/1
1. Assume stream temperature = 30ฐC
D.O. saturated = C =7.63 mg/1
s
DC = 7.63 mg/1 - 5.0 mg/1 = 2.63 mg/1
From Figure 10a, L = 21.5 mg/1
"""""" Q,
2. Assume stream temperature = 20ฐC
Cs = 9-17 mg/1
DC = 9.17 mg/1 - 5.0 mg/1 = U.17 mg/1
From Figure IQa, L =3^.5 mg/1
EL
3. Assume stream temperature = 10ฐC
C = 11.33 mg/1
S
DC = 11.33 mg/1 - 5.0 mg/1 = 6.33 mg/1
From Figure IQa, L =53.0 mg/1
~r~-L-LL
-------
-------
23
4. Assume stream temperature = 5 C
C = 12.80 mg/1
s
D = 12.80 mg/1 - 5-0 mg/1 = J.BO mg/1
From Figure IQa, L =66.0 mg/1
- EL
5. Using the values obtained in steps 1 through 4, plot
Log L versus temperature on semi-log paper, as
shown in Figure 11.
6. Select temperatures such as 5ฐC, 10ฐC, 25ฐC, from
Figure 11, and obtain the corresponding L values.
Construct a table to convert BOD from mg/1 to
pounds BOD by assuming flow values.
7. Plot the values for pounds of BOD from the table on
log scale versus temperature, then add constant flow
lines, as shown in Figure 12.
The family of curves (Figure 12) developed using the preceding
steps can now be used to determine necessary flows for assimila-
tion, or maximum BOD loadings, at any temperature. The curves
constructed in Example IV are only applicable where D =1.0 mg/1
and the minimum acceptable D.O. is 5.0 mg/1. Other families of
curves must be constructed for different D values or different
Q
D.O. objectives.
When making an analysis of stream assimilative capacities, the
reduced quality of the waste water returned must be considered.
For example, if 8 mg/1 is the stream D.O., stream flow is 150
cfs, water use = 40 cfs, D.O. of water (waste) returned = 2 mg/1;
then only a portion of the 150 cfs will be .available for waste
assimilation, i.e., 150 cfs - 40 cfs { mg/^ " . mg/JJ Or 120
cfs available. mg/1
The above analyses assumed that K and K did not vary with fluc-
tuation in stream flows. When there are large flow fluctuations,
K will show significant variations, found to follow the following
relationship:
K2 = aQb
Q equals stream flow.
a and b are constants evaluated from the stream cross-
section, Q, relationship.
-------
-------
SATURATION D.O. CONCENTRATIONS
IN DISTILLED WATER vs TEMPERATURE
AND PRESSURE
EXAMPLE
GIVEN
ELEVATION
TEMPERATURE
= 500 FT.
= 20.5ฐC
SATURATION
D.O. = 8.92mg/l
626mm Hg - 5000 ft elevation
651 mm Hg - 4000 ft elevation
67?mm Hg - 3000 ft
704mm Hg - 2000 fl
732 mm Hg - I 000 ft
elevation
elevation
e levotion
-------
-------
25
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TIME
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observed D.O. concentration
D.O. deficit at any time t, C = C
9
initial D.O. deficit
coefficient of reaeratjon (sorption of
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GRAPH SHOWING STREAM
REAERATION REACTION
Figure 7
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TIME
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GRAPH OF A TYPICAL
SAG REACTION
OXYGEN
Figure 9
-------
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CRITICAL DEFICIT, Dc vs POLLUTION LOAD,LQ
Figure 10a
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CRITICAL DEFICIT, D vs POLLUTION LOAD,L
Figure 16b
-------
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36
D0s3.00jng/i = initial deficit
14
12
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CRITICAL DEFICIT, D vs POLLUTION LOAD,L
Figure lOc
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Figure 12
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TABLE OF CONTENTS
Page
INTRODUCTION ........ ..... 1
Pour-Thirds Law 2
Random Process Analogy , U
Turbulent Pipe Flow Analogy ..... 5
DISCUSSION ............ 6
CONCLUSIONS ....................... 8
BIBLIOGRAPHY ..... ..... 9
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ESTIMATING DIFFUSION CHARACTERISTICS OF TIDAL WATERS
I. INTRODUCTION
1 2
The mathematical models available ' for the analyses
of pollution and other problems involving mixing in tidal waters
require a knowledge of the turbulent diffusion characteristics
of the system being studied. These characteristics may be eval-
uated in an estuary by using external tracers such as dyes or
internal tracers which are already present, as in the case of
salinity intrusion or a recognizable continuous pollutant dis-
charge. Similar procedures may be applied to a verified hydraulic
model of the system, where such a model exists. However, these
methods can be expensive and time consuming.
In cases where preliminary calculations are being made,
and general order of magnitude answers will suffice, it is most
useful to be able to make satisfactory estimates of diffusion
characteristics using readily available hydrographic information.
Furthermore, in planning dye tracer studies, it is helpful to
have some reasonable estimate of diffusion properties, to permit
better design of field activities.
Several methods which have been proposed for estimating
a diffusion coefficient for tidal waters are described below.
In each case, it is the turbulent analog of the Fickian coeffi-
cient of molecular diffusion which is used. This has been variously
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-------
referred to in the literature as the coefficient of turbulent,
eddy, or longitudinal (for the one-dimensional case) dispersion,
diffusion, or mixing.
Four-Thirds Law
It has been almost universally observed that the magni-
tude of the turbulent diffusion coefficient increases greatly
with the size of the area, or volume, containing the diffusing
substance. This has led to the formulation of a "four-thirds
law" wherein the diffusion coefficient is proportional to the
four-thirds power of the scale of the diffusion phenonema, L.
3
This is quoted by Bowden as:
D 2, = 0.02l*6L '3 Eq (1)
cm /sec
Where L is in cm.
For the one-dimensional estuary, the characteristic
scale (L) may be considered as the length of a tidal excursion,
or the maximum longitudinal distance a particle of water would
travel during a flooding or ebbing tide. This length would be
given by:
L = Vt Eq (2)
L = length
V = average tidal velocity
t = period of time between slack waters (generally
estimated at 6.2 hours for the Potomac Estuary)
If a sinusoidally varying tidal current is assumed:
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-------
V = -V Eq (3)
IT max Mp
From Eq. (2)
L =-V t Eq
cm ir max
Where: V is in cm/sec
max
t is in sec
L = - (6.2 hrs.) (3600 sec/hr.) V
cm ir max
L = lH,200 V
cm max
By substituting into Equation (l):
D 2, = 0.02U6 [1U.200 V ]
cm /sec max
= 0.021*6 [333,000] V
= 8.21 x 103 V /3 vith V in cm/sec Eq (5)
max max
Equation (5) may be restated using units of knots for V
ITlclX
This form of the equation may be more convenient, as values for
V in knots may be obtained from published tables for many
max ^ J
h
estuarial locations.
D 2, = 1.56 x 106 V k/3 ----------------------- Eq (6)
cm /sec max ^
Where V is in knots
max
Other forms of Equation (6) are as follows:
D .2,, =5. 2V /0 ------------------------------ Eq (6a)
mi /day max H v
Where V is in knots
max
D 2. = 1.68 x 103 V ----------------------- Eq (6b)
ft /sec max H
Where V is in knots
max
This procedure vas carried out for the Potomac River
below Washington, D. C., and the results are plotted in Figure 1^.
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Random Process Analogy
The process of tidal mixing and dispersion has been des-
cribed by Diachishin as a random walk type of process. Using
probability theory, he has developed equations which resemble
solutions of the classical diffusion equation. For this simi-
larity to be complete, it was concluded that the diffusion
coefficient must be described as follows:
D = St- Eq (7)
where L is the length of each random step and n is the frequency
of steps (one per tidal cycle or 1/12.^ per hour). Applying a
procedure similar to that above for defining the scale length,
an average step length is used which is equivalent to the tidal
excursion length, as given in Equation (k). Combining these
expressions results in the relationship:
Dcm2/sec ' I
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-------
Coefficients for the Potomac Estuary calculated using
this equation are also shown in Figure !_.
Turbulent Pipe Flow Analogy
Taking Taylor's expression for the longitudinal disper-
sion coefficient for turbulent flow in pipes as a starting point,
Harlemann has developed an analogous expression for tidal waters.
In this development, it has been assumed that the required steady,
turbulent flow velocity may be approximated by the time average
of the tidal velocity over a half tidal cycle. In addition, a
sinusoidal velocity variation has been assumed. The resulting
expression is:
where R (ft) is the hydraulic radius for which the mean depth
is a satisfactory approximation, n is Manning's roughness coef-
ficient, and V ( f ps ) is the maximum tidal velocity. For the
TOelX
Delaware Estuary, Harlemann estimated n to be 0.025. It is also
recommended, however, that the final result be multiplied by
1ซ5ป to account for bends and section changes, so an effective
n of 0.038 has been used in the following reduced equation:
D 2, = 2.92 x 103 V R 5/6 ------------ - --------- Eq (10)
cm /sec max H
with V in knots and R in feet.
max
In a similar manner, but employing a slightly different
7
set of assumptions, Bowden derived the expression:
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6
D 2, = 235 V R Eq (ll)
cm /sec max ^
With V and R defined as above.
max
Results obtained using these formulas on the Potomac
Estuary are shown in Figure !_.
II. DISCUSSION
The first two methods described (Equations 6 and 8) pro-
duce somewhat similar results (Figure 1). These coefficients,
in turn, differ from those obtained by the turbulent pipe flow
analogy formulas by two to three orders of magnitude.
In order to provide a basis for comparison of the abso-
lute values obtained by these formulas, the coefficient of
diffusion was also calculated from the salinity distribution in
this portion of the estuary. The solution to the classical dif-
fusion equation may be expressed in forward finite difference
form as:
Q S 2Ax
D _ Eq
x x+Ax x-Ax
Knowledge of the longitudinal salinity distribution (S),
net advective flow (Q) and cross-sectional area (A) in the estuary
will permit solution for D. This was carried out for relatively
steady flow conditions near 2000 cfs in the Potomac Estuary, using
chloride data provided by the District of Columbia Department of
Sanitary Engineering.
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7
Coefficients obtained by solution of Equation (12) are
closely approximated by the "four-thirds" model and are less
than those obtained by the random process formula by a factor
of about three. The turbulent pipe flow analogy equations, how-
ever, produce coefficients for the Potomac Estuary that are
lower by multiples of 100 to 1000 than the observed values.
Coefficients calculated for the Patuxent Estuary ( using the
above equations, showed differences of the same order of magni-
tude as those calculated for the Potomac.
This large discrepancy was also noted by the respective
sources from which these equations were obtained. Harlemann
stated that the low values obtained by Equation (10) are valid
for the fresh water portions of tidal streams. The much higher
diffusion coefficients observed in the brackish portions of
tidal waters he attributes to density effects. The longitudinal
salinity gradient existing in estuaries is said to cause a large
scale gravitational circulation with the more saline waters
moving upstream along the bottom and downstream near the water
surface. The over-all effect of this circulation, referred to
by Bowden as a density current, is to cause a large increase in
the observed effective diffusion coefficient. Harlemann has
demonstrated tne validity of Equation (10) in hydraulic models,
but, apparently, not as yet in prototype estuaries.
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8
III. CONCLUSIONS
Both the "four-thirds law" and random process analogy-
formulas yield effective diffusion coefficients in the proper
order of magnitude for the brackish portion of the Potomac
Estuary. Either of these formulas should provide useful ap-
proximations for other estuaries where good information on
salinity variations is not readily available. These formulas
should be used with caution in the fresh water portion of tidal
rivers, in view of the possible important influence of salinity
gradient induced density currents on diffusion. Prototype tracer
studies in such locations appear to be necessary to provide
reliable estimates of the appropriate diffusion coefficient.
Accumulation of experience gained by such studies will permit
evaluation of the validity of Equations (10) and (ll) for pre-
dictive purposes.
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BIBLIOGRAPHY
1. Thomann, R. V., "Mathematical Model for Dissolved Oxygen,"
JSED, ASCE, 89, Wo. SA5, (October 1963)
2. O'Connor, D. J., "Oxygen Balance of an Estuary," JSED,
ASCE, 86, No. SA3, (May I960)
3. Bowden, K. F., "The Sea, Volume One, Section VI, Turbulence,"
p. 819, Interscience Publishers, New York (1962)
U. "Tidal Current Tables, Atlantic Coast of Worth America,"
U. S. Coast and Geodetic Survey, Department of Commerce,
U. S. Government Printing Office (1965)
5. Diachishin, A. N., "Waste Disposal in Tidal Waters,"
JSED, ASCE, j39, No. SAU, (August 1963)
6. Harlemann, D. R. F., "The Significance of Longitudinal
Dispersion in the Analysis of Pollution in Estuaries,"
Presented at Second International Conference on Water
Pollution Research, Tokyo, Japan, (August 1963)
7. Bowden, K. F., "The Mixing Processes in a Tidal Estuary,"
Advances in Water Pollution Research, Vol. 3, Pergamon
Press, The MacMillan Co., New York (196*0
8. Stommel, H., "Computation of Pollution in a Vertically
Mixed Estuary," SIW, 25, 9, (September 1953)
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10
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EQ. 8 -
EQ 12
+ -
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EQ. II
13 14 15 16 17 18 19 20 21 22 23 24 25 26
DISTANCE BELOW KEY BRIDGE (THOUSANDS OF FEET)
DIFFUSION CHARACTERISTICS, POTOMAC RIVER ESTUARY
FIGURE
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USE OF RHODAMINE B DIE .45 A TRACER
IN STREAMS OF THE SUSQUEHANNA RI?ER BASIN
PDHPOSE AND SCOPE
This paper relates the experiences of the Susquehanna Field Sta-
tical - Chesapeake Bay-Susquehanna River Basins Project - in the
use of Rhodamine B dye techniques in the stream environments of
the Susquehanna River Basin Particular problems encountered
in the use of fluorescent tracer techniques, and the solution
of many of these problems will be discussed Instruments and
equipment found most suitable for strearas in the Susquehanna
Basin are listed in Appendix I,
ACKNOWLEDGMENTS
The assistance and cooperation of the Pennsylvania Department
of Health^ Uซ S. Geological Survey; and Dr0 James H. Carpenterf
Chesapeake Bay Institute, is gratefully acknowledged.
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TABLE OF CONTENTS
ฃงฃฃ
I. INTRODUCTION ..................... 1
II. CONSIDEBATIOMS WHEN USING FLUORESCENT DYE
TECHNIQUES . . . . . . . . . . . . . . . 1
Heat Transfer During' Calibration . . . . , . . 1
Dye Adsorption on Metal Parts of the Equipment , . 2
Type of Pump . . 0 . . . . , . . 2
Volume of Sample Through the Fluorometer Curvette, . 2
Power Supply ..,.............. 2
Interference Materials in the Streams ..., 3
Effects of pH on Emission 0..<ปo.u.....o 3
Temperature ao.<.ou.,......o..ป..o 4
Dye Loss at Power Stations <> o.. .ซ.<,..,. 4
Dye Adsorption In the Stream . 0 . . . 4
Metal Inhibition in the Stream 0 ซ, , . . 4
Limits of Dye Concentration . 0 . 4
OBSERVATIONS . ซ, . . 0 0 . . , 6
BIBLIOGRAPHY ................. u .... 8
APPEND;DC i .........,... o .... 0 .. 9
APPENDIX II ......... t .. o ........... 10
FIGURE 1 8 0 o 0 . 0 , . . 12
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I. INTRODUCTION
The use of Rhodamine B, or similar fluorescent, organic dyes, for
studying the physical characteristics of streams and bodies of
water has become extensive since introduction of the technique
by Carpenter-% These dyes are primarily used for studying "time,, /
of passage" and/diffusion characteristics in estuaries , bays-^ ,
and streams^ . The technique involves use of a substance (dye
in this case) which can be detected in very dilute concentrations
by an instrument such as a fluorometer. The dye has physical
properties which allow it to mix and be transported as an integral
part of the water,, effectively siirrulating movement of wastes or
other materials introduced into the system,
The use of Rhodamine B dye in Susquehanna River Basin streams
brought to light several problems not encountered when using
the technique in other streams or in estuaries The chemical
composition, velocity, mixing, and current characteristics of
streams were found to present unusual problems for analysis.
II. CONSIDERATIONS WHEN USING FLUORESCENT DYE
The use of fluorescent dye techniques requires consideration
and evaluation of the following factors:
10 Instrument calibration and natural background
20 Hydrogen ion concentration
3 o Temperature
4o Decomposition - oxidation, reduction, etc,
5 Sorption
60 Photochemical decay
7. Metal inhibition
Project use of Rhodamine B dye and the fluorometer produced
several specific problems and solutions. Outlines of the
problems encountered, along vd.th the solutions found most satis-
factory, are presented below.
Heat Transfer During Calibration
The use of submersible pumps in the calibration medium proved
unsatisfactory because of gross heating of the medium from pump
operation. The heat generated from the pump after repeated re-
circulation affected dye stability and caused fluorescence loss.
To avoid this problem, a small centrifugal pump was utilized in
the laboratory during instrument calibration. Submersible pumps
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-------
were quite satis fact Dry in n^M IT-A illation? where reclrcula-
tion was eliminated3
Metal parts , particularly
&r a:;ci bras*
Considerable
affinity for the dye0
this adsorption and s
it interferes wHt -..uliD' n4 10^ ini
tion during laboratory and. i:<,c-lc ^
pomp used during calibration was <:-i
adsorption onto the pump during t'i'e
A pujnp having a primarily bra^ in ..-j
exhibit a great
ffleulties arise from
release of dye on equipment,, as
ini evaluation of dye concentra-
The small centrifugal
r-i- material, avoiding
an.
l
ng periods of reoirculationซ
w^- -.B^d io the field; how-
the pump was very short y and
there was no reciroalat-ioTu Ltitrt materials 5uch as polyethylene
tubing and fittings were 'jt^.ilz^d both ii) the laboratory and in
the field 0
ever, contact time of the .med a
A Little Giant Model 4-!2MB ??-utme.rsit.le pomp was unsatisfactory
for field installation because of poor lift characteristics A
Demming Model 2ALF4-115V, 1/3 HP submersible pump provided the
necessary capability,,
yQjjume.,.oฃ Sample Through, ^ft EiUy
Sample volumes passing rdn rugh the ฃluorometer eurvette in excess
of about I0y gall on/'hour result In turbulent flow>, with subse-
quent light scattering aTid. lastruineiit l.i"'^tabilit.yu Control of
flow from the pump was ai'jcosp.li.dheij by uh>e of a man.ifold with a
bleeder valve io> grces volume ป:-."-trtrcl, in series with a needle
valve for opt?nfjK ad.fiiotmtrtf,0 Set >'.;g'ij-e 10
Power requirements fox- the f:ield .-'tudiea were initially supplied
by a portable 4 HP, 13 ampere5 ,1'ii volt, AC generator The
fluorometer requlies ar- AC power supply regulated between 105
and 130 volts for -stable ijerieratior.o This generator unit was
found to be of irssiifficiest eapa'r-ft,7 to prcvode power for the
1/3 HP sample pump ar:d !;' maantri:ซ: rhft vistaDt voltage supply
required for the fluoxonie-* bf u
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-------
A possible solution was the use of separate power supplies for
the pump and the fluorometer. This would require a DC-AC convert-
er utilizing a 12 volt DC battery or generator; however, the
converters are relatively expensive To eliminate the converter
and second power source^ a Baker Heavy Duty 12v DC - 115v AC
generator was installed on the Ford Econovan field vehicle in
place of the standard 12 volt generator. This unit supplies the
regulated 115 vclt AC power for the fluorometer, pump and light-
ing requirements, as well as 12 volt DC power for vehicle operation.
Interference Materials _in the_Stoeai!S
Some streams contain materials which flucresce at the same wave
length as the dye being used or within the band pass of the
emission filter., This is particularly true of streams receiving
pulp and paper mill wastesป The high background contributed
from these materials in the stream mask and compromise the sensi-
tivity of the methodซ, Where low concentrations of dye which
barely exceed the expected variations in background are used,, high
background becomes most problematical <,
Effects of pH on Emission
It has been stated that Rhodamine B dye appears relatively stable
over the pH range of 2 to 10; however, these limits were established
in estuaries where the buffering capacity of the water is consider-
able The Project found that emission is adversely affected at
each end of this pH range, as streams in the study area did not
have a large buffering capacity Project experiments conducted
in streams and on stream samples under laboratory conditions
reveal a loss of emission below a pH of 4 and above a pH of ?
Emission loss does not appear quantitatively recoverable when
the pH is adjusted, i0eป, from 3=5 to 4ฐ0 or from 7^5 to ?.!
This would indicate a reaction resulting in dye destruction,
dye conversion to a form flucreseing at a different wave length,
or formation of a non-fluorescing compound,, An additional
problem results from the dye having different soluabiliti.es at
high and low pHซ
pH is a very acute problem in the Susquehanna River Basin, and
the ranges of pH discussed above are quite commonly encountered
during passage of the dye in the streams
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4
Temperature
There was a loss of fluorescence with increasing temperature
(approximately 2^ with each degree Centigrade increased). With
tap or distilled water, recovery of emission after cooling is
essentially quantitative; however,, when stream water was used
as a substrate, emission recovery after a prior temperature rise
was variable This variability indicates a change in the dye
composition may occur, which is a function of stream conditions
and temperature
Dye Loss at Power Stations
Dye passing through heat exchangers showed very high reductions
in quantity or- fluorescence upon return to the stream. Probable
cause of the loss was dye decomposition at the high temperatures j;
however^ adsorption and metal inhibition probably contributed to
the problem.
Qye Adsorption in the Stream
Adsorption of dye in streams having significant amounts of sus-
pended solids and/or obstructive matter is visually evident,,
This adsorption greatly affects the concentration of the dye
front, as well as the time of resolution for the passage of the
peak concentration Also, the shape of the recovery curve is
considerably affected,, particularly as a result of the release
of adsorbed dye0
Metal Inhibition in. the Stream
Various metal ions, e0g^ copper, aluminum, arid zinc,, are known
to inhibit fluorescence emission The extent of fluorescence
inhibition from metal concentrations in the stream can be deter-
mined by comparing results with streams having low metal ion
concentrations and low inhibition,,
Limits of Dye Concentration
Fluorescence emissions of Rbodaudne B dye are characteristically
linear over a finite rar-ge of dye concentration,, The lower limit
of concentration is set by natural background or interfering sub-
stances in the sample medium. The upper limit of dye concentra-
tion is determined by the absorption o,t' incident ultraviolet
-------
-------
light, with the consequent deviation from linear!ty. Where work
is required at dye concentrations greater than the maximum range
selection of the instrument, a neutral density filter may be
used with the secondary filter to decrease sensitivity, i.e,,
extend the range of the fluorometer.
Estimation of amount of tracer required will be the function of
the physical and hydrologic characteristics of the stream, assum-
ing consideration has been given to the various inhibitory mech-
anisms which may be present Mr0 R. L0 O'Connell, Director,
Annapolis Field Station, Chesapeake Bay-Susquehanna River Basins
Project, has suggested a method for estimating dye requirements.
This information is contained in Appendix 11. It should be noted
that where amounts of dye may be critical, e.g., dispersion and/or
comparison with previous studies^ consideration should be given to
the possible variation in dye content of the manufacturer's prep-
arations. It is recommended that samples of the dye be compared
with each other, compensating for differences as required,, On
this basis, the initial dye preparation used could be considered
to be the reference standardซ,
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OBSERVATIONS
I. As stream flow decreases, time for peak concentra-
tion resolution increases
II. Both leading and following edges of the dye front
become diffuse, causing an alteration in the shape of the con-
centration vs. time curve. This alteration results in a positive
displacement in time of both the centroid of mass and the peak
concentration.
III. Using a single injection of tracer, greater dis-
placement and alteration of the shape of the curves are observed
at stations downstream,, Peak concentrations are decreased at
downstream stations; and comparison of curves at various stations
will serve to indicate diffusion and/or inhibitory characteris-
tics of the reach of stream under consideration.,
IV. The time of passage curve for dye may be used to
estimate the time of arrival and probable concentration of waste
at a given point from a single waste injection, such as an ac-
cidental spill. The leading and following edges of the curves
can be used to estimate duration of critical or emergency condi-
tions in the stream,,
V. At present, there appears to be little exploratory
work on other light fast tracers It is suggested that lignin
and/or lignin derivatives might be investigated These compounds
flucresce at the same wave length as the Rhodamines^ and,, based
on their method of preparation, these compounds might be applicable
for use in both acidic and normal stream environments.
VI. It is essential that a field reconnaissance be
made, sites selected, and the stream sampled for calibration and
water quality to determine the feasibility of use of a tracer,
Further determinations should be made at this time for auxiliary
equipment requirements 0
VIIo Estimated tune of travel should be established
for the reaches under consideration, in order to reduce excessive
time requirements in the field.
VIII. Injection of the dye into the environment should
be accomplished in such a manner to insure immediate maximum
dispersion. Addition of concentrated dye preparation without
dilution may result in incomplete dispersion, particularly in
shallow streams, with cdnsequent undesirable effects on
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visualization of both the dye fiont and the shape of the time
of passage curves,,
IX,, An analysis of peak dye concentration should "be
made at the first and each succeeding station to determine if
enough dye exists to insure a measurable quantity at the next
station downstream,, If dye additions are necessary, they should
be made at the time of peak concentration,,
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BlBLlOClRAHff
10 Carpenters J. H.s The Use of flhodamine B as a Field Tracer.
Chesapeake Bay Institute, The Johns Hopkins Universityป
20 Feverstein, D0 L,, and Selleck, R. '&,, Fluorescent, Tracers
for Dispersion Measurements. Journal of the Sanitary
Engineering Division,, A.S.C.Ee> August 1963.,
30 0'Connell? R0 L0 and Walter., Ct, M0, A .Study of Digpgrgion
in Hilo Bay. Hawaii^ U. S, Public Health Service^ Robert A,
Taft Sanitary Engineering Center, Cincinnati, Ohio, (1963).
4. Buchanan^ T. J0|9 Tjjae M__Travel,_o_ฃ.S_Qluble__CQntaminants in
Streams. Journal of the Sanitary Engineering Division,, AoSo
June 19640
5<, 0'Cornell, R. !., et alป, Report of Survey of the Truckee
River., U/S. Public Health Servicey Robert A. Taft Sanitary
Engineering Center, Cincinnati, CMo,. (1962).
6Q O'Connor^ Dc J^ Report __on. Arialysis oi" the Qye Diffusion
Data in the Delaware River jajtuarg;^ Delaware Estuary Compre
hensive Study Technical Report Nou 1, U. S, Public Health
Service^ August 1962,,
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APPENDIX. I
INSTRUMENTS AND BQMEvQiM HJUND MOST SUITABLE
FOR STREAMS IN THE SOSQUEHANNA BASIN
I. Fluorometar - All measurements utilized the Turner
Model 111 fluorometer equipped with"a 20 millimeter continuous
flow curvette door arปd recorder
II. Pump - in the field, a 1/3 HP Lemming Model 2ALS4-
115V submersible pump was utilized.,
Ill, Power Supply - A Baker Heavy Duty generator was
used to provide 11$ volt AC power for instrument, pump, and
lighting requirements, plus 12 volt DC' power for vehicle opera-
tion
IV. Laboratory - A modified Ford Econovan provides
mobility and basic laboratory capability, including' cabinets,,
sinlc^ and sufficient counter space for the fluorometer and its
accessories.,
Vu Irradiation Lamp - Maximum sensitivity was obtained
using a G. E. G4T4/1 lamp as a light source^ plus the proper
excitation and fluorescence filters,,
1
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10
APPENDIX: n
ESTIMATION OF DYE REQUIREMENTS FOR TIME OF TRAVEL STUDIES
An instantaneous release of dye to a river is planned to determine
travel between two points To find the amount of dye to be released,
M
M =
M - Weight of dye in grams
Where:
Cx = Pealc concentration desired at downstream point x
parts per billion
X = Distance between release and monitoring points in
feet
A = Cross sectional area of stream at release point in
square feet
R = Mean depth of stream between release and monitoring
points
N = Manning's coefficient n for stream roughness
For example, in a stream where:
Width = 100 feet
Depth = 4 feet
Cx = 200 ppb (approximately 100 on 30 x scale for
Rhodamine B)
X = 3 miles
R = 4 feet
N = 0.04
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11
APPENDIX II (Continued)
3
l.lxicr
M = 32.6 grams required assuming 100$ dye content by weight
Use M = 33 grams
Dye to be used: Ktiodamine in Acetic Acid - 40$ (weight basis) -
sp0 gray, 1012
Volume of dye (V) = n W /Q) = ?3 milliliters
Use 75 milliliters
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^~*
B
Figure 1
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TABLE OF CONTENTS
Page
INTRODUCTION 1
RESPIROMETER DESIGN 2
METHOD OF OPERATION 3
INTERPRETATION OF DATA U
PRELIMINARY RESULTS OBTAINED 6
CONCLUSION 8
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AN IN-SITU BENTHIC RESPIROMETER
INTRODUCTION
In attempting to describe the oxygen balance of natural
waters, it is essential that all significant sources and sinks of
oxygen be considered. Oxygen uptake by the bottom muds found in
rivers, lakes, and estuaries is such a sink and, in some situations,
a most significant one. It's magnitude, however, is usually dif-
ficult to evaluate with the desired degree of confidence. Most
methods of evaluation in current, use require removal of the muds
from their natural environment for oxygen uptake measurements in
the laboratory. However, it is extremely difficult to reconstruct
the natural layering of solids in a laboratory flask, which would
appear to be a necessary condition for obtaining realistic results.
In addition, the interstitial water in bottom sludges is likely to
contain soluble constituents having a high oxygen demand, and these
materials may be lost or diluted in collecting the sludge sample.
The quality of water overlying the sludges may also influence oxygen
uptake rates in the natural environment. For these reasons a benthic
respirometer capable of measuring the oxygen uptake rates of bottom
muds in-situ is highly desirable. Such a device has been developed
and is described below.
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2
RESPIROMETER DESIGN
The operating principle of the respirometer is to trap and
confine a volume of overlying water in contact with the bottom while
observing any reduction in dissolved oxygen content resulting from
uptake by the bottom muds. The apparatus shown schematically in
Figure JL was designed to accomplish this purpose. The respirometer
chamber was constructed from a 21-inch length of 19-inch diameter
metal pipe having a 1/16-inch wall thickness and a flange on both
ends. The pipe was cut lengthwise along its centerline, creating
two sectionseach of which could serve as a shell of a respirometer
chamber. The semi-circular ends were closed with metal plates, and
a U-inch right angle metal section was attached around the periphery
of the 19-inch by 21-inch rectangular opening, providing a vertical
cutting edge and a horizontal supporting ledge. A lifting ring and
a submersible 12-volt pump were attached to the exterior of the
curved top surface. A hole was drilled through the top of the respi-
rometer to receive the pump intake line, while the pump discharge
was conducted by a length of plastic tubing to a flexible U-liter
rubber bag. Another piece of plastic tubing connects this bag to
the respirometer chamber, entering through a port in the end wall.
The presence of the flexible bag permits the removal of samples from
the system without the necessity for replacement of an equivalent
volume of water.
The respirometer chamber joints were sealed with sheet rubber
gasket material to prevent leakage, and all metal surfaces were coated
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3
with an epoxy paint before assembly to minimize the possibility of
corrosion accompanied by oxygen loss. All elements of the system
were made impervious, to Light to eliminate possible photcsynthetic
effects.
METHOD OF OPERATION
The respirometer is lowered through the water from a pier
or boat using the lifting ring. The submersible pump, powered by a
battery at the water's surface, is operated while the chamber is
lowered,, so as to empty it of the surface water originally present.
The chamber is lowered to within a foot of the bottom and held there
for a few minutes while the pump draws bottom waters into the chamber
and tubing. The pump discharge tubing is then connected to the
flexible bag from which the flow is returned to the respirometer
The recirculating system may be purged of air through the sampling
port located in the tubing line at the surface. The respirometer is
then lowered carefully to the bottom The weight of the chamber
(approximately 38 pounds) forces the cutting edge into the bottom,
while the supporting ledge prevents the chamber from sinking below
the sediment surface
The pump is run continuously throughout the test, providing
continuous mixing of the water in the chamber. The pump discharge
rate may be varied to simulate the degree of turbulence believed to
exist at the water-bottom interface. Since the water pumped from
the chamber is recirculated, no significant change in the volume of
pressure of the chamber contents will ocsur.
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u
The test period begins when samples are initially taken from
the sampling port at the surface for dissolved oxygen analyses. Du-
plicate 300 ml, samples are collected for immediate analysis, while
another pair of samples are withdrawn into dark bottles which are
incubated in the water during the period of the test. Another pair
of samples are withdrawn at the end of the test period. Dissolved
oxygen is measured in this final pair and in the incubated dark bottles,
As an alternate to this method of operation, a dissolved
oxygen probe may be inserted into the recirculation system. The use
of a probe would permit continuous measurements to be taken without
the necessity for removing samples from the system. The flexible bag
and sampling port shown in Figure JL could be eliminated.
With either of these measurement systems, it is clear that
some dissolved oxygen must be initially present in the water overly-
ing the bottom in order to conduct a test. Where anaerobic waters
are encountered, the approach described could be modified so as to
artificially introduce oxygenated waters into the respirometer.
INTERPRETATION OF DATA
The difference between the initial and final dissolved oxygen
concentrations observed in the respirometer is directly related to
oxygen uptake by the bottom. This change in concentration may be
expressed as an areal uptake rate (S) if the confined water volume (V)
and bottom area (A) are known. In the expression;
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5
? (Ci - Cf} V
S (gm/rn /day) = ^ A (l)
t is the test period in days; C. and C are, respectively, the initial
and final observed dissolved oxygen concentrations (as milligrams per
liter or grams per cubic meter), and V and A are expressed in metric
3 2
units, being O.OU3 m and 0.276 m , respectively, for the respirometer
previously described. The oxygen concentrations of the incubated dark
bottles, as determined at the end of the test period, may be substituted
in equation (l) for C. if a significant difference exists between these
values. This difference represents oxygen uptake of the waters over-
lying the bottom and will usually be negligibly small for a short test
period.
The length of test period required depends both on the size of
the respirometer and the uptake rate being measured. A minimum oxygen
change of 1 mg/1 is considered desirable for reliable results, and this
also influences the test period length. For the respirometer described
above, the length of test required to give a 1 mg/1 oxygen change is
given as a function of uptake in Figure 2_.
In order to minimize the length of the test period, the ratio
of confined volume to bottom surface area or the effective depth
should be minimized. This consideration influenced the respirometer
design adopted, in that the semi-circular cross-section of the chamber
has a relatively low volume:area ratio. The effective depth of this
cross-section is y- or 0.78^ times the radius of the semi-circle.
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The units used to express the areal uptake rate (grams/square
meter/day) can be readily converted to volumetric units "by dividing
S by the depth of the overlying water in meters. This quotient has
the units gm/m /day, or mg/liter/day, and refers to the DO change
expected in the full depth of the vater due to the oxygen sink at
the bottom.
PRELIMINARY RESULTS OBTAINED
The benthic respirometer shown in Figure !_was used to measure
bottom uptake rates in the Potomac estuary near Washington, D. C., dur-
ing August and September, 1965. A total of 25 tests were carried out
in a twenty-mile length of the estuary. Uptake rates from 0.15 to 8.5
gms/square meter/day were found at water temperatures in the range of
22.5 to 33 degrees centigrade. To provide a basis for studying the
longitudinal variation in uptake rates along the estuary, the results
were converted to a common temperature of 25ฐ The temperature correc-
tion factor of 6.5 per cent per degree centigrade, as determined by
Fair for benthal decomposition, was used. At this common temperature,
the adjusted uptake rates averaged 2.5 gms/square meter/day. Slightly
higher values were usually found near the main waste source, and rates
below 1 gin/square meter/day were found at distances five miles above
and fifteen miles below this location.
Since there is no known method for absolute measurement of
in-situ benthal oxygen demands, it is not possible to make any state-
ment regarding the accuracy of the measurements obtained using the
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7
benthic respirometer, The magnitude of the rates observed, however,
generally fall within the range of those believed to exist in natural
P
water subject to pollutional loads, O'Connor , for example, states
that typical values range from 1 to 10 grams/square meter/day with
the majority of values lying between 3 "to 5 grams/square meter/day
for relatively polluted streams. These conclusions were apparently
based both on laboratory studies and analyses of field stream survey
data.
Certain operational difficulties were encountered in using the
benthic respirometer. These were generally associated with disturbing
the surface sediment layer and led to anomalous test results. It was
found that the respirometer must be brought into contact with the
bottom very carefully, to avoid putting any of the settled solids into
suspension.
The water recirculation rate used in the Potomac tests was
estimated from measurements of the time required to fill a sample
bottle of known volume through the sampling port at the water surface.
The approximate horizontal velocity over the bottom muds confined by
the chamber was calculated from this flow rate to be less than 0.5
feet per minute. Such a velocity is not believed to be sufficient to
unduly agitate the surface sediment layer,. This conclusion was sup-
ported by the absence of unusual amounts of suspended material in the
water samples removed from the system for oxygen analyses during the
tests.
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8
An initial concern in the operation of the respirometer was
whether an effective seal with the bottom could be obtained. This is
essential to prevent the exchange of the oxygen-depressed chamber
contents with the surrounding waters. To investigate this condition,
samples of unconfined water were routinely collected near the respi-
rometer at the beginning and end of a test. Changes in dissolved
oxygen content occurring within the respirometer were not reflected
in the external samples, and differences greater than 1 mg/1 between
the two samples were frequently observed at the end of a test. It
was concluded that for the particular respirometer and bottom mud
characteristics of these tests, an effective seal was obtained. The
weight of the respirometer shown in Figure _!, being 38 pounds in air,
undoubtedly was an important factor in maintaining this condition
throughout a test.
CONCLUSION
Preliminary field tests of an in-situ benthic respirometer
yielded reasonable results which are believed to be a satisfactory
measure of the benthal oxygen demands actually occurring in the waters
studied. Further tests of this measurement technique under a variety
of conditions would be desirable to determine more precisely its reli-
ability and general applicability.
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BIBLIOGRAPHY
1. Fair, G. M.; Moore, E. W.; and Thomas, H. A., Jr., "The Natural
Purification of River Muds and Pollutional Sediments," Sewage
Works Journal, 13, 270 (l9^l).
2. O'Connor, D. J., "Stream and Estuarine Analysis," Mimeo notes,
Summer Institute, Manhattan College, New York, N. Y. (June 196U)
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LIFT RING
4 ANGLE
SAMPLE
PORTS
AT
SURFACE
4 ANGLE
-* 19'
4 ANGLE
BENTHAL OXYGEN DEMAND MEASUREMENT SYSTEM
FIGURE I
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EFFECTIVE DEPTH OF
RESPIROMETER * 0.156
meters
0 2 4 6 8 IO
BOTTOM UPTAKE RATE, S(gm/m2/doy)
TEST PERIOD REQUIRED FOR Ippm D. 0. DROP
FIGURE 2
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TABLE OF CONTENTS
Page
INTRODUCTION ........... 1
THE SEGMENTED ESTUARY MODEL 3
TEST CONDITIONS 6
Dye Source ........... 6
Observed Dye Concentrations ...... 8
Segment Volumes 10
Dye Loss Rate Constant 12
Net Water Flow ih
Turbulent Exchange Factor ...... 18
Proportionality Factor .... 20
ANALOG SIMULATION ...... ... 21
DISCUSSION . 2k
CONCLUSIONS 29
ACKNOWLEDGMENT 30
BIBLIOGRAPHY 31
APPENDIX ......... 32
LIST OF TABLES
Table 1 Segment Volumes 11
Table 2 Calculated Net Advective Flows 16
Table 3 Model ParametersFinal Analog Computation ... 23
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LIST OF FIGURES
(Figures Follow Page 35)
1 Potomac River Study Area
2 Dye Discharge Rate
3 Dye Loss Rate
k Observed and Calculated Dye Concentrations vs Time
(Segments 1, 2, 3, and *0
5 Observed and Calculated Dye Concentrations vs Time
(Segment 5)
6 Observed and Calculated Dye Concentrations vs Time
(Segment 6)
7 Observed and Calculated Dye Concentrations vs Time
(Segments 7 and 8)
8 Observed and Calculated Dye Concentrations vs Time
(Segments 9 and 10)
9 Observed and Calculated Dye Concentrations vs Time
(Segments 11 and 12)
10 Observed and Calculated Dye Concentrations vs Time
(Segments 13 and lh)
11 Observed and Calculated Dye Concentrations vs Time
(Segments 15 and 16)
12 Daily Stream FlowPotomac River at Washington, D. C.,
June-July 1965
13 120 Amplifier PACE Model 231-R
lU Chloride Concentration vs Distance from Chain Bridge
15 Dispersion Coefficient vs Distance from Chain Bridge
16 Effect of River Flow on Pollutant Distribution in
Potomac estuary
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A STUDY OF TIDAL DISPERSION IN THE POTOMAC RIVER
BY
L. J. Hetling and R. L. O'Connell
INTRODUCTION
The Chesapeake Bay-Susquehanna River Basins Project of
the Federal Water Pollution Control Administration, U. S. Depart-
'ment of the Interior has as its primary objective the development
of a comprehensive program for water pollution control in the
Chesapeake Bay drainage basin. The lU,170-square mile Potomac
River Basin, second in size only to that of the Susquehanna River
(27,000 square miles) in this drainage area, possesses a variety
of water pollution problems which are most significant perhaps in
that portion of the tidal estuary near Washington, D. C. (Figure
1). To permit a better understanding of this complex body of
water and to provide a satisfactory means for analysis of present
and future pollution problems and selection of optimum control
methods, an attempt has been made to model the system in mathe-
matical terms.
To mathematically describe the fate of pollutants enter-
ing such a tidal system, knowledge of its turbulent dispersion
properties is required. To gather this type of information for
the upper Potomac estuary, a dye tracer study was carried out by
the Project during the 3^-day period from June 10 to July lU, 1965.
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The purpose of this paper is to describe the procedure
used in this large scale tracer experiment, the results obtained,
the methods used in the analysis of these results, and, finally,
to present the conclusions reached regarding turbulent dispersion
properties of this tidal system.
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THE SEGMENTED ESTUARY MODEL
The mathematical model employed in this study was that
7
developed by Thomann . This model consists of a system of "n"
equations, each describing a mass balance of the material being
studied for each of the "n" segments of an estuary. For an
estuary where good vertical and lateral mixing may be assumed,
these segments are selected along the longitudinal axis of the
estuary. The segmentation of the Potomac estuary, as used in
this tracer study, is shown in Figure 1.
The mass balance over each of the 16 segments shown in
Figure 1 includes terms describing changes in dye concentration
caused by advection, dispersion, losses, and, in the case of the
segment to which the dye was added, a dye source. A mass balance
constructed for the "i" th segment takes the form:
dC.
- C.) + E.+1 (C.+1 - C.)
-d V. C. + P. (l)
11 i v '
where
V. = volume of "i" th_ segment, cubic feet (cf)
C. = mean dye concentration in "i" th segment (ib/cf)
1
Q. = net waterflow across the upstream boundary of the
1 "i" th segment (cf/day)
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ฃ. = a dimensionless proportionality factor used to
estimate concentration at upper boundary of the
"i" th segment
E. = turbulent exchange factor for upstream boundary
1 of the "i" tb_ segment (cf/day)
d = dye loss rate constant (day )
P. = rate of dye addition from external source (ibs/day)
t = time (days)
Since for this study sixteen estuary segments vere employed,
a like number of expressions similar to equation (l) were obtained.
This system of sixteen linear first order, non-homogeneous, ordinary
differential equations may be solved simultaneously by numerical
methods using a digital computer or by programing the equations on
a relatively large analog computer. In either case, all terms of
the equations must be known in order to solve for the dye concen-
tration of each segment as a function of time. In this dispersion
experiment, however, the segment concentrations were known from the
results of sampling the estuary, while the turbulent exchange factor,
"E," for each segment was unknown. It was necessary, therefore, to
solve for the "E.'s" by trial and error methods. By this procedure,
initial values for "E." were chosen and a solution for "C." obtained.
The calculated concentrations were then compared with observed
values, suitable adjustments made to the "E." values, and a new
solution for "C." found. This process was repeated until a satis-
factory agreement between observed and calculated concentrations was
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found. Because of the repetitive calculation-comparison process
required, analysis by analog computer was considered to be the
most efficacious method for obtaining a solution in this case.
In the following sections, each of the terms of equation
(l) is discussed in terms of the dye tracer experiment.
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TEST CONDITIONS
Dye Source (P.)
A dye was released into estuary segment 5 via the outfall
sever of the District of Columbia Water Pollution Control Plant
(Blue Plains). This outfall consists of two parallel 90-inch
diameter lines and extends 900 feet into the estuary from the
eastern shore, terminating at the eastern edge of the shipping
channel in about 17 feet of water at mean tide level (MTL). The
*
dye used was Rhodamine WT , selected for its fluorescent proper-
ties and relatively low affinity for adsorption on particulate
matter. The dye was added as a 20 per cent solution in methanol
to the elutriation wash water discharge sump which rapidly drained
to the outfall sewer line. Travel time in this sewer was esti-
mated to be less than five minutes. Chlorine was not applied to
the waste during the period of these tests.
The dye solution was pumped to the sewer initially at a
rate of 19 milliliters per minute (ml/min.), or approximately 12
pounds of dye/day. It was intended that a constant dye addition
rate be maintained throughout the 13-day dye release period. How-
ever, on two occasions sudden large fluctuations in pressure of
the flushing water line connected to the discharge side of the dye
feed pumps caused the pump ports to jam, and large amounts of dye
See disclaimer at end of paper.
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were released to the estuary in a short period of time. The
actual rate of dye addition is shown in Figure 2. During the
test period, a total of 3^1 pounds of dye was used.
Since dye was added to only one segment of the estuary,
the "P." term in each of the model equations was zero except in
segment 5. In this segment the actual dye addition rate, which
varied with time, as shown in Figure 2, was used as input to the
model.
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Observed Dye Concentrations (C.)
During the 13-day period of the dye release, and for 21
days thereafter, dye concentrations vere measured in the estuary.
Measurements were made using a fluorometer (G. K. Turner & Assoc.)
which was equipped with exitation and emission light filters
designed to selectively measure the fluorescence of the dye being
used. With this tracer measurement system, a sensitivity of 0.01
parts per billion (ppb) may be attained.
Samples were pumped continuously from the estuary to a
moving boat which carried the fluorometer. The estuary waters
were pumped directly to the fluorometer which was equipped with
a recorder so that a continuous record of dye concentrations was
obtained for the waters through which the boat moved. The sample
was withdrawn from 18 inches below the water's surface into a
hollow streamlined metal strut suspended from the side of the
moving boat.
Measurements were made along the complete 25-mile length
of the upper segmented estuary at time of slack water. Two suc-
cessive slack waters were normally measured, so that by averaging
the measurements obtained at a given location, a mean value for
the tidal cycle could be obtained.
In addition to this longitudinal surface sampling, dye
distribution in the vertical and lateral directions was determined
*
See disclaimer at end of paper.
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periodically at each of 32 cross-sections. These cross-sections
were located at varying intervals along the length of the estuary,
being more closely spaced near the dye release point. By means
of this sampling network, an adequate knowledge of the temporal
and spatial distribution of dye in the estuary was obtained.
The dye concentrations found in each segment through the
period of the test are shown in Figures k - 11.
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10
Segment Volumes (V.)
The segment volumes were determined from the latest (1965)
USCGS navigation charts for the Potomac estuary which give sound-
ings at mean low water. The water volumes determined by planimeter-
ing these charts were increased by an appropriate amount to give
estimates of mean tide level volumes. The product of these mean
tide level segment volumes and the mean of the high and low water
dye concentrations shown in Figures h - 11 give the total mass of
dye in each segment during each day of the test. No corrections
were made for the small deviations of the mean tidal elevations
occurring during the period of the test from the long term mean
values upon which the volume calculations were based. The segment
volumes used are given in Table 1.
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11
TABLE 1
SEGMENT VOLUMES
Distance from Chain Bridge
to Upper Boundary of Segment Volume at MTL
/_-T \ /_.ฃ> TI-I~I\
Segment
1
2
3
It
5
6
7
8
9
10
11
12
13
Ik
15
16
Lower Limit
(miles )
3.3
k.Q
5.8
6.7
7.7
11.8
12.8
13.6
Ik. 6
15.9
17.1
18.3
19.3
20. k
21.9
23-5
25.8
(cf x 10" ' )
25.3
30.6
35. k
HO. 7
62.3
67.6
71.8
77.1
8H.O
90.3
96.6
101.9
107.7
115.6
124.1
136.2
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12
Dye Loss Rate Constant (d.)
It was expected that some loss of dye vould occur, pri-
marily due to adsorption on bottom sediments and silt suspended
in the waters of the estuary. This loss was estimated by observ-
ing the change in total dye mass in the estuary over a 20-day
period immediately following the dye release period. Since dye
was observed below the downstream boundary of the most seaward
segment on the 15th day of the test, the sampling network was
extended downstream, as necessary to assure that all of the dye
in the system was being measured. The observed change in dye
mass, as shown in Figure 3, appears to follow first order reac-
tion kinetics. Determination of the slope of the line in Figure
3 yielded a reaction rate constant "d" of 0.03^ per day (base e).
This means that 3.U per cent of the dye present in the estuary
is lost from solution each day, equivalent to a half-life of
2 1
20.k days. These loss rate kinetics have been observed by others '
for similar dyes, although most of the reported values for "d"
exceed that found in the Potomac for Rhodamine WT.
It may be noted from Figure 3 that the total dye mass
found in the estuary on the day following cessation of the dye
release (lUth day of test) was 270 pounds, while the total
amount of dye released was 3^1 pounds. Using a dye loss rate
constant of 0.03^, the dye mass remaining on the lUth day may
be calculated and compared to the observed value to provide an
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13
additional check on the accuracy of the rate constant. The mass
of dye present in the estuary at any time, M , may be calculated
t
from the expression
(2)
vhere t and tp are times since instantaneous dye releases M and
Mp, respectively,- and the other terms as previously defined.
Results of performing this calculation for the l^th day
of the test indicated that 267 pounds of dye should be remaining
in the estuary. Since essentially the same amount of dye (270
pounds ) was actually found to be present at that time , it vould
appear that the value used for "d" is a satisfactory estimate
for the dye loss rate constant.
It should be noted, however, that any dye present in the
estuary at concentrations below the lower limit of the detection
instrument would also appear to have been "lost." The rate con-
stant value found thus reflects this apparent loss as well as
actual losses by adsorption or other mechanisms. Although it is
believed to be small, the significance of this apparent loss has
not been evaluated, and thus, the value determined for "d" must
be considered as an upper limit.
-------
-------
Met Water Flow (Q.)
'""" ~"~.._._.,- ]_
The term "Q." refers to the net flow into the "i" th
i ~~~
segment from the adjacent upstream segment, i.e., the net flow
across the i-l,i or upstream boundary of the "i" th segment.
Net flow in the seaward or positive direction across a boundary
occurs as the net result of river inflows, waste discharges,
water withdrawals, and evaporation.
For this study, the inflow to the first segment was taken
as the Potomac River flow reported for the U. S. Geological Survey
gaging station iLeiter Gage) at Washington, D. C. , adjusted for
inflows and evaporation occurring in the 5-8-mile stretch of the
river between the gage and the upper boundary of the first seg-
ment. The daily flow rates reported for this gage during the
study period are shown in Figure 12. These flows, adjusted as
described above, were assumed to occur through all segments of
the upper estuary on the same day they were measured at the gage.
Losses by evaporation from the segmented portion of the
estuary were subtracted from the adjusted river inflow. The
daily evaporat;on loss was calculated for the upper estuary us-
ing Meyer's formula and data from the Washington National Airport
weather station and the District of Columbia Water Quality Monitor-
ing Station at t.'-e Woodrow Wilson Bridge. The calculated net
evaporative loss -eached a maximum of ^00 cfs on one day of the
test, but averagec: 135 cfs for the 25-mile length of the upper
estuary during the ibudy period.
-------
-------
15
There are no significant withdrawals of water from the
upper estuary. Daily inflows of natural drainage to each segment
were calculated based on its tributary area and the average daily
flow per unit area obtained from U. S. Geological Survey records
for the gaging stations shown in Figure 1. A major inflow was
the waste effluent from the District of Columbia Water Pollution
Control Plant which discharged an average flow of 339 cfs to seg-
ment 5 during the study period. Significant waste flows from the
five additional waste treatment plants shown in Figure 1 were also
included. The few remaining waste flows discharged to the estuary
are relatively small in volume and were disregarded.
Summing up these flows gave a net flow rate across each
boundary for each day of the tracer test. Upon examination of
these net flows, it was found that the inflows to the estuary
(excluding the Potomac River flow and the District of Columbia
waste discharge) were approximately balanced by losses due to
evaporation. Therefore, in order to reduce the number of flow
input functions, Q through Q were taken as being equal to Q ,
the adjusted Potomac River flow, and Q,- through Q s were set
equal to Q^, essentially the adjusted river flow plus the District
of Columbia Water Pollution Control Plant discharge. These net
advective flows are given in Table 2.
The net tidal flow into and out of each segment was as-
sumed to be zero over a complete tidal cycle. No consideration
-------
-------
16
Date
June 10
11
12
13
11+
15
16
17
18
19
20
21
22
23
21+
25
26
27
28
29
30
July
1
2
3
6
7
8
9
10
11
12
13
11+
TABLE 2
CALCULATED NET ADVECTIVE FLOWS (Q.)
(cfs)
1
2
3
1+
5
6
7
8
9
10
11
12
13
Ik
15
16
17
18
19
20
21
22
23
2k
25
26
27
28
29
30
31
32
33
3k
T.6
k390
3881+
3081*
2761
2562
238)4
2367
2377
221+6
2235
2181+
2173
2121+
1883
1962
1932
1790
1661
11+31
1201
1199
1109
1339
1371+
1261+
1397
1301+
1168
1132
1150
1622
291+6
2691
2096
(cfs)
1+831+
1+115
31+88
3106
2937
2778
269!+
2803
2653
2619
2553
2578
2538
2293
21+32
2311+
21+07
2116
201+2
1839
1596
1560
11+70
1760
1727
1733
1826
1693
1597
1535
1611+
3000
3566
3196
2570
-------
-------
IT
was given to the small changes in tidal elevation and, therefore,
tidal flow which occur on succeeding days during a lunar tidal
cycle.
-------
-------
18
Turbulent Exchange Factor (E. )
The turbulent exchange factor "E" is calculated for each
segment boundary from the expression:
K A
Ei
. ^
where the "i" subscript refers to the boundary between segments
i-1 and i, "K" is the longitudinal dispersion coefficient (analo-
gous to the classical Fickian diffusion coefficient, expressed in
areal units per day), "A" is the cross-sectional area of the
boundary plane, and "L" is the segment length.
The above expression is based on Fick's first law of
diffusion, i.e. ,
Ni (Ib/sf/day) = K ~ (k)
where "N" is the rate of mass transfer of substance per unit area
across a boundary where the spatial gradient of the substance is
"dC/dx" ("C" is in Ibs/cf) and "K" is defined as above.
If the mean concentration in two adjacent segments is
assumed to occur at their midpoints, and the gradient between
these midpoints is linear, it can be shown by geometry that:
ac _ ci-i " ci
dx 0.5 (L^ + L.)
Substituting (5) into equation (k) gives:
K (C. - C.)
N. (Ibs/sf/day) = 0.5 fc^ A.) (6)
-------
-------
19
Multiplying equation (6) by the cross-sectional area across which
the turbulent exchange takes place, yields the mass flow rate "D. :"
A. K. (C. - C. )
D. (Ibs/day) = ^(^T.t- (7)
Substituting equation (3) into (7) yields:
which is the expression used in equation (l) to describe the mass
flow of substance across a boundary due to turbulent exchange.
The "E" term, or more specifically "K," was the unknown
parameter which the study was designed to evaluate. The "K" term
as used herein is defined as the coefficient of longitudinal dis-
persion. This term applies to net longitudinal mass transport
resulting not only from turbulent diffusion but also from velocity
and concentration variations in a cross-section. The latter effect
has been shown to be of greater significance in estuary type flows.
It has been assumed that dispersion is analogous to Fickian diffu-
sion with the diffusion coefficient replaced by a dispersion
coefficient.
As mentioned previously, initial values of "K" were assumed
for each boundary. These values were then adjusted to obtain good
agreement of the model output with the dye concentrations observed
in the estuary. The initial values were chosen on an empirical
^
basis and ranged from 1.5 sq mi/day for the boundaries at the
upper end of the estuary to 5.9 sq mi/day at the lowest boundary.
-------
-------
20
Propprtionality Factor (ฃ. )
The proportionality factor "ฃ." is used in the first two
terms of equation (l) that describe the advective movement of dye
into and out of a segment. This mass movement across the i-l,i
boundary due to advection may be expressed simply as the product
of the net advective flow "Q." and the concentration at the
boundary. However, since only the average concentration of the
adjacent segments is considered in the model, the concentration
at the boundary must be calculated. It can be shown by geometry
that for the case of a linear gradient between the midpoints of
two adjacent segments, the concentration at the boundary is given
by the first two terms in brackets in equation (l) where:
i-l i
Equation (9) gives a satisfactory first approximation for the
proportioning factor applicable to the i-l,i boundary. To assure
a realistic solution, however, the following relationship must
be observed:
(10)
To simplify computations where "E" was changed frequently, the
inequality given by (10) was treated as an equality. So long as
the proportionality factor "ฃ" remains within the lower limit
defined by equation (10) and an upper limit of unity, the solu-
tions obtained by the model are relatively insensitive to the
value chosen for "ฃ."
-------
-------
21
ANALOG SIMULATION
The set of sixteen differential equations similar to
*
equation (l) were programed on an EAI 231-R analog computer,
pictured in Figure 13. The output selected from the computer
was a record of concentration versus time for each of the six-
teen segments of the estuary. These calculated concentration-
time histories were automatically plotted as a continuous ink
trace on graph paper, as shown in Figures h - 11. The other two
lines on these plots describe dye concentrations observed in each
segment at high and low slack water. Repeated solutions were
obtained by the computer for each different set of "K" values
supplied as input. The objective of each succeeding run was to
bring the ink trace output of the computer closer to a point
midway between the observed high and low slack water values.
The set of "K" (and associated "ฃ") values which gave the best
fit are shown in Table 3.
In carrying out such computations, it is necessary to
specify the proper initial and boundary conditions for the test.
Prior to the start of the dye release there is, of course, no dye
present in the estuary and the "C.'s" are all initially set to
zero. For the upper and lower boundaries of the system, the
concentration-time histories actually observed were used as the
boundary condition input function. Since no dye was ever found
*
See disclaimer at end of paper.
-------
-------
22
at the upper boundary of segment 1, the upper boundary condition
vas zero throughout the test. The lower boundary condition vas
likewise zero until the 15th day of the test when dye was found
there. The dye concentration at the lower boundary then gradually
increased over the succeeding twelve days when a relatively steady
level was maintained for the remainder of the test period.
-------
-------
23
TABLE 3
MODEL PARAMETERS
FINAL ANALOG COMPUTATION
i
1
2
3
U
5
6
7
8
9
10
11
12
13
lU
15
16
17
K.
i
(sq mi/day)
0
0.2
0.2
0.2
0.25
0.3
0.3
o.i*
Q.k
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
fi.
1.0
0.95
0.94
0.92
0.93
0.5
0.88
0.70
0.91*
0.88
0.77
0.88
0.84
0.85
0.87
0.89
0.89
-------
-------
DISCUSSION
In general, the final curves obtained as output from the
analog computer correspond satisfactorily with the observed data.
Good agreement was obtained for the segments at and near the dis-
charge point during the dye release period when changes in dye
concentration took place most rapidly. In the six segments just
below the discharge point, there was an obvious tendency for the
computed concentrations to drop off faster toward the end of the
test than was actually observed. No reasonable manipulation of
the dispersion coefficients was capable of eliminating this anomaly.
It was concluded that this effect was produced by the two large
instantaneous dye releases which occurred midway through the dye
discharge period, as shown in Figure 2. Quite possibly, some
significant portion of this large amount of dye was trapped in
the coves and inlets along the shoreline near the release point.
This entrapped dye could then have fed slowly back into the main
channel of the estuary and thereby maintained higher dye concen-
trations for a longer period of time than otherwise would have
occurred. This effect has also been observed in hydraulic model
studies when instantaneous dye releases were carried out . It is
also possible that the upper limit value used for the dye loss rate
constant was too large. This would tend to cause the concentra-
tions calculated for the later stages of the test period to be
smaller than those observed.
-------
-------
25
The variations in river flow during the study period and
the superposition of the two instantaneous releases upon a con-
tinuous release provided a rather severe simulation test for the
mathematical model. In addition, the simplifying assumptions
required for use of the one-dimensional model were obviously not
met in certain respects. In spite of these factors, the degree
of agreement between calculated and observed dye concentrations
leads to the conclusion that the model with the estuarial disper-
sion properties as finally established can be expected to describe
the distribution of soluble pollutants in the Potomac estuary with
a reasonable degree of accuracy.
During the initial simulations on the analog computer, it
was apparent that good agreement would not be possible near the
discharge point with the segment sizes originally employed. It
was necessary to enlarge segment 5, which received the dye dis-
charge, to approximately three times its original size to achieve
meaningful results. The reason for this is related to the water
movement occurring during a tidal cycle. Dye added as a continu-
ous discharge to oscillating tidal waters will be rapidly distrib-
uted above and below the release point during a single tidal cycle
over a distance equivalent to a tidal excursion, or about four
miles in this case. This distribution, of course, is not related
to net advective movement or dispersion, but simply to the physical
movement of the receiving waters themselves. A similar effect
-------
-------
26
could be achieved by visualizing the receiving water as being
stationary while the discharge pipe moved upstream and downstream
a total distance equivalent to a tidal excursion. It would be
possible to account for this effect in the model in a similar
manner by distributing the tracer inflow to adjacent segments
above and below the outfall. However, this procedure was not
used, and instead, the segment to which the tracer was discharged
was enlarged to half the tidal excursion distance in both the up-
stream and downstream directions.
The range of dispersion coefficients finally determined,
0.2 to 0.6 square miles/day, were significantly lower than those
commonly calculated from observed chloride distributions in more
brackish waters. This is in agreement with the findings of Harle-
man and others that the dispersion coefficients found in saline
waters are strongly influenced by longitudinal density currents.
This circulatory movement which occurs where vertical salinity
gradients exist is the result of upstream movement of the denser
bottom waters and downstream flow of the less saline surface waters.
This type of gravitational circulation would tend to be reflected
in higher dispersion coefficients in the classical advection-
diffusion model such as employed in this study.
Estuary chloride concentrations measured during the tracer
test are shown in Figure lU. The low concentrations of chlorides
measured in the study area indicate that the density current effects
-------
-------
27
mentioned above would not be expected in the upper Potomac estu-
ary during the test period. Since salinity steadily increases
downstream toward the Bay, a downstream rise in the dispersion
coefficient might also be expected. This was the case, as shown
in Figure 15. The higher values shown for the estuary below the
point where the tracer study terminated were obtained from anal-
ysis of historical chloride records using a digital computer
solution of the model. The solid line in Figure 15 represents
a visual approximation of a. line of best fit to both sets of data
and will be used in future calculations requiring solution of the
model. The dramatic change in the value of the dispersion coef-
ficient over the upper ^0 miles of the Potomac estuary illustrates
the hazards involved in extrapolating brackish water dispersion
phenomena to tidal fresh waters.
The knowledge of dispersion characteristics of the upper
Potomac estuary which was gained in this study will permit the
mathematical model described previously to be used with a reason-
able degree of confidence in analysis of the water pollution
control problems of this area. One such use, for example, would
be an examination of the influence of river inflow upon the dis-
tribution of pollutants in the estuary. Using the dispersion
coefficients described by the smooth curve in Figure 15, a digital
solution of the model for various rates of fresh water inflow
produced the family of curves shown in Figure l6. The same set
-------
-------
28
of dispersion coefficients was used for each river inflow investi-
gated, since it is not known to what extent the magnitude of net
advective flow may affect the value of the dispersion coefficient.
These effects, however, are not believed to be significant over
the range of flows shown in Figure 15, based on their relatively
small contribution to the total tidal flow which is experienced
in the estuary.
In these calculations, the pollutant was assumed to enter
the estuary ten miles below Chain Bridge, which is the location of
the District of Columbia Water Pollution Control Plant effluent
discharge. The pollutant is non-conservative with a first-order
decay rate constant of 0.23 per day (base e) comparable to the
rate of exertion of the biochemical oxygen demand of organic
materials in waste effluents. A waste flow of 350 cfs also
enters the estuary at the pollutant discharge point. The condi-
tions depicted are those which would exist at steady state.
Figure 16 shows that the magnitude of pollutant concentra-
tions in the estuary is influenced by the amount of flow entering
from the Potomac River, and that this influence varies depending
upon the distance below the head of the estuary. This type of in-
formation, of course, is extremely useful in conducting a rational
examination of the benefits of flow regulation as well as various
other pollution control measures which must be considered before
the optimum program can be selected.
-------
-------
29
CONCLUSIONS
1. The segmented estuary model satisfactorily describes
the distribution of an artificially introduced tracer in the up-
per 25 miles of the Potomac estuary and, similarly, can be used
to predict the distribution of soluble pollutants which may be
introduced in this area.
2. The turbulent dispersion characteristics found dur-
ing the period of this study are best described by coefficients
which increase from 0.2 sq mi/day near the head of tide to about
1.0 sq mi/day at a distance of 25 miles downstream.
3. The loss of Rhodamine WT dye found in the relatively
fresh waters of the upper Potomac estuary can be described by a
first order reaction rate constant which has an upper limit of
O.Q3h day"1.
Mention of products and manufacturers is for identification
only and does not imply endorsement by the Federal Water
Pollution Control Administration and the U. S. Department
of the Interior.
-------
-------
30
ACKNOWLEDGMENT
The cooperation and assistance rendered "by Messrs. A.
Fay and H. Schreiber of the District of Columbia Department of
Sanitary Engineering were invaluable to the conduct of this study
and are gratefully acknowledged.
-------
-------
31
BIBLIOGRAPHY
1. Feuerstein, D. L. and Selleck, R. E. , "Fluorescent Tracers for
Dispersion Measurements," Journal of the Sanitary Engineering
Division, American Society of Civil Engineers, Vol. 89, No. SAh,
pp. 1-22, August 1963.
2. Gunnerson, Charles G. and McCullough, Charles A., "Limitations
of Rhodamine B and Pontacyl Brilliant Pink B as Tracers in
Estuarine Water," presented at Symposium on Diffusion in Oceans
and Fresh Waters, Lamont Geological Observatory, Palisades, New
York, August 31 - September 2, 196k.
3. Harleman, D. R. F., "The Significance of Longitudinal Dispersion
in the Analysis of Pollution in Estuaries," presented at the
Second International Conference on Water Pollution Research,
Tokyo, Japan, August 1963.
k. Hetling, Leo J. and O'Connell, Richard L., "Estimating Diffusion
Characteristics in Tidal Waters," Water and Sewage Works, Vol.
112, No. 10, pp. 378-380, October 1965.
5. Holley, E. R. , Jr. and Harleman, D. F., "Dispersion of Estuary
Type Flows," MIT Hydrodynamics Laboratory Report No. jk,
Cambridge, Massachusetts, January 1965ฐ
6. Pritchard, D. W., "The Movement and Mixing of Contaminants in
Tidal Estuaries," Proceedings, First International Conference
on Waste Disposal in the Marine Environment, p. 512, Pergamon
Press, Inc., New York, July 1959.
7. Thomann, Robert V., "Mathematical Model for Dissolved Oxygen,"
Journal of the Sanitary Engineering Division, American Society
of Civil Engineers, Vol. 89, No. SA5, Proc. Paper 3680, pp.
1-30, October 1963.
-------
-------
32
APPENDIX A
Procedure Used to Reduce and
Validate Observed Dye Measurements
SLACK RUN MEASUREMENTS
1. Slack water run fluorometer recorder tapes were
digitized at lA-inch intervals. With a tape speed
of 30 inches/hour and a boat speed of approximately
25 miles/hour, readings were obtained at approximately
1000-foot intervals along the length of the estuary
at low and high slack water for almost every day of
the test.
2. These digitized fluorometer readings were converted
to dye concentrations by using appropriate calibra-
tion curves and correcting for water temperature.
3. Slack water dye concentrations were plotted against
distance along the estuary. This type of plot is
referred to as Figure A in the succeeding discussion.
h. From the Figure A plots , two plots of dye concentra-
tion versus time (days) were constructed for each of
32 points along the estuary, one for low water slacks
(Figure B) and one for high water slacks (Figure C).
5. Background (apparent) dye concentrations were then
subtracted from the Figure B and C plots.
-------
-------
33
CROSS-SECTION MEASUREMENTS
6. The fluorometer readings obtained at each of 32 cross-
sections were converted to dye concentrations as in
step 2 above. These dye measurements obtained laterally
across the estuary and vertically through the water
column were contoured at each cross-section.
T. The average concentration in each cross-section was
determined by planimetering the contour plot and
calculating a weighted average of the planimetered
areas.
ADJUSTMENT OF SLACK WATER CONCENTRATIONS
8. For each day of the test period, a mean concentration
was available at each of 32 cross-sections during
either low or high water slack (step 7). The ratio,
R, of each mean cross-section concentration to the
appropriate slack run concentration found at that
cross-section and slack water (from Figure B or C)
was determined.
9. For each cross-section the ratio R (step 8) was
plotted against time (date) as Figure D and a smooth
curve was drawn through these points.
10. Taking values from Figure D, the ratio R was plotted
against distance along the estuary, and a smooth
curve drawn through these points (Figure E).
-------
-------
31*
11. Step 9 was repeated using data from Figure E. Steps
9, 10, and 11 were carried out to average R over both
space and time.
12. The R values obtained in Step 11 were used to convert
all slack run concentrations in Figures B and C to
mean concentrations applicable to the complete cross-
section.
13- The mean concentrations obtained in step 12 were
plotted against distance along the estuary. Two
plots were developed for each day of the test period;
one each for low (Figure F) and high (Figure G) slack
water.
lU. The dye concentrations given in Figures F and G were
used to determine the mass of dye in each of 16 pre-
viously selected longitudinal volume segments. The
total mass of dye in the estuary at a given time was
found by adding the calculated mass in each segment.
15- For the period following the end of the dye release
when the total amount of dye in the estuary should no
longer be changing, the logarithm of the calculated
total mass was plotted against time. The downward
slope of this line is a measure of the rate (K) of
dye loss in the estuary due to adsorption on silt,
photochemical decay, and possibly other mechanisms.
-------
-------
35
l6. The mass of dye, ฃM, which should have been present
in the estuary each day of the test was calculated
as follows:
_.. lr / . ~K."C \ _. ""iC'G
ZM. = (i - e )+M.e
0 IV 1
where P = constant dye discharge rate
M. = instantaneous dye releases
k = dye decay rate
i
t ,t = elapsed time
IT- The mean segment dye concentrations (Figures F and G)
were adjusted by multiplying them by the ratio of the
calculated dye mass (EM ) to the observed dye mass
"C
(step Ik) for each segment and each slack water. This
correction resulted in 32 plots of final validated
mean segment concentrations against time; a high and
low water slack plot for each of l6 volume segments.
-------
-------
\ LEGEND
PENNSYLVANIA
LOCATION MAP
= MAJOR WASTE
TREATMENT PLANT
= ESTUARY SEGMENTS
= GAGING STATIONS
LITTLE FALLS BRANCH-
BETHE5DA, MD
POTOMAC RIVER-
WASHINGTON, D C
ROCK CR -SHERRILL DRIVE-
WASHINGTON, D C
N E BR ANACOSTIA RIVER-
RIVERDALE, MD
N W BR ANACOSTIA RIVER-
HVATESVILLE , MD
FOURMILE RUN-
ALEXANDRIA, VA
LITTLE PIMMIT RUN -
ALEXANDRIA, VA
CAMERON RUN-
ALEXANDRIA, VA,
HENSON CREEK -
OXEN HILL , MD
POHICK CREEK-
LORTON, VA
MATTAWOMAN CREEK-
PO MON KEY, MD
DISTRICT OF COLUMBIA
ARLINGTON COUNTY
ALEXANDRIA SANITATION
AUTHORITY
FAIRFAX COUNTY - WESTGATE
PLANT
FAIRFAX COUNTY - LITTLE
HUNTING CREEK PLANT
FAIRFAX COUNTY - DOGUE
CREEK PL ANT
POTOMAC RIVER STUDY AREA
FIGURE 1
-------
-------
1 1 1 1 1 1 1 1 1 1
UJ.
h-
UJ
X
o
co
Q
UJ
n
*
to
CM
7
o
t-
UJ
1-
oo
u_
N o
>-
(S> <
Q
m
t
ro
CM
_
O OฐOOOOO Q O O
O OO^^f CM 0 CO CO ^ CM
FIGURE 2
-------
-------
DYE LOSS RATE
SLOPE (d) = 0.034
33
DAY OF TEST
FIGURE 3
-------
-------
5
15
UJ
U)
>
en
z
o
UJ
o
o
o
>-
Q
O
UJ
13
O
O
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z
0
UJ
>
CE
UJ
in
CD
o
in
o
CM
1-
T
LU
S
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en
c
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(
0-
ro
CM
O
o>
(0
^~
CM
CJ
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-
1
to
h-
SEGMEf
d
d
1
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\
*
ro
CJ
O
CO
CO
ID
CM
-------
(qdd)
3 Ad
-------
I-
10
2
O
h-
<
CE
O
2
O
O
0
UJ
CJ
Q
2
Q
UJ
>
Ct
UJ
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o
(qdd)
NOIlVaiN3DNOD
axa
-------
3AQ
-------
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H
<
or
o
z
o
o
UJ
o
o
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1-
o
z
o
UJ
>
(T
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(O
CD
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(E
in
o
(qdd) NOIlVdlNSDNOD 3AQ
-------
(qdd) NOI1VH1N30NO3 3AQ
-------
llj
co
z
g
t-
-
Q
Q
LJ
13
O
O
O
UJ
CO
CD
o
>-
<
Q
(qdd) NOIlVaiNBONOD
3AO
-------
2
t-
CO
z
o
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o
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CD
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(qdd)
NOI1VUJ.N3DNOO
-------
ซ*-
o
O
4750
450O
4250
4OOO-
3750-
3500-
3250-
3000-
2750H
250O-
225O-
< 200O-
LU
CT
(/)
1750-1
I50O-
I25O-
IOOO-
750-
5OO-
250-
J\
DAILY STREAM FLOW
POTOMAC RIVER AT WASH., D.C.
JUNE - JULY 1965
STUDY PERIOD
10 15
JUNE
20 25 301
10 15
- JULY
20 25 3O
DATE
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A MATHEMATICAL MODEL FOR THE POTOMAC RIVER--
WHAT IT HAS DONE AND WHAT IT CAN DO
"In a comprehensive water pollution program it is not suf-
ficient to know what the existing situation is. To operate ration-
ally and efficiently the program must be able to forecast water
quality and predict what will happen if waste loads are changed or
other control measures are taken."-1- The most significant area with-
in the Chesapeake Bay-Susquehanna River Basins Project study area
is probably the Potomac estuary in the Washington Metropolitan Area.
To satisfy this need for prediction capability, it was
necessary to develop a mathematical model capable of simulating
water quality in the Potomac River estuary.
Several models capable of simulating water quality in an
estuary have been developed. After detailed investigation of the
models available, the segmented estuary model developed by Dr. Robert
Thomann while he was employed by the Federal Wnter Pollution Control
Administration at the Delaware Estuary Comprehensive Project was
selected as the one which most nearly conformed to the requirements
of the Project. The model is highly flexible, capable of being
utilized to describe any conservative or nonconservative substance.
Solutions are available for both transient and steady state condi-
tions. Its accuracy is sufficient for engineering design purposes.
Coulter, James B. "What Is A Comprehensive Water Pollution Control
Program?" Journal Water Pollution Control Federation, Vol. 38,
No. 6, pp. 1011-1022, June 1966.
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2
Wait a minute. What am I talking aboutmathematical models,
simulation, conservative, nonconservative, steady state, transient,
engineering design
This technical jargon of a new breed of engineers now stands
in the way of the use of many new techniques which make us capable of
better design and operation of the huge public facilities now con-
sidered as necessary to control water quality.
What I would like to do here is to describe in simple, under-
standable terms what a mathematical model for prediction of water
quality in the Potomac estuary means, the progress made in its develop.
ment to date, and its possible future uses.
A scientific model is a representation of some subject of
inquiry. In our case, it is the quality of water in the estuary.
Perhaps the most vivid examples of scientific models are the physical
models of river systems and estuaries constru :ted and operated by the
U. S, Corps of Engineers at Vicksburg, Mississippi, These are actual
scale models of the estuary with every significant detail built in.
With a machine capable of simulating tides and pumps discharging water
into the estuary to simulate river inflow, all of the major physi 'al
properties of the actual estuary are represented. These include such
things as salinity distribution, tidal heights, and currents. With
this model operating, it is possible to evaluate the effects of such
physical structures as jetties and piers on currents, sediment dis-
tribution, dredging needs, etc. Since the time scale is approximately
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3
1 to 100, it is possible to evaluate effects which would take years
to occur in the estuary by operating the model for a few days.
A mathematical model is similar to the physical model in
concept. But, in a mathematical model, instead of using concrete,
the physical system is represented by equations which describe all
of its significant details.
Anyone who has a checking account works with a mathematical
model. All deposits are positives, and all withdrawals are negatives.
Monthly service charges and a charge per check further completes the
model. Using technical jargon we can say that the model has a lower
limit (or boundusing the correct mathematical term) in that a
negative balance cannot in theory exist. Knowledge of all the inputs
(deposits and withdrawals), the initial conditions (original balance)
and other sources and sinks (service charges), it is possible to com-
pute the balance at any time (a transient model).
In the same way, by proper bookkeeping and a knowledge of
bounds or limits, inputs, initial condition, sources and sinks, it
is possible to develop a set of equations which describe water quality
in the estuary. The number of computations, of course, in this
system when compared with a checking account is enormous. To solve
such a system would require many man-years. But, luckily, most of
the computations are routine addition, subtraction, and multiplica-
tion. Within recent years digital computers have been developed
which can do such routine computations in a fraction of a second.
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u
Properly instructed (programed),, the digital computer makes possible
solutions of the system available in minutes.
A key step in the development of any model is its verifica-
tion, i.e., to check and see if the model truly simulates water
quality. This involves a comparison of measured or observed values
with compared values
A checking account is verified every so often when a state-
ment is received from the bank. When we compare the balance in our
checkbook with the balance in the bank statement, we find time after
time that we made a mistake. More often than not, it is a blunder;
an input (deposit or withdrawal) was forgotten, the bank service
charge was changed, or perhaps even the "bank made a mistake
This is what we have been doing with the Potomac Estuary
Model for the past few years. For each water quality parameter we
started by writing the equations utilizing all the inputs which we
felt would affect the given water quality parameter, Then, the model
(equations) would be solved and compared with what is actually
measured. We would find at first that the calculated values did not
match the measured values We would then search for our mistake and
find that we missed an important input or that a biochemical reaction
which was assumed to occur did not occur. By this process of trial
and error, we have finally arrived at what we have now--a verified
model.
I would like to describe a large-scale experiment which was
carried out to verify the model and discuss some other verification
results in order to give you a better feel for its capabilities,
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5
Because most natural water quality parameters are involved
in so many complex chemical, biochemical, and physical reactions,
they do not lend themselves to a good simple test of the model.
Our first serious attempt at verification was a dye diffusion study.
We injected a lipstick dye (Rhodamine WT) into the river at a con-
stant rate and measured the resultant concentrations of dye in the
river. In this case, the only significant input was the dye which
we pumped into the river, and we knew the rate of pumping exactly.
The dye was pumped into the river through the effluent pipes
of the District of Columbia water pollution control plant just above
Marbury Point (Figure l). Figure 2 shows the resulting average dye
concentration measured opposite the plant outfall. The solid center
line shows the concentration of dye predicted by the model, while
the other two lines represent the actual measured concentrations at
high and low water. This nice matching of the observed data and
calculated data did not, of course, occur on our first try with the
model. Many repetitive runs of the model were required to get the
match you see here. Each run required a correction of some error
or a change in a coefficient in order to get closer to the measured
values.
The close agreement between the measured and calculated dye
concentrations found in the above experiment shows that the segmented
estuary model can satisfactorily describe water quality which will
result from the introduction of a simple soluble pollutant into the
estuary if the correct coefficients are known.
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6
Getting to some more complicated parameters, I would like
to show our results in modeling chlorides, dissolved oxygen, and
phosphorus
Figure 3 shows the observed and calculated variation in
chlorides in the estuary at Possum Point near Quantico. Chlorides
enter the estuary by diffusion upstream from the bay. The rate of
diffusion depends on the tidal currents and river flow. Here you
can see that, during the spring months when the river flow is high
and chloride concentration is low and in the late fall when the
river flow is low, the concentration of chlorides rose dramatically.
Figure 3 shows a good match between predicted and observed chloride
values.
Dissolved oxygen (DO) is probably one of the most important
parameters to know when talking about the quality of the estuary.
It is also the most difficult to model, since it can enter or leave
the estuary in so many different ways. Figure k* will give you an
idea of the system which involves DO concentration in an estuary.
Our results in modeling DO, however, have been very encourag-
ing. Figure 5 shows measured and computed values of DO at Woodrow
Wilson Bridge in 1965.
* Thaddeus A0 Wastler, III, Physical Science Coordinator, Chesapeake
Field Station, Chesapeake Bay-Susquehanna River Basins Project,
Federal Water Pollution Control Administration, U. S, Department
of the Interior, Annapolis, Maryland.
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7
One of the problems which has recently become more prominent
in water quality control is algal blooms. The system which controls
algal blooms in estuaries is so complex that no one has even dared to
suggest that a mathematical model of it is possible. I do not think
that such a model is now technologically possible; however, models of
the sub-systems which affect algal blooms are possible. One of our
own efforts in this direction can be seen in Figure 6. A significant
factor in prediction of algal blooms is the concentration of phosphorus,
This preliminary attempt to model phosphorus (as shown in Figure 6)--
while not as good a match as that for DO and chloridesshows promise.
Experiments are now being carried out to refine this model.
This is where we are now. The only question that remains is
what do we use the model for? This is where you come in.
You are the people who will decide the fate of tidewater
Potomac. You represent the engineers, the biologists, the planners,
the heads of the leading citizens' groups who collectively influence
the actions of government. What the model offers you is a method of
trying ideas and learning the consequences without great economic
loss.
Let us look at some examples. A frequently heard proposal
is that the Washington Metropolitan Area use the estuary as a source
of water supply. Another proposal is to clean up the present pollu-
tion in the upper Potomac estuary by pumping all of the waste-water
from the Metropolitan Area to the Chesapeake Bay or the Atlantic
Ocean. Such action would certainly drastically change the biological
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8
and chemical state of the estuary. One of the most significant
changes would be in the concentration of chlorides (sea salts) in
the estuary. The concentration of chlorides which diffuse upstream
from the Chesapeake Bay is affected by the net downstream river flow.
The proposed pumping of waste-waters to the Bay or the ocean would
reverse the direction of flow and, in this way, significantly change
the chloride concentrations. The proposal raises the following
questions! Would the chloride concentrations at the head of the
estuary- be so high as to interfere with the use of the estusry as a
water supply? What would the change in chloride concentrations do
to the ecology of this portion of the estuary? Certainly the type
and quantity of fish would be affected. Would there be crabs and
oysters at Indian Head? Would boat owners be plagued with barnacles
attaching to their craft? What would happen to the oyster industry
now prospering in the lower reaches of the estuary? Certainly any
dramatic changes in chlorides will affect it. These questions can
be answered only if the quality of the water can be known. The
mathematical model gives us a method of obtaining this knowledge.
In answer to the first question, a simulation run using the
chloride model gave the results shown in Figure 7. As you can see
with this figure, such a proposal would cause the chloride levels
in the upper estuary to rise so high that desalinization of the upper
estuary would be necessary to make it fit for drinking water. In
a similar manner, the model can be used to determine the day-to-day
variations in chloride concentration at any point in the estuary and,
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9
in this way, give the engineers and scientists the necessary data
to answer the above questions.
Let us look at another example. Figure 8 shows the varia-
tions in DO that can be expected at the Woodrow Wilson Bridge in
1985 under several different levels of waste-water treatment and
flow. Here it is immediately evident that in 1985, if the river
flow is kept at a minimum of 1,500 cfs, only 92% removal of BOD
will be required at the treatment plants to maintain a minimum DO
of k mg/1; while, if the river flow drops to 500 cfs, 95fo removal
of BOD will be required.
These are examples of the basic uses of the model. There
are others. One of the most promising is its use in conjunction
with economic techniques such as linear or dynamic programs, but
that is a different story as long as the one I have just related,
and I am sure that I have given you enough to absorb in one afternoon,
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PENNSYLVANIA
J TM n ^
LOCATION MAP
MAJOR WASTE
TREATMENT PLANT
= ESTUARY SEGMENTS
GA6ING STATIONS
LITTLE FALLS BRANCH-
BETHESDA, MO
POTOMAC RIVER-
WASHINGTON, D C
ROCK CR -SHERRILL DRIVE-
WASHINGTON, D C
N E BR ANACOSTIA RIVER-
RIVERDALE, MD
N W BR ANACOSTIA RIVER-
HYATE SVILLE , MD
FOURMILE RUN-
ALEXANDRIA, VA
LITTLE PIMMIT RUN
ALEXANDRIA, VA
CAMERON RUN-
ALEXANDRIA, VA,
HENSON CREEK -
OXEN HILL, MD
POHICK CREEK-
L 0 R T 0 N , VA
MATTAWOMAN CREEK-
PO MON KEY, MD
DISTRICT OF COLUMBIA
ARLINGTON COUNTY
ALEXANDRIA SANITATION
AUTHORITY
FAIRFAX COUNTY - WESTGATE
PLANT
FAIRFAX COUNTY- LITTLE
HUNTING CREEK PLANT
FAIRFAX COUNTY- DOGUE
CREE K PLANT
POTOMAC RIVER STUDY AREA
FIGURE 1
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ABSTRACT
The diffusion coefficients presented in this tabulation
hare been computed for a velocity range from 0.01 knots
t-
to 5.00 knots at an interval of 0.01 knot. The equations
employed for the computation vere derived from the FOUR-
THIRDS law and the RASDOM PROCESS analogy equations. A
difference function and mean value function are also
tabulated.
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BIBLIOGRAPHY
TABLE OF CONTENTS
i'a,
SECTION I
INTRODUCTION
GENERAL DISCUSSION OF THE DIFFUSION
COEFFICIENT EQUATIONS
SECTION II
Tabulation of the Diffusion Coefficients
as a Function of Velocity. Values are
given in units of centimeters squared/
second; miles squared/day; and feet
squared/second. (For each tabulation) 1-13
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SECTION I
INTRO r^'TICN
Down through the apes ra^n have been fascinated ty math-
ematical formulation and. the solving of complex problems, but
usually nave been bored witn the drudgery c f computation. In
utilizing mathematical models fcr pollution snaiynis in estuarine
systems, theoretical estimates of the diffusion coefficients are
usually required. The strong point in favor of obtaining these
coefficients from theoretical equations rests on the fact that
information utilized in the equations is readily available in
tidal current tables published by the United States Coast and
Geodetic Survey.
The estimated values of the diffusion coefficients may
havซ to suffice until auch time as empirical data is obtained
either from dye tracer studies or a knowledge of the longitudinal
salinity distributions of estuaries. When empirical information
is obtained, it would be preferred over the equation, since
characteristics pertaining to a particular system would be repre-
sented by the observed data that may not be expressed in the
equations.
It is hoped tnat this tabulation of diffusion coefficients
will help to relieve the investigator from a certain amount of
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computational drudgery. For thus reason, trie units >.'
ficients are expressed in centir- ev-r s aquared/secorja,
squared/day, and feet squarei/se .ona.
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GENERAL DISCUSSION OF, DIFFUSION COEFFICIENT KCWri
is the maximum
max max
The basic equation state,- by Bowcien as:
(l) K(cm /sec) * 0.02U6I where L is Jn cent^ireters an-
may be cons -ae red as trie length
of ซ tiaa'j excursion,
was reformulated by Hetling and C'Connell in a form more suit-
able for calculation of the diffusion coefficient in te;rn:: of
readily available hydrographic data to be:
(2) K = CV /3 vhere V
n
velocity in knots and may t>e
obtained for most estuaries
from tidal current tables.
The value of the constant "C" in the FOUR-THIRDS equa-
tion was varied in the computation of the diffusion coefficients
in this tabulation to yield diffusion coefficients in centimeters
squared/second; miles squared/day; and feet squared/second.
These values for "C" are given be.ow as:
/-~
C = 1.56 x 10 for K in centimeters'Ysecond.
r
- 5.;
C = 1.66 x 10 for K jn feet'/seccn-?
and were derived by Hetling and O'Connell,
Tne second equation employed in computing coefficients
tabulated nerein was originally proposed by Diachishin and
described as:
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(3) K ซ nL /2 where L is the length of each
ranaom step, and n is the fre-
quency of steps. For the tidal
system, n = 1/12.U per hour.
The above equation vac developed, using probability theory
and has as its origin a random walk type of process. The equa-
tion is often referred to as the RANDOM PROCESS analogy equation.
In terns of the BAXLBUB velocity V , equation (3) may
toe written as:
(k) K ป Dv where V is defined the same
max max
as it is in (2) above.
For calculating "K" in the same units as equation (2),
the constant employed is given as:
6 ?
D = 6.2 x 10 for K in centimeters /second
D ซ 20.7 for K in miles /day
D - 6.68 x 103 for K in feet2/second
The tabulation of the coefficients has been arranged
sซ that the FOUR-THIRDS and RANDOM PROCESS analogy equations,
reformulated in terms of the maximum velocity in knots, are
grouped according to the units of "K" desired, i.e., centimeters
squared/second is the first tabulation; miles squared/day is the
second; and feet squared/second is the last. Section II of this
Paper contains these tabulated coefficients.
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Each tabulation is arranged by first shoving the line
number. The velocity in knots is the next column, and on each
nev line the velocity is incremented by 0.01 knot. The third
column represents the value of the diffusion coefficient corres-
ponding to that velocity computed for the FOUB-THIRDS equation.
The fourth column gives the diffusion coefficient value computed
for the RANDOM PROCESS analogy equation. The fifth column gives
a mean value function for both equations (2) and (M and was
coaputed as:
(5) FT- [CV^3 + DV2 ]/2 for V from 0.01 to 5-00 knots
max BMX max
It has been generally found that in the brackish portions
of estuaries, both equations (2) and (k) yield coefficients in
an order of magnitude that makes both acceptable for reasonable
estimates .
Column six of the tabulation shows the computations for
the difference function. This was computed as:
When JK_[ is small, the investigator nay find either the
values for equations (2) or (k) may be employed for an estimate.
When JKpl is large, it may be desirable to use the value computed
for equation (.5)
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BIBLIOGRAPHY
1. HetJing and O'Connell, "Estimating Diffusion Characteristics
of Tidal Waters," CB-SRBP Technical Paper No. 4, Department
of the Interior, FWPCA, Middle Atlantic Region.
2. IBM 7090/709^ IBSYS Operating System, Version 13, IBJOB
Processor, File So. 7090-27, FORM C28-6389-1.
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I. INTRODUCTION
Much concern is voiced over the pollution potential of
boating activity, but little definitive data exists concerning
the extent of human fecal pollution contributed from pleasure
boats.
A scheduled rendezvous of the Annapolis Yacht Club on
July 22-26, 1966, at the Miles River Yacht Club located on Long-
haul Creek, adjacent to the Town of St. Michaels, Talbot County,
Maryland, afforded the Chesapeake Field Station an opportunity
to conduct a study under field conditions to determine the rela-
tionship of coliform densities to pleasure boat count in the
Area. Temporary bacteriological laboratory facilities were set
up in a nearby motel to determine coliform and fecal streptococci
population densities, and sampling stations in the vicinity of
the Yacht Club were established (Figure l). The sampling program
began at 12:00 Friday, July 22, 1966.
II. MATERIAL AND METHODS
Coliform confirmed population estimates were made by
the 5-tube, 3-dilution MPN method. Difco lauryl tryptose broth
was used for presumptive media, and Difco Brilliant Green lactose
bile broth, two per cent, was used for confirmation of coliforms.
Fecal streptococci were estimated with the same MPN
technique, with presumptive Difco azide broth and confirmed in
BBL ethyl violet azide broth.
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Samples were gathered from a lU-foot aluminum jon boat
by hand dipping into sterile 6-ounce prescription bottles. Im-
mediately after collection, samples were returned to shore and
inoculated into the media, using the,back end of a station wagon
for working area. Consequently, samples were inoculated approxi-
mately 15 minutes after collection.
Incubation of tubes was at 35ฐ C. in bacteriological
incubators established in the nearby motel, and transfers from
positive tubes were accomplished in the makeshift laboratory
using a portable propane torch to flame the bacteriological loops.
III. THE INVESTIGATION
Preliminary to sampling, a reconnaissance was made of
Longhaul Creek (Figure l). In addition to the Miles River Yacht
Club facility, four homes were located along the creek, and the
adjacent land was cultivated farmland. One home, approximately
150 yards upstream from Station D, had two dozen or so domestic
ducks penned on the bank of the creek. An occupied house trailer
was noted on the west shore of the creek.
A count of the number of boats in the Area was made during
the study. All boats were counted during the reconnaissance, but
during the study only occupied boats with toilet facilities were
counted. The initial count made at 11:30 Friday, July 22, showed
IT small boats with no toilets and 32 unoccupied boats with
toilets. The number of small boats without toilets remained
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essentially the same throughout the study, except for a few
satellite dinghies with the transient craft.
Observation of activities at the Miles River Yacht Club
indicated that, although it is in rural surroundings, the Club
is contantly a focal point for various activities. The Club has
a swimming pool and, apparently, a swimming team. During the
study, two separate crab feasts were catered on the veranda of
the Club House. One of these was rather small, restricted to
the Annapolis rendezvous group only. The other was sponsored
by a local organization for the general public and was well
attended. At the outset of the study, several boats with New
Jersey registration were noted, apparently the departing vestiges
of a smaller rendezvous or cruise of a New Jersey club activity.
The rendezvous during the study period, however, far exceeded the
normal weekday routine activity.
No precipitation occurred during the study, and weather
conditions could best be described as a portion of a drought cycle,
Samples were collected from four stations (see Figure l)
three times daily, at approximately 0800, lUOO, and 2000 hours.
Station A was located by the red nun buoy No. 12 in the Miles
River, approximately 500 yards from the mouth of the Creek.
This control station was presumed to indicate the quality of
water inflow into the Creek on flooding tide.
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Station B was located at the mouth of Longhaul Creek,
approximately 30 yards off the offshore end of the docking area,
and approximately in mid-stream. All boats were docked or moored
inside the Creek with respect to this station.
Station C was located in mid-stream at the opposite end
of the dock facilities, at approximately the point where the
Creek "bifurcates. This station was often in the area of anchored
*
boats.
Station D was made at the entrance of the southwest branch
of Longhaul Creek, This was upstream from all yacht club boating
activities, yet downstream from three homes, including the one
with ducks penned on the Creek bank.
IV. RESULTS
Data resulting from this study are shown in Table 1.
Tides were estimated from the U. S. Coast and Geodetic Survey
Tide Tables, 1966, corrected for St. Michaels, Miles River.
Two things should be noted from the tabular presentation:
(l) fecal streptococci were nearly always so low in density as
to be immeasurable during the study, at all stations; (2) no
apparent relationship seems to exist between tidal stage and
bacterial population density.
Coliform bacteria and number of boats are shown graphi-
cally in Figures 2 through 5. Station A, Figure 2, in the Miles
River, showed a low incidence of coliforms throughout the study.
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Station B, Figure 3, at the mouth of the Creek, showed
a low incidence of coliforms before the boats arrived, then a
general increase to 200-500 coliforms/100 ml. Persistence of
these counts after the departure of the boats is evident,,
Figure h shows Station C, off the marina in the Creek.
An anomalous figure of 2,^00 coliforms/100 ml is shown, before
the boats arrived. This study assumes the integrity of the
shore facilities, and a "rested" condition from previous boats,
which may riot be entirely sound. However, two of the initial
bacterial determinations showed counts less than 20, and the
same general increase with the arrival of the boats as found at
the other two stations in the Creek.
The station farthest upstream, Station D, is shown in
Figure 55 and again the same trend of a coliform increase with
the arrival of the boats and persistence after the departure is
apparent
V. DISCUSSION
These data collectively indicate a slight increase and
persistence of coliforms with the congregation of pleasure yachts,
An estimation of the degree of significance of yacht contribution
was attempted by analyzing the coliform counts with respect to
increased number of boats. The data from the initiation of the
study to the point where the maximum number of boats with toilets
(85) occurred, were analyzed with simple regression. This does
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not take into account any persistence of bacteria after the
departures, and assumes also that only boats contributed coliforms,
Logarithms of the number of coliforms, rather than
arithmetic figures, were used because the logarithms of coliform
MPW's have been shown to be normally distributed, while the raw
data are generally skewed. For these analyses, a zero count of
boats was assumed to be one, and coliform densities less than 20,
the lower limit of determination with the procedure used, assumed
to be 2 coliforms/100 ml. These assumptions tend to make errors
on the conservative side.
Station A, Figure 6, shows no relationship between number
of boats and coliforms, as should be expected from the control
station.
Station B, Figure 7, shows the regression between the
increase of boats and the logarithm of coliform MPN. The slope
of this line showed a significant fit at the five per cent level
with the "t" test- This slope, b = 0.0225, indicated an incre-
ment of approximately 1 coliform per 100 ml water for each boat
(antilog 0,0225 = 1.053).
Station C, Figure 8, showed no significant regression
when all data were considered. If the 2,^00 coliform MPN,
anomalously found before the boats arrived, were disregarded, a
good regression was found, b = 0.01316, t = 3.26, d.f. = U.
This slope, shown as the dotted line on Figure 8, agrees fairly
close with Stations B and D.
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7
Station D, Figure 9, indicates an increase similar to
that at the other Creek stations, b = 0.0097, but the "t" test
for goodness of fit fell just short of significance at the five
per cent level.
These data collectively indicate the order of magnitude
of the increase of pollution by boats, under the conditions of
this study. The persistence of bacterial counts is not con-
sidered, nor is the duration of stay of boats, in this case a
little over 2k hours, and these factors should be considered
in future study designs.
Boundary conditions undoubtedly affect values, due to
mixing and dilution. The estimated size of Longhaul Creek,
taken from a U. S. Geological Survey topographic map, was
1,800,000 square feet or kl.3 acres. With depths from the
appropriate U. S. Coast and Geodetic Survey chart, an approxi-
mate volume of 18,266,000 cubic feet or 136.6 million gallons
was calculated. With a tidal range of 1.2 feet, or 2,l60,000
cubic feet, or l6.1 million gallons, this would indicate a 12
per cent augmentation on the average flood tide. No stratifi-
cation of termperature with depth was found at any station during
this study, as measured with an electronic thermometer. Exchange
or excursion values were not obtained from these data, but this
Creek would seem to be relatively homogeneous, with respect to
the sampling program undertaken.
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8
Another factor to "be considered is marina habits; i.e.,
the degree to which on-board facilities are used with respect
to the facilities available on shoreside. This factor would
probably vary with each study situation.
A second study was contemplated by the Chesapeake Field
Station staff in 1966 at the Rose Haven Marina, Herring Bay,
Anne Arundel County, Maryland. Preliminary to an extensive study,
the waters were sampled to establish background bacteriological
levels under conditions of minimum boat occupation. These results
are shown in Table 2.
As can be noted from Table 2, the degree of change in
bacterial level anticipated from approximately UOO boats, an
estimated increase of UOO coliforms/100 ml/boat/day, could probably
not have been detected because of the pollution contribution
from one shore-based septic tank system.
These observations indicate that the relative significance
of pleasure boats contaminating the waters is much less than
contributions from nearby domiciles, served with individual septic
tank systems, and under conditions of these studies.
The results of this study are illuminating, but not
definitive.
Further elucidation of the magnitude of bacterial con-
tribution from pleasure boats can be accomplished in field designs
which incorporate:
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-------
1. More extended observations of the background bacterial
densities in "rested" water prior to occupation by boats.
2. Determination of coliform, fecal coliform, and fecal
streptococci, for possible interpretation of human and animal
contribution, and as an indicator of recent, as opposed to remote,
pollution.
3. Observations extending to include the subsequent
decline of bacterial densities, which would depend on local
boundary conditions, duration of boat stay, etc.
i+. If possible, detailed studies of the hydrology that
would further quantitate the effects of small boats per unit
volume of water should be concurrently executed.
5ป Studies conducted in different aquatic environments,
to minimize local effects, are necessary to quantitate the cause
and effect relationships.
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10
BIBLIOGRAPHY
I, Sanderson, A, E. , and Hopkins, T. C., Coliform and E_. coli
bacteria counts at a major Chesapeake Bay boating-bathing
site during the Independence Day holiday period 196^.
Mimeographed report. Maryland Department of Water Resources,
Water Quality Division.
2. Hopkins, T. C., and Sanderson, A. E., Report Number Two on
coliform and E_. coli bacteria counts at a major Chesapeake
Bay boating-bathing site during the Independence Day holiday
period 1965. Mimeographed report. Maryland Department of
Water Resources, Water Quality Division.
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Table 1
Bacterial Counts in Longhaul Creek, Maryland
During a Yacht Rendezvous
11
Station Date /Time
A. Red nun "12" 22
in Miles River
off Longhaul
Creek.
(Control 23
Station)
2k
25
26
Be Longhaul Creek 22
mouth. Sea-
ward of
moorings. 23
2k
25
26
C. Longhaul Creek. 22
Directly off
docks and
among moored 23
boats
- 111*5
1335
1650
1958
- 0755
131*5
1952
- 0802
131*5
191*8
- 0813
1320
1957
- 0807
131A
161*8
- 13UO
1702
2005
- 0801
1353
1956
- 0805
131*9
1955
- 0818
132'4
2003
- 0812
131*8
1653
- 131*3
1701*
2008
- 0803
1356
1959
Coliform
<20
20
<20
1*5
<20
<20
<20
18
<20
<20
<20
<20
20
1*5
<20
1*5
<20
<20
20
220
78
330
170
1*90
170
1*90
20
220
110
1*90
110
2,1*00
20
170
1*5
230
330
Fecal
Streptococci
20
<20
18
<20
<20
<20
<20
<20
20
20
<20
<20
<20
<20
<20
20
<20
<20
<20
<20
<20
20
20
<20
<20
<20
<20
<20
<20
20
<20
<20
18
<20
<20
<20
<20
Occupied
Boats With
Toilets Tide
0
0
10
23
29
6k
81*
85
10
0
0
0
2
2
0
0
0
10
23
29
6k
81*
85
10
0
0
0
2
2
0
0
0
10
23
29
61*
81*
Ebbing
Ebbing
Flooding
Flooding
Slack Flood
Ebbing
Flooding
Flooding
Ebbing
Flooding
Flooding
Ebbing
Flooding
Slack Ebb
Ebbing
Ebbing
Ebbing
Flooding
Flooding
Slack Flood
Ebbing
Flooding
Flooding
Ebbing
Flooding
Flooding
Ebbing
Flooding
Slack Ebb
Ebbing
Ebbing
Ebbing
Flooding
Flooding
Slack Flood
Ebbing
Flooding
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Table 1 (Continued)
12
Station Date /Time
C. (Continued) 2 it - 0808
1351
1958
25 - 0820
1326
2005
26 - 0815
1352
1656
D. Longhaul Creek .22 - 1135
Upstream from 13UU
all boats. In 1707
mouth of south 2008
branch, 23 - 0805
1358
2001
2k - 0811
11*00
2001
25 - 0822
1329
2007
26 - 0817
1351*
1659
Coliform
330
1*90
1*90
170
330
790
110
1+90
790
20
20
330
ll*0
1*5
1*90
130
330
110
5,1*00
790
330
700
68
790
790
Fecal
Streptococci
<20
<20
1*5
20
<20
<20
52
<20
20
<20
<20
<20
<20
<20
<20
<20
20
<20
1*5
20
<20
20
<20
<20
<20
Occupied
Boats with
Toilets Tide
85
10
0
0
0
2
2
0
0
0
0
10
23
29
6k
81*
85
10
0
0
0
2
2
0
0
Flooding
Ebbing
Flooding
Flooding
Ebbing
Flooding
Slack Ebb
Ebbing
Ebbing
Ebbing
Ebbing
Flooding
Flooding
Slack Flood
Ebbing
Flooding
Flooding
Ebbing
Flooding
Flooding
Ebbing
Flooding
Slack Ebb
Ebbing
Ebbing
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13
Table 2
Bacterial Population Density Estimations
Rose Haven Yacht Club, Herring Bay, Anne Arundel County, Maryland
10U Boats, 150 Empty Slips
August 29, 1966
1.
2.
3 =
h.
5.
Location
Pier, farthest upstream
J-Dock, upstream from
clubhouse
Apparent septic discharge
behind clubhouse
Main dock behind clubhouse
Channel into harbor
Coliform
MPN/100 ml
170
2,UOO
>l60,900
5,^20
TOO
Pecal Coliform
MPN/100 ml
50
50
27,800
50
100
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LOCATION MAP OF STUDY AREA
FIGURE
-------
-------
CD
90-
80-
70'
u. 60-
o
O
Z
O
5O-
40
O '
O 30-i
a.
s
20
a:
o
U.
_j
O
O
/
/ BOATS
1 0
JULY
!
!
NOON
22
ป ! !
I 1
o
to
i j
1 1
0 NOON
O
5 23
i i
0 M
O
00
j
I
o
o
o
t 1 i
1 1 1
NOON 0 M
O
24 -
\ 1
1 1
ONOON
o
ฐ 25
| I
1 I -
0 M
0
CO
! 1
1 I
g tfBON' '
CO
0 26
1
t
o
o
CO
1
1
M"'
COLIFORM POPULATIONS AND NUMBER OF
STATION A
BOATS
FIGURE 2
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-------
600
500 -j
400
!
3OO-1
20O
CO
t-
23
O
24
ฐ25
1 1
0 M
o
~
h
o
o
to
o
1
NOON
26
-i
o
o
~
1
M
COLiFORM POPULATIONS AND NUMBER OF BOATS
STATION B
FIGURE 3
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-------
I.OOO
900-
800-
TOO-
600-
500-
400
300-r-
200-j
CO
<
O
CD
U-
O
d
z
Q
O
O
X
Z
IX
O
U_
o
o
lOO-i
i
90-,
80-i
60-j -
50-j
301 -
20
10
JULY
1 j
MOON g
0
Y 22
i
M 0
CD
O
1
NOON
23
1 J
0 u
o m
?
it
1 1
ONOON
O
24
! j
0 u
O N
5
|
i
0
0
1
1
NOON
25
j i
I I
o u
o
1 1
0 NOON
s
26
I
T
o
0
9
1
1
M
COLIFORM POPULATIONS AND NUMBER OF BOATS
STATION C
FIGURE 4
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-------
5400'
COLIFORM POPULATIONS AND NUMBER OF BOATS
STATION D
FIGURE 5
-------
-------
5
o:
o
LL
_)
O
O
or
UJ
co
CD
O
100 i
90'
80
70
60
SO-
40
30
10
9
8-
7
*
1 1 i i i
1 1." II 1
10 20 30 40 50 60
1
7O
1
1
80
I
90
NUMBER OF BOATS
REGRESSION OF
INCREMENTS OF BOATS AND COLIFORMS
STATION A
FIGURE 6
-------
-------
1,00 O <-
900 ซ
aoo f
5 OC
40O
30O
200
CO
IOO
9O
80
70
6O
r
40-
o
30
CD
o
-T-
-isf-
10 2O 30 40 50 6O
NUMBER OF BOATS
70
80
90
REGRESSION OF INCREMENTS OF BOATS AND COLIFORMS
STATION B
FIGURE
-------
-------
3,OC 0
I.OOO
9 0 O
8 O O
700
6 OO
500
400
<ฃ
or
O
LL
s
O
O
a:
UJ
on
2
ID
^
1 1\
U?
O
30 o -I
f j
^
!
2 0 0 ~| w
-J ^ .
I
5
I
1 CO -j .-
9 O *ปKK -i nป
son ^ -^
7O-
6O-
50-
-SO -
^
x*
X
^
^
/
^
~ v-
20 -f
,o -*-
2O
30 40 50 60
NUMBER OF BOATS
70
8O
9O
ss,ON OP
STATION C
BO.TS ANO COL1FORMS
FIGURE 8
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-------
,OOO '
9OO
8OO
fOO
t>oo
;. oo
4OO
4-
-\ 1-
IO 2O 3O 4O SO 60
NUMBER OF BOATS
7O
80
90
REGRESSION OF INCREMENTS OF BOATS AND COLIFORMS
STATION D
FIGURE 9
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