TECHNICAL APPENDIX
to the
REPORT on the WATER QUALITY OF CHARLESTON HARBOR
and the EFFECTS THEREON of the
PROPOSED COOPER RIVER REDIVERSION
UNITED STATES DEPARTMENT OF THE INTERIOR
FEDERAL WATER POLLUTION CONTROL ADMINISTRATION
Southeast Water Laboratory
Charleston Harbor - Cooper River Project
Charleston, South Carolina
August 1966
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TABLE OF CONTENTS
Page No.
INTRODUCTION 1
FIELD OPERATIONS !
Sampling Station Selection 1
Sampling Programs 2
Sampling Methods 3
Sample Handling and Preservation 8
LABORATORY ANALYTICAL PROCEDURES AND OPERATION 9
Discussion 9
Chloride Determination Employing Automatic Tiration Procedure 14
Dissolved Oxygen Determination Employing Automatic Titration
Procedure 20
Total Phosphate 30
Laboratory Data Collection and Reporting 33
SPECIAL STUDIES 35
Organic Carbon-Organic Nitrogen Ratios of Sediments 39
Dye Dispersion Studies 45
Hydraulic Model Studies 47
Sample Preservation 58
Free Carbon Dioxide 66
Organic Carbon 77
Oxygen Uptake by Sediments 81
DATA ANALYSIS 94
Basic Statistical Methods 94
Computer Programs 106
COMPILATION OF BASIC DATA 156
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LIST OF TABLES
Page No,
1 - Intensive Survey Sampling Schedule 4
2 - Intensive Sampling Program 5
3 - Comparison of Sampling Methods Based on Dissolved Oxygen Samples 6
4 - Laboratory Analytical Procedures 11
5 - Comparative Chloride Data for Manual and Automatic Titrations 18
6 - Standard B.O.D. Bottle Volume 24
7 - Comparative Dissolved Oxygen Data for Manual and Automatic Titrations 26
8 - Results of Modified Total Phosphate Procedure 32
9 - Data Reporting . 33
10 - Special Studies 36
11 - Source of Organic Materials in Benthic Deposits 41
12 - Organic Analysis of Bottom Sediments 42
13 - Summary of Intensive Surveys 48
14 - Comparison of Mean Values of Chloride Data 50
15 - Comparison of Surface to Bottom Chloride Data 51
16 - Comparison of Overall Response of Chlorides to River Discharges 52
17 - Summary of Model Dye Studies 53
18 - Analysis of Model Dye Studies - Mean Travel and Residence Times
in Tidal Cycles for Given Cooper River Flow 57
19 - Descriptive Statistics of Total Phosphates - Sample Preservation
Study 60
20 - Descriptive Statistics of Nitrate Nitrogen - Sample Preservation
Study 62
21 - Descriptive Statistics of Ammonia Nitrogen - Sample Preservation
Study 64
22 - Descriptive Statistics of Organic Nitrogen - Sample Preservation
Study 65
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Page No.
23 - Ashley River, Carbon Dioxide Study - Municipal Marina Station 71
24 - Ashley River, Carbon Dioxide Study - Buoy #3 Station 72
25 - Ashley River, Carbon Dioxide Study - Atlantic Coast Railway
Bridge Station 73
26 - Ashley River, Carbon Dioxide Study - Buoy #15 Station 74
27 - Ashley River, Carbon Dioxide Study - Highway #7 Bridge Station 75
28 - Ashley River, Carbon Dioxide Study - Buoy #13 Station 76
29 - Comparative Data for Total Organic Carbon - 5day B.O.D. Relationship 79
30 - Comparative Data for Total Organic Carbon - Long Term B.O.D.
Relationship 80
31 - Experimental Results of Oxygen Utilization by Benthic Deposits 86
32 - Descriptive Statistics of Experimental Results 92
33 - Data Processed Through Descriptive Statistics Program 95
34 - Routine Monitoring Data 157
35 - Intensive Survey Data 206
36 - Environmental Data 764
37 - Model Chloride Data 803
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LIST OF FIGURES
Page No.
1 - Charleston Harbor Sampling Stations 2a
2 - Titration Curve for Chloride Determination Employing
the Automatic Titration Procedure 16
3 - Potentiometric Titration Curve for Dissolved Oxygen
Determination Employing the Automatic Titration
Procedure 27
4 - Potentiometric Titration Curve for Dissolved Oxygen
Determination Employing Manual Titration Procedure 28
5 - Laboratory System for Measuring Utilization of
Oxygen by Harbor Deposits 82
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INTRODUCTION
The purpose of this technical appendix 1s to present all of
the supporting documentation for the summary report entitled
"A Report on the Water Quality of Charleston Harbor and the Effects
Thereon of the Proposed Cooper River Rediversion". The material
presented in this appendix includes the following:
(1) A description of the field operations including the
criteria for selecting sampling stations and a description
of program used to substantiate the fidelity of all phases
of the water sampling techniques;
(2) A discussion of the laboratory operations and of the
laboratory analytical procedures and modifications of these
procedures;
(3) A complete description of the special studies;
(4) A detailed discussion of the data analyses techniques
including a listing of the computer programs used; and,
(5) A display of all basic data not contained in the summary
report.
This appendix does not contain any conclusions pertaining to the
study's objectives but serves as a readily available repository
for the large amount of information collected by this project,
FIELD OPERATIONS
SAMPLING STATION SELECTION
The results of any estuarine water quality survey are greatly
dependent on the selection of representative sampling stations in
the area under study. It becomes a problem of maximizing the amount
of information gained under the constraints of available manpower,
equipment resources and laboratory capability. The capability of
the laboratory controls the number of samples that can be collected
while the rationale used for station selection governs the utility
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of the data obtained from the analysis of each sample.
The following criteria were used for selecting the sampling
stations in Charleston Harbor. The stations are shown in Figure 1 .
1) The station had to be in an area that would be affected
by the proposed flow reduction from the standpoint of hydraulic
characteristics.
2) The station had to be accessible during all tide conditions
and had to be referenced to either existing navigational
aides or prominent land marks.
3) The station had to be located so that the data resulting
from sample analyses would not be overly biased by external
factors such as nearby waste outfalls.
4) All stations had to be located within an area that could
be covered with the existing sampling boats in a time period
less than one-half of tide frequency of 12.2 hours to approach
an optimum sampling frequency.
5) The overall number of stations was limited by the number
of samples that could be analyzed by the laboratory staff and
the number of field personnel available for sampling duty.
SAMPLING PROGRAMS
Three specific types of sampling programs were used during the
Charleston Harbor Study. The first type was a routine weekly program
for preliminary reconnaissance or surveillance purposes. The results
from the analyses of these samples were used to plan further studies
and to monitor the water quality in the harbor. The second type of
sampling program was an intensive, high frequency, round-the-clock
operation to obtain sufficient environmental information to establish
the quality characteristics and dynamics of the harbor system. The
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2a
DEPT. OF THE INTERIOR
FV/PCA
W. Va. Pulp a Paper Mttlf
outfall area
Baresford Creek ;
V. C. Chemicl ^
Co.
UPPER
HARBOR /. "..'-.-.: '
A.C. L. Railroad
Hwy. 17
LOWER
R
Shules
e,
Ft.Sumter
01234
nautical miles
Ocean
CHARLESTON HARBOR
Sampling Locations
FIGURE
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intensive surveys were designed to yield data amenable to various
statistical techniques of analysis. The third type of sampling
program was one especially designed for the special studies. This
program generally involved the collection of specific types of
samples such as sediment, water under mineral oil, or a series of
samples at a specified time or tide condition.
The sampling runs were scheduled in the following manner:
1) Routine Sampling - One run per week scheduled until the
occurrence of low flow periods when the frequency was increased
to twice a week to maintain adequate surveillance. Single
rund scheduled on Thursdays so that the analyses of the 5-day
BOD samples and the membrane filters could be completed during
a regular work day.
2) Intensive Sampling - Samples for this program were collected
on a four hour frequency at each station beginning at 12:00
am on Monday and ending at 12:00am on Saturday. Six sampling
runs were conducted every 24 hour period and all samples were
collected within 10 minutes of the specified time. Table 1
shows the sampling schedule used for the intensive surveys.
Each sampling run took about three hours to complete and one
hour was available between runs for routine boat maintenance.
Table 2 summarizes the intensive surveys completed. Each
intensive survey involved a considerable amount of coordination
between laboratory and field crews. In addition, the round-
the-clock operations were more expensive. Consequently, each
survey was planned in detail to ensure adequate stand-by
equipment and manpower.
SAMPLING METHODS
During the course of the Charleston Harbor Study a considerable
amount of time was expended in developing sampling techniques to
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improve the reliability and uniformity of the samples collected.
The critical parameters from the sampling standpoint were dissolved
oxygen and coliform bacteria. Dissolved oxygen was used as the
controlling factor in the development of the sampling techniques.
The major factors that were considered in collection of the
dissolved oxygen samples were to ensure the collection of a
representative sample and to prevent the loss or gain of oxygen
while it was being collected. The basic underlying premise was
that any method that gave reliable and representative dissolved
oxygen samples would give equally reliable samples for measurement
of other parameters. Three separate sampling techniques were tested
against each other. These were standard 1 liter Kemmerer Bottle,
a Sargent D.O. , Sampler and a submersible pump connected to
an onboard sink by plastic hose. Forty-six replicate samples were
taken to test the methods against each other. Table _3 summarizes
the test data. TABLE 3
COMPARISON OF SAMPLING METHODS BASED ON DISSOLVED
OXYGEN SAMPLES
TYPE OF
SAMPLE
Kemmerer
Sargent
Submersible
NUMBER
OF
SAMPLES
46
46
RANGE OF VALUES
mg/1
High Low
6.01 2.68
6.01 2.68
MEAN
mg/1
4.51
4.60
VARIANCE
(mg/1)2
0.63
0.52
Pump
46
5.99
2.67
4.58
0.58
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The difference between the means were tested for statistical
significance and was found not statistically significant at 99.7%
confidence level In all cases. An analysis of variance was also
made resulting in the same conclusions. It was concluded that any
of the three methods would give equally reliable results. However, the
submersible pump technique was more flexible, easier and faster to
use, and afforded a greater degree of safety for field personnel
during rough weather; and therefore, it was used for the majority
of the field work.
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SAMPLE HANDLING AND PRESERVATION
The majority of water samples were collected with a submersible
pump; however, on several occasions the samples were collected with
Kemmerer and Sargent samplers due to either boat and pump failure
or checking of submersible pump sampling versus conventional sampling.
The samples for dissolved oxygen determination were collected
in conventional glass BOD bottles and immediately dosed and placed
in dark chests. The dosed and acidified samples were returned to the
floating laboratory where they were automatically titrated utilizing
the Fisher Titralyzer. The time from collection to titration was
about four hours.
Prior to April, 1965 the samples were collected in BOD bottles
and delivered to the laboratory in dark ice chests. They were then
dosed and titrated in the lab within four hours after collection.
An algae bloom developed in the harbor in early April and prohibited
the icing procedure for D.O.
Samples for BOD determinations were collected in half-
gallon plastic jugs. The BOD in Charleston Harbor is less than
1.0 mg/1. At first the BOD samples were delivered to the lab in
ice chests; however, after several months of low BOD the samples
were not iced. Samples for BOD tests were set up within three to
five hours from time of collection.
Samples for bacteriological examination were collected in clean,
sterilized, bacteriologic bottles. They were immediately placed in
iced chests and delivered to the lab. Total and fecal coliform tests were
set up as soon as possible and always within five hours from time of
collection.
The remaining samples for chemical analyses were collected in one-
gallon plastic bottles. A portion of the samples was preserved with
1 ml of concentrated 1*2804 per liter of sample and stored in cubitainers
for nutrient determinations. The remaining chemical analyses were run
as soon as possible.
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LABORATORY ANALYTICAL PROCEDURES
DISCUSSION
The chemical and bacteriological procedures used by the Charleston
Harbor Project are listed in Table 4. Insofar as possible the
analytical procedures as outlined in Standard Methods for the
Examination of Water and Waste Wateri( llth Edition were followed.
Standard Methods was written using fresh water
procedureswhichin many instances are not compatible with analyses
of estuarine and sea waters. Many of the* procedures were modified
to meet the analytical needs for this Project. Such modifications
are also listed on Table 4 and those for chlorides, dissolved oxygen
and total phosphates are discussed in the detail following Table 4 .
and physical
The chemical/parameters included dissolved oxygen, biochemical
oxygen demand, chemical oxygen demand, chlorides, conductance, pH, temperature,
turbidity, total suspended solids, volatile suspended solids, ammonia
nitrogen, nitrite nitrogen, nitrate nitrogen, organic nitrogen, ortho
phosphates and total phosphates. The bacteriological examinations were
limited to total coliform and fecal coliform. The precision and accuracy
of chemical analytical procedures which were greatly modified are
discussed in the analytical procedure section.
The chloride concentration in Charleston Harbor varied from
500 to 19,000 mg/1 depending upon the station and tide. At the time
of sampling,the estuary was vertically stratified and also carried
a large suspended load which resulted in a widely varying turbidity.
The variable chloride and turbidity concentrations caused considerable
difficulty with several of the laboratory analytical procedures. The
ammonia procedure as outlined in Standard Methods has many short-
comings when used in estuarine waters and is definitely not recommended
for these studies. When the chloride concentration exceeds 12,000 mg/1
and the ammonia concentration exceeds 0.4 mg/1 of ammonia-nitrogen,
results obtained are erratic using the pre-floc procedure. Distillation
Hereafter referred to as Standard Methods.
-------
10
of ammonia using the micro-Kjeldahl distillation apparatus and
mercury catalyst, even with pH correction, would not suffice. The
ammonia is chelated or held back in the distillation apparatus and
ammonia
in most instances harbor samples had less/than the reagent blank.
COD values of less than 100 mg/1 are not reproducible
when chloride concentration approaches that of sea water. Data
obtained cannot be corrected for chloride interference. Thus the
modified mercuric sulfate procedure is of little use in relatively
clean sea water. Diluted samples with COD concentrations near
1000 mg/1 are reproducible and can be chloride corrected.
The membrane filter technique worked quite satisfactorily
for bacteriological tests even with the high suspended solid
concentrations. At one station located adjacent to the paper mill
outfall, atypical fecal coliform colonies were encountered perhaps due to
sulfur bacteria or the sulfate waste.
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TABLE 4
LABORATORY ANALYTICAL PROCEDURES
11
PARAMETER
TEST INITIALLY
USED
MODIFICATIONS
OF TEST
REFERENCE
1 Dissolved
Oxygen
Winkler Alsterberg
Azide Modification
2 Biochemical Dilution Method
Oxygen Demand
3 Chemical Dichromate reflux
Oxygen Demand Method with mercuric
Sulfate modification
4 Chloride
Mercuric Nitrate
Method
5 Conductance
Conductivity Cell
Method
Floe settled only
one time, 300 ml
sample automatically
titrated with 0.038
N Sodium Thiosulfate
None
None
Standard Methods,
llth Edition.
Standard Methods,
llth Edition.
1) Standard Methods.
llth Edition
2) Dobbs, Richard A.
Williams, Robt. T.
"Elim. of Chloride
Interence in the
Chemical Oxygen
Demand Test",
Analytical Chem.
Vol.35, July, 1963,
Pg. 1064-7.
3) Chemical Analytical
Procedures -Raritan
Bay Project
Standard Methods.
10th Edition.
0.2000N NaCl standard
and 0.2000N Hg(N03)2
used. Sample automat.
titrated with or with-
out indicator.
Resistance in ohms Standard Methods.
measured on Industrial llth Edition.
Instruments, Inc.Model
RC-8 conductivity bridge
at temperatures less than
30°C. Data are converted
to specific conductance at
25°C with a temp.-Specific
conductance table prepared
by Chas.Harbor Proj. 0.1M,
0.2M, and 0.5M, KC1 used to
calibrate cells.
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12
6 pH
7 Turbidity
8 Total Susp.
Solids and
Volatile
Susp. Solids
9 Ammonia
Nitrogen
Glass Electrode
Method
Jackson Candle
Method
Gooch Crucible
Method
10 Nitrite
Nitrogen
11 Nitrate
Nitrogen
PreFloc and
Direct Nessler-
ization
PreFloc and
Sulfuric acid-
Naphthylamine
Hydrochloride
Method.
Modified Brucine
Method
Fisher 13-639-90
Combination
Electrodes
None
Reeve angel glass
fiber filter, 934
AH, size 2.4cm
employed.
2 ml Zinc Sulfate
and 5 ml of sodium
hydroxide solution
added to 200 ml
sample.
2 ml Zinc Sulfate and
5 ml of sodium
hydroxide to 200 ml
sample for PreFloc
treatment. pH adjust.
made with 10% HC1
solution.
Reagent Blank is
not boiled.
Standard Methods,
llth Edition.
Standard Methods,
llth Edition.
Standard Methods,
llth Edition.
Standard Methods^
llth Edition.
Standard Methods.
llth Edition.
1) Standard Methods,
llth Edition.
2) Jenkins, David and
Medsker, Lloyd L.,
"Brucine Method
for Determination
of Nitrate in Ocean
Estuarine, and
Fresh Waters".
Analytical Chem.,
Vol. 36, No.3,
p.610-12.
3) Finger, James H.
"Nitrate Determin.
in Saline and est.
Waters: Comp. of
Hydrozine reduct-
ion and Brucine
Modification
Methods" Lab.Inves.
No.3, Tech.Adv. &
Inves.Section, TSB,
Robt.A.Taft Sani.
Eng. Center,C inn.,
Ohio.
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13
12 Organic
Nitrogen
Micro Kjeldahl
None
13 Ortho and
Total
Phosphate
14 Total
Coliforin
15 Fecal
Coliform
16 Temperature
Stannous Chloride
Method
Membrane Filter
Method with M-Endo
Broth procedure
Technique
Improvements
None
Membrance Filter
Method with
M-FC Broth
Procedure
Standardized
thermometer
None
1)Standard Methods,
llth Edition.
2)Kabat, Elvin A.,
and Maver,Manfred
M., Experimental
Immunochemis try.
C.C. Thomas Publ.
2nd Printing (1953).
Standard Methods,
llth Edition.
Standard Methods,
llth Edition.
"Recent Developments
in Water Microbiology"
conducted by Water
Supply and Pollution
Control Trng. Prog.,
PHS, Robt.A. Taft
Sanitary Eng. Center,
Cinn., Ohio
(Same as #14 above)
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14
CHLORIDE DETERMINATION EMPLOYING AUTOMATIC TITRATION PROCEDURE
The mercuric nitrate method for chloride determinations
as outlined in Standard Methods, 10th Edition for water was
modified for us in sea water. The concentrations of reagents
were increased and instead of hand titrations an automatic titration
procedure was used. The modified procedures are simple, rapid and
accurate. An aliquot of sample is diluted with distilled water,
acidified with nitric acid to a pH of 2 or less, and then titrated
automatically with or without the indicator. Using this procedure
one aide can make over 250 determinations per day including necessary
calculations.
A Fisher Titralyzer equipped with a glass general purpose
electrode and a silver billet electrode was used for the chloride
titrations. The pH must be 2 or less to prevent sodium ion
interference at the glass electrode. A potentiometric titration
curve based on the scale of 0-1400 millivolts has an end point in
the titration a£ 740 millivolts. However, due to the peculiarities
of the instrument involving the end point's anticipation, an end point
of 727 millivolts was used on our particular instrument.
The diphenylcarbazone-bromophenol blue indicator described
in Standard Methods, 10th Edition, is stable and much more independent
of pH as compared to the indicator-acidifier reagent described in
Standard Method, llth Edition.
An indicator is not necessary for automatic titrations on the
Fisher instrument; however, if an indicator is used to check end
points then the choice of indicators is the diphenylcarbazone-
bromophenol blue due to the range of pH.
Apparatus
1. Fisher automatic titrator, "Titralyzer".
2. Electrodes. Beckman #41263 glass general purpose electrode
and Fisher #13-639-122 silver billet electrode.
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15
Preparation of reagents
1. Sodium chloride standard, 0.2000N. Dissolve 11.6894g of ACS
grade NaCl, which has been dried in an oven at 103°C over-
night, in distilled water and dilute to 1 liter.
2. Nitric acid solution, 0.2N. Place 12.9 ml of cone. HN03 in
distilled water and dilute to 1 liter.
3. Mercuric nitrate solution, 0.2000N. Dissolve 35.5g of Hg(N03)2 .
H20 in approximately 900 ml of distilled water. Add 4 ml
of cone. HNC>3 . Make preliminary standardization against 10 ml
of 0.2000N NaCl. Adjust the mercuric nitrate solution to exactly
0.2000N and perform a final standardization.
4. Diphenylcarbazone-bromophenol blue indicator. Dissolve 0.5g
diphienylcarbazone and O.OSg bromophenol blue in 100 ml 95 per-
cent ethyl alcohol.
Procedure
1. Use a 10.00 ml sample or an aliquot with a chloride content of
about 70 mg. This will requiretapproximately 10 ml of 0.2000N
mercuric nitrate titrant.
2. Dilute with distilled water to approximately 300 ml in a 400 ml
tall-form beaker.
3. Add 1 ml of 0.2N HN03 with a medicine dropper.
4, Set the millivolt end point on the titralyzer. This millivolt
end point can be determined either by running a potentiometrie
curve on a sample or by titrating 10.00 ml of 0.2000N NaCl with
10.00 ml of 0.2000N Hg(N03)2 with instrument in manual position.I/
The indicator is not necessary but may be used if desired. The
10.00 ml of 0.2000N NaCl will require 10.00 ml of 0.2000N
Hg(N03>2 . An end point of 727 millivolts, based on 0-1400 millivolt
range, was used on our particular instrument.
-' See Figure #2
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17
5. Place the instrument under automatic control. Chloride samples
placed in the turntable will be titrated automatically, with or
without indicator, and the volume of titrant will be recorded
automatically by the instrument on a tape.
6. The instrument can be checked by placing NaCl standards in the
turntable or by adding indicator to a titrated sample.
Calculations;
/I Cl - ml Hg (N03)2 x normality of Hg (1*03)2 x 35460
ml sample
Precision and Accuracy;
Forty-one replicate samples were titrated by hand using the
indicator and with the titralyzer in automatic position without
the indicator. On 20 samples titrated by hand, the calculated
average was 7100 mg/1. Twenty titrated on the instrument had a
calculated average of 7101. The variance on the hand titration
was 346.9 with a standard deviation of 18.6. The variance by
automatic titration was 1308.9 with a standard deviation of 36.2.
Thus for the Project's purpose, the gain in speed with automatic
procedure justified the small loss in accuracy compared to hand
titration. Table 5 presents the comparative data for the hand and
automatic titrations. Figure 2 shows the potentiometric titrating
curve for end point determination.
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TABLE 5
18
CHLORIDES
AUTOMATIC
mg/1 Cl
7162.9
7070.7
7077.8
7092.0
7120.4
7035.3
7092.0
7070.7
7070.7
7106.2
7092.0
7184.2
7113.2
7092.0
7077.8
7127.4
7092.0
7134.6
7148.7
7070.7
x = 7101.5
t(x - £)2 =
tr _ ^(X -
v n - 1
S « -f\T =
TITRATIONS
(x - X)2
3770.0
948.6
561.7
90.2
357.2
4382.4
90.2
948.6
948.6
22.1
90.2
6839.3
136.9
90.2
561.7
670.8
90.2
1095.6
2227.8
948.6
24,870.9
x)2 = 1308.9
36.2
HAND TITRATIONS
mg/1 Cl
7092
7092
7085
7142
7099
7099
7106
7099
7085
7092
7092
7156
7092
7092
7092
7120
7085
7092
7099
7092
x = 7100
(x - x)2
64
64
225
1764
1
1
36
1
225
64
64
3136
64
64 .
64
400
225
64
1
64
x - x)2 = 6591
v =
n - 1
= \nr «
- x) _ 6591
19
346.9
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19
REFERENCES
1. American Public Health Association, Inc.; Standard Methods
for the Examination of Water and Waste Water. 10th Edition. (1955)
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20
DISSOLVED OXYGEN DETERMINATION EMPLOYING AUTOMATIC TITRATION
, PROCEDURES
The Alsterberg azlde modification of the Winkler method as
outlined in Standard Methodswas followed with the exception of the
titration procedure. The hand titration procedure was modified
to an automatic potentiometric titration procedure to enable
a greater number of D.O. and BOD , determination^ to be run.
A Fisher Titralyzer equipped with a glass general purpose
electrode and a platinum inlay electrode was employed in D.O.
determination. A potentiometric titration curve based on the
scale of 0 to 1400 millivolts has an end point in the titration
at 650 millivolts. However, due to the peculiarities of the
instrument involving the end point's anticipation, an en<^ point
of 681 millivolts is used on our particular instrument. A sample
is collected and dosed in the conventional manner. 'Chen 300 mis,
or a complete BOD , bottle volume, is titrated with 0.038N
sodium thiosulfate*
Apparatus
1. Fisher Automatic Titrator, "Titralyzer."
2. Electrodes. Beckman #41263 glass general purpose electrode
and Fisher #13-639-102 platinum inlay electrode.
Preparation of r,.eagents
1. Manganous sulfate solution. Dissolve 364 g MnSO^ . 1^0 in
distilled water, filter, and dilute to 1 liter.
2. Alkali-iodide-azide reagent. Dissolve 500 g NaOH and 135g
Nal in distilled water and dilute to 1 liter. To this
solution add lOg NaN3 dissolved in 40 ml distilled water.
-------
21
3. Sulfuric acid, cone. Reagent grade.
4. Starch solution: Dissolve approximately 2 grams of Superlose
50(>i'in approximately 200 ml of cold distilled water. This
solution is stable for several months.
5. Potassium biniodate stock standard, 0.152N. Dissolve
4.9384g KH(I03>2 in distilled water and dilute to 1 liter.
6. Potassium biniodate stock standard, 0.038N. Dilute 250 ml
of 0.152N potassium biniodate to 1 liter in a volumetric
flask.
7. Sodium thiosulfate stock solution, 0.152N. Dissolve 37.73
grams NaS203 5H2<> in freshly boiled and cooled distilled
water. Dilute to approximately 900 ml and add 1 g NaOH.
Standardize against 0.152N £11(103)2 according to standardization
procedure below.
8. Sodium thiosulfate working solution, 0.038N. Dilute 250 ml
of 0.152N sodium thiosulfate stock solution to 1 liter.
Standardization procedure for 0.152N sodium thiosulfate stock
1. Dissolve 2 to 3 g KI, free from iodate, in a 400 ml tall form
beaker with 250 ml of distilled water. Add 10 ml 1+9
H2S04 followed with exactly 20.00 ml of 0.152N biniodate.
Titrate with sodium thiosulfate stock solution using starch
?/
and with the Titralyzer in manual position^' When the solutions
are of equal strength 20.00 ml of 0.152N biniodate will require
20.00 ml of sodium thiosulfate. Also 20.00 ml of 0.038N
biniodate will require 20.00 ml of sodium thiosulfate. Add
starch toward the end of titration and the blue color will
disappear at the end point.
(Available from Stein Hall & Company, Inc.
605 3rd Avenue
,New York, N.Y.
[The millivolt end point is different in this titration compared to a
conventional dosed D.O. and cannot be titrated with Titralyzer
using automatic procedure unless end point setting is changed.
J.
-------
22
Procedure for Dissolved oxygen determination
1. To a sample collected in a 300 ml BOD bottle*1 add 2 ml
MnS04 solution followed by 2 ml of alkali-iodide-azide
reagent well below the surface of the liquid. Stopper with
care to exclude air bubbles. Mix the dosed sample by inverting
the bottle several times. If the precipitate settles to bottom
of bottle in less than 20 minutes then again mix the sample,.
When settling has produced at least 100 ml clear supernatant,
remove the stopper and add 2.0 ml of cone HoSOA by allowing
side of the
the acid to run down the/ neck. Restopper the bottle and
mix by inverting the bottle several times.
2. Pour 304 ml of the dosed sample, or the complete BOD bottle
volume into a 400 ml tall form beaker and place on Titralyzer
turntable.
3. Set the millivolt end point On the Titralyzer. This millivolt
settine flan be determined either by running a potentiometric
curvet'on a dosed D.O. sample or by titrating a dosed sample with
the Titralyzer in manual position using starch to determine the
end point. An end point of 681 millivolts, based on 0 - 1400
millivolt range, is used on our particular instrument.
4. Place the instrument under automatic control. Dosed samples
placed in the turntable will be titrated automatically,
without starch, and the volume of titrant will be recorded
by the instrument on a tape.
5. The instrument can be checked by adding starch to a titrated
sample. 0.05 ml of 0.038N biniodate will turn the colorless
sample to a blue-purple color.
The average volume of 100BOD bottles was 304.9 ml. The
variance was 1.14 with a standard deviation of 1.07. See
! Table 6. ___._|
-' |See Figure; 3. !
-------
23
Calculations
Each mllltliter of 0.038N ^28203 is equivalent to 1 mg/1
D.O. if a volume equal to 300 ml of original sample is titrated.
Precision and accuracy
Forty-one replicate samples were titrated both by hand and the
Titralyzer. On 20 samples titrated by hand, the calculated
samples
average was 7.66 mg/1. Twenty/titrated on the titralyzer had a
calculated average of 7.65. The variance on the hand titration was
0.0020 with a standard deviation of 0.045. The variance on the
titralyzer was 0.0025 with a standard deviation of 0.050. Thus for
all practical purposes, the instrument's titration was as
accurate as hand titration. (See Fig. 3).
A potentiometric titration was run on the remaining D.O. samples (Fig. 4).
The end point was 7.45 mg/1. The difference in the answer obtained
with the titration curve as compared to the automatic titration
or the hand titration is due to the time required to run the
potentiometric curve as iodine gas is being stirred out, thus
producing a lower result.by the potentiometric method.
-------
TABLE 6
STANDARD BOD BOTTLE VOLUME
24
BOTTLE
NUMBER
76
64
137
458
426
275
472
522
838
8
95
633
9
455
440
433
849
162
997
619
204
667
164
575
610
55
687
389
27
778
771
429
775
976
786
225
BOTTLE
VOLUME
(x - x)2
305
304
305
306
302
307
304
307
305
303
304
305
304
305
304
305
305
306
306
305
304
305
305
305
305
304
307
306
304
305
306
305
308
303
306
303
.0081
.8281
.0081
1.1881
8.4681
4.3681
.8281
4.3681
.0081
3.6481
.8281
.0081
.8281
.0081
.0081
1.1881
1.1881
.0081
.8281
.0081
.0081
.0081
.0081
.0081
1.1881
.8281
4.3681
1.1881
.8281
.0081
1.1881
.0081
9.5481
3.6481
1.1881
3.6481
BOTTLE
NUMBER
714
30
61
132
65
644
178
15
855
521
47
586
899
595
38
347
681
279
953
624
239
927
547
519
33
779
.774
360
662
5
301
467
446
728
736
219
BOTTLE
VOLUME
(x -
305
304
304
305
305
305
304
303
306
305
305
306
305
305
306
304
305
305
305
305
305
305
306
305
303
306
306
305,, .
304
306
306
305
304
305
305
305
.0081
.8281
.8281
.0081
.0081
.0081
.8281
3.6481
,1.1881
.0081
.0081
1.1881
.0081
.0081
.0081
.8281
.0081
.0081
.0081
.0081
.0081
.0081
1.1881
.0081
3.6481
1.1881
1.1881
.0081
_ .8281
1.1881
1.1881
.0081
.8281
.0081
.0081
.0081
-------
25
TABLE 6, Cont.
STANDARD BOD } BOTTLE VOLUME (Page 2)
BOTTLE
NUMBER
151
949
773
4
982
548
176
211
571
184
696
523
325
493
BOTTLE
VOLUME
305
305
305
305
303
307
305
304
305
306
305
306
302
302
(x - x)'
.0081
.0081
.0081
.0081
3.6481
4.3681
.0081
.8281
.0081
.8281
.0081
1.1881
8.4681
8.4681
BOTTLE
NUMBER
648
893
492
646
462
770
532
224
582
444
409
616
7
944
BOTTLE
VOLUME (x - it)2
304
307
304
305
304
306
306
304
305
306
393
305
304
305
.8281
4.3681
.8281
.0081
.8281
1.1881
1.1881
.8281
.0081
,1881
,6481
.0081
.8281
.0081
1.
3,
H - |OO
x - 304.91
£(x - X)2 - 112.54
V - l(x - x)2
n - 1
S >Tv" - 1.07
112.54
99
1.14
-------
TABLE 7
26
DISSOLVED OXYGEN
AUTOMATIC TIT8ATION VS. HAND TITRATION
AUTOMATIC TITRATIONS
HAND TITRATIONS
mg/1 D
7.68
7.69
7.62
7.67
7.72
7.65
7.68
7.67
7.62
7.59
7.55
7.65
7.67
7.55
7.72
7.62
7.66
7.65
7.61
7.72
x
V
S
.0. (x - x)2
1 , 0.0009
0.0016
0.0009
0.0004
0.0049
0.0000
0.0009
0.0004
0.0009
0.0036
0.0100
0.0000
0.0004
0.0100
0.0049
0.0009
0.0001
0.0000
0.0016
0.0049
= 7.65
(x - x)2 = 0.0473
- £(x - x)2 0.0473 - 0.0025
n - 1 19
« 4V 0.050
mg/1 D.
7.73
7.67
7.70
7.70
7.61
7.69
7.60
7.70
7.71
7.70
7.70
7.60
7.63
7.63
7.71
7.62
7.69
7.61
7.67
7.61
x =
V =
S =
0. (x - x)2
0.0049
0.0001
0.0016
0.0016
0.0025
0.0009
0.0036
0.0016
0.0025
0.0016
0.0016
0.0036
0.0009
0.0009
0.0025
0.0016
0.0009
0.0025
0.0001
0.0025
7.66
- x)2 = 0.0380
£(x-- x)2 = 0.0380
n - 1 19
^V~ - 0.045
0.0020
-------
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-------
29
REFERENCES
1. American Public Health Association, Inc.; Standard Methods
for the Examination of Water and Waste Water, llth Edition. (1960).
-------
30
TOTAL PHOSPHATE PROCEDURE
method
The acid molybdate - stannous chloride/is satisfactory for sea water.
However, for the Charleston Harbor Study samples, the turbidity
*
correction step as outlined in Standard Methods is misleading. The
high suspended solid concentration in Charleston Harbor produced high
turbidity interference with the spectrometric determination necessitating
a procedure modification in the turbidity correction step and calculation,
The time for color formation was increased to 13 minutes for the
convenience of handling 20 samples, the reagent blank.and three
standards.
Apparatus and -jteagents
See Standardjttethods for the Examination of Water and Waste Water,
llth Edition.
Procedure
Two 100 ml portions of each sample are taken for analysis,
one for color development and the other for turbidity correction.
To each of the 100 ml portions and, two 100 ml distilled water
blanks, add one drop of phenoIphthaliein : indicator solution. If a
pink color develops, add strong-acid solution drop by drop until the1
color disappears, and then add one ml in excess to each portion.
Digest each portion on a hot plate for 90 minutes, adding
distilled water to keep the volume above 25 ml. Cool and to one
portion of each sample and one distilled water blank adjust the pH
by adding sodium Hydroxide until a faint pink color appears. Restore
each portion to the original 100 ml with distilled water.
To these pH adjusted samples and blank, add 4 ml of molybdate
solution, mix well and add 10 drops of stannous chloride. Mix
well again and read on photometer 13 minutes after addition of the
stannous chloride- Use I distilled water to zero the instrument.
-------
31
Zero the instrument again using the remaining distilled water
blank and read the digested turbidity blanks.
Three standards are run with each set of samples.
Calculations
a = O.D. of reagent blank (distilled water + acid + NaOH
+ molybdate + stannous chloride)
b s O.D. of sample turbidity blank
c = O.D. of sample
Corrected O.D. = c - b - a
mg/1 Total P04 = Corrected O.D. x F
Where F is a chart factor obtained from the three standards
by dividing the mg of PO^ in the standard by the corrected O.D.
for the standard.
Table 8 shows the results from the analysis of 20 raw and spiked
samples using this modified procedure.
-------
32
TABLE 8
TOTAL PHOSPHATES
REPLICATES
RAW
mg/1
0.11
0.11
0.08
0.09
0.09
0.10
0.10
9.09
0.08
0.11
0.09
0.08
0.08
0.08
0.09
0.11
0.13
0.10
0.11
0.09
x = 0.10
V - 0.004
19
s = VoT5obT
(x - x)2
0.0001
0.0001
0.0004
0.0001
0.0001
O.OOOQ
0.0000
0.0001
0.0004
0.0001
0.0001 .
0.0004
0.0004
0.0004
0.0001
0.0001
0.0009
0.0000
0.0001
0.000}.
£= 0.004
= 0.0002
- 0.00145
SPIKED
.WITH 0.25 mg/1
0.36
0.37
0.37
0.34
0.37
0.37
0.35
0.39
0.38
0.38
0.39
0.37
0.36
0.35
0.36
0.35
0.35
0.36
0.39
0.33
x = 0.36
V = 0.0054
19
S -10.0003 =
% Recovery 104
(x - x)2
0.0000
0.0001
0.0001
0.0004
0.0001
0.0001
0.0001
0.0009
0.0004
0.0001
0.0009
0.0001
0.0000
0.0001
0.0000
0.0001
0.0001
0.0000
0.0009
0.0009
4- = 0.0054
= 0.0003
0.017
Chloride" « 12,800 mg/1
-------
33
LABORATORY DATA COLLECTION AND REPORTING
All laboratory data were recorded tn ink on 5" x 8" bench
cards. These raw data were then calculated and rechecked by either the
project chemist or laboratory director. Once the data were rechecked
were
and rounded off to the most significant figures they /tabulated
on engineering pads. The bench cards were then separated as to
determination and specific study and filed in chronological
order in a filing cabinet. This enabled one to check any piece of
tabulated data on the engineering pads against the raw data in a
matter of several seconds. The sub-groups of data for this
particular study were routine data, intensive survey data (Surveys
AA, AB, B, C, D, and E) and special studies.
The laboratory data were rounded off to the most significant
figures as illustrated below:
TABLE 9
DATA REPORTING
PARAMETER HOW REPORTED EXAMPLE
1) Dissolved Oxygen Hundredth 4.23 mg/1
2) Biochemical Oxygen Tenth 0.9 mg/1
Demand!'
3) Chemical Oxygen <100 mg/1 <100 mg/1
Demand='
4) Chloride Three significant 15,200 mg/1
figures
5) Conductance Expressed as Chloride
6) pH Tenth 7.6
7) Turbidity
0-25 <25 <25
26 - 100 Nearest unit 32
8) Total Suspended
and Volatile
Solids Nearest unit 12 mg/1
About 50% of data collected was less than 1.0 mg/1. Rather than recording
BOD as <1 mg/1 it was recorded to the nearest tenth.
2/
COD values of less than 100 mg/1 in salt water are not accurate and
are meaningless. On all harbor samples examined the COD was less than
100 mg/1.
-------
34
TABLE 9 (Cont'd)
PARAMETER
9) Ammonia Nitrogen
10) Nitrite Nitrogen
11) Nitrate Nitrogen
12) Organic Nitrogen
13) Ortho and Total
Phosphates
14) Total Coliforms
and Fecal Coliforms
HOW REPORTED
Tenth
Thousandth
Tenth
Tenth
Hundredth
Whole number
EXAMPLE
0.2 mg/1
0.002 mg/1
0.3 mg/1
0.6 mg/1
0.34 mg/1
1,240
per 100 ml
' The precision of total phosphate determination in sea water
is not this good and should probably be reported to
the nearest tenth.
-------
35
SPECIAL STUDIES
Results from the preliminary analysis of data collected during
the early intensive surveys and routine monitoring indicated several
areas requiring special investigation. A series qf special laboratory
more detailed
and field studies were initiated to develop/information on certain
segments of the system interactions.
These studies are
table
described in Table 1° i This/is followed by a detailed discussion
of the methods and procedures used in those studies which were either
carried to completion or utilized special field and laboratory techniques,
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39
ORGANIC CARBON - ORGANIC NITROGEN RATIOS OF SEDIMENTS
The purpose of this study was to characterize sediments as
to
organic or inorganic and/identify the source of any organic
material as domestic or industrial by organic carbon-organic
nitrogen ratios. This study is based upon the premise that the
ratio of organic carbon to organic nitrogen (C:N) in sewage is
sufficiently different from the corresponding ratio in the major
types
industrial waste/present and that this ratio can be used to
differentiate between the two types of wastes in sludge deposits.
Procedure
Sediment samples were taken with a scoop sampler such as used
by the Corps of Engineers. The samples were dried in an oven at
103°C overnight and then ground and stored in glass vials.
The chemical oxygen demand of the dried samples was determined
utilizing the dichromate reflux method with the mercuric sulfate
modification. The size of sample varied from 0.0300 grams near the
paper mill outfall to 8.0000 grams in clean portions of the Cooper
River. The weighed dry samples were placed in 500 ml (J24/40)
Erlenmeyer flasks and 50 ml of distilled water added. The COD
procedure outlined in the references given in Table 4 was
followed after the distilled water was added. The organic carbon
content was then stoichiometrically calculated.
C + G£ ^ C02
For every one gram atom of carbon oxidized, 2.67 gram atoms of oxygen
-------
40
simplification
is utilized. This equation is a / and does not account for.
all intermediate reactions, for organics not completely oxidized* or
for inorganic oxidation.
The COD value is substituted in the chemical equation above for
the oxygen, thus to calculate the organic carbon the following
equation is employed:
mg of organic carbon/gram dry sediment =
(a - b) (N) (8)
2.67 x weight of dry sediment in grams
a = ml Fe (1^4)2(804)2 used for blank
b = ml Fe (^4)2 (804)2 used for sample
N = normality of Fe (^4)2 (804)2
The organic nitrogen was determined by the micro-Rjeldahl /procedure.,
.which varied
A weighed amount of dried sediment/from 0.0200 gram
t
near the paper mill outfall to 1.5000 grams in clean portions of
the Cooper River, was placed in a micro-Kjeldahl digestion flask
and 50 ml of distilled water added.
% organic nitrogen = mg of O.N. in aliquot X 0.1
wt. of dried samples in grams
A summary of the data collected during this special study is
shown in Table 11 It can easily be seen from the-se-data that
there is a distinct difference in the composition of the sludge
deposits, depending on the source of organic material, and that the
organic carbon to organic nitrogen ratio presents a clear indicator
of this source. Table 12 presents all of the data developed
from this study.
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42
TABLE 12
ORGANIC ANALYSIS OF BOTTOM SEDIMENTS
Station
SA-1
SA-2
SA-3
SA-4
SA-5
SA-6
SA-7
SA-8
SA-9
SC-1
SC-2
SC-3
SC-4
SC-5
SC-6
SC-7
SC-8
SC-9
SC-10
SC-11
SC-12
SC-13
SC-14
SC-15
SC-16
SC-17
SC-18
SC-19
SC-20
1
Date
11/3/64
11/3
11/3
11/3
11/3
11/3
11/3
11/3
11/3
11/4/64
11/4
11/4
11/4
11/4
11/4
11/4
11/4
11/4
11/4
11/5/64
11/5
11/5
11/5
11/5
11/5
11/5
11/5
11/9/64
11/9
% Volatile
Solids
3.1
0.7
13.3
7.6
6.1
1.0
2.9
1.7
14.4
1.0
12.8
13.2
12.2
12.5
13.1
12.7
10.3
12.8
5.0
13.3
1.1
9.3
8.7
11.2
8.9
12.8
9.7
8.6
9.8
% Organic
Carbon
0.13
0.11
5.00
2.31
2.13
0.18
0.90
0.65
4.01
0.18
4.45
4.22
3.73
3.99
3.63
3.97
2.40
4.94
2.09
4.56
0.30
2.34
3.63
3.49
2.83
5.87
2.71
3.30
4.14
% Organic
Nitrogen
0.010
0.005
0.118
0.131
0.124
0.111
0.054
0.037
0.314
0.011
0.337
0.319
0.275
0.136
0.295
0.334
0.338
0.180
0.093
0.418
0.021
0.177
0.213
0.237
0.203
0.353
0.167
0.197
0.224
-' OC:ON
13.0
22.0
42.4
17.6
17.2
16.4
16.7
17.6
12.8
16.4
13.2
13.2
13.6
.29.3
12.3
11.9
7.1
27.4
22.5
10.9
14.3
13.2
17.0
14.7
13.9
16.6
16.2
16.8
18.5
Theoretical Oxygen
Demand
mS 6*2 / S"1 dry wt.
3.9
3.2
138.9
67.7
62.5
9.9
26.5
19.0
121.4
5.3
134.2
127.2
112.2
112.7
110.4
121.3
79.5
140.1
80.0
140.8
9.0
70.6
106.6
104.0
84.8
172.9
80.0
97.1
120.8
I/
Ratio of organic carbon to organic nitrogen
-------
TABLE 12 (Cont.)
43
Station
SC-21
SC-22
SC-23
SC-24
SC-25
SC-26
SC-27
SC-28
SC-29
SC-30
SC-31
SC-32
SC-33
SC-34
SC-35
SH-1
SH-2
SH-3
SH-4
SH-5
SH-6
' SH-7
SH-8
SH-9
SH-10
SH-11
SH-12
Date
11/9/64
11/9
11/9
11/9
11/9
11/9
11/9
11/17/64
11/17
11/17
11/17
11/17
11/17
11/17
11/17
11/12/64
11/12
11/12
11/12
11/12
11/12
11/12
11/12
11/12
11/12
11/12
11/12
% Volatile
Solids
12.5
14.3
8.7
13.6
7.4
10.1
0.6
0.2
3.2
.0.1
t
0.01
0.4
0.2
0.02
0.02
__ _
10.8
7.5
1.9
1.8
4.1
0.01
...
% Organic
Carbon
5.45
6.34
4.49
13.84
2.25
4.85
1.52
0.03
1.70
0.02
0.03
0.02
0.04
0.05
0.06
3.18
2.12
1.98
0.49
0.34
1.26
0.56
1.06
0.28
0.55
0.26
0.13
7o Organic
Nitrogen
0.310
0.398
0.171
0.287
0.088
0.289
0.008
0.002
0.077
0.003
0.003
0.002
0.003
0.003
0.003
0.234
0.244
0.228
0.070
0.035
0.090
0.051
0.099
0.029
0.037
0.026
0.013
OC:ON
17.6
15.9
26.2
48.2
25.6
16.8
190.0
15.0
22.1
6.7
10.0
10.0
13.3
16.7
20.0
13.6
8.7
8.7
7.0
9.7
14.0
11.0
10.7
9.6
14.9
10.0
10.0
Theoretical Oxygen
Demand
mg 02 / gm dry wt.
159.7
187.5
127.7
382.6
64.1
142.7
40.9
0.9
48.9
0.7
0.9
0.6
1.2
1.5
1.7
95.6
67.8
63.3
16.3
10.7
37.8
17.3
32.8
8.8
16.4
8.1
4.1
-------
TABLE 12 (Cont.)
44
Station
SH-13
SH-14
SW-1
SW-2
SW-3
Date % Volatile
Solids
11/12/64 5.0
11/12
11/12/64
11/12
11/12 3.4
% Organic
Carbon
3.29
3.02
0.77
0.60
1.22
% Organic
Nitrogen
0.317
0.267
0.115
0.056
0.043
OC:ON Theoretical Oxygen
Demand
nig 02 / S1 dry wt«
. 10.4
11.3
6.7
10.7
28.4
102.3
92.8
25.8
18.6
34.5
-------
45
DYE DISPERSION STUDIES
During the initial planning of the Charleston Harbor Project,
it was envisioned that the Corps of Engineers hydraulic model would
be used for examining the characteristics of the harbor under conditions
of reduced inflow. This approach was predicated on the premise that
the dispersion characteristics of the model could be verified by a
series of prototype dye studies which would establish the reliability
the
of/model for use as a predictive tool. A series of six dye releases
was planned for developing the necessary prototype information. Only
two of these six releases were made , and the data obtained were
not usable for model verification.
The first dye release was made between the jetties at the entrance
of the harbor. The purpose of this release was to establish the
hydraulic characteristics of the bottom currents in the salt wedge.
Two barrels of 40% Rhodamine B in acetic acid were injected into the ,
center of the channel at a depth of 30 feet during low water slack
tide. A slack water monitoring program was started on the following
high water slack and was to be continued until all traces of the dye
had disappeared. About three hours after the dye was released, winds
reaching velocities between 20mph and SOmph hit the harbor from a
direction exactly opposite the direction of the flooding tide. As
a result,waves between 4 and 6 feet developed, and the dye from the
salt wedge was brought to the surface. After the following ebb tide,
all traces of the dye/vanished.
The second dye release was made in the Ashley River at River
Mile 7 as measured from the channel junction near Fort Sumter. Two
barrels of \ 20% Rhodamine WT solution were injected as a line source
-------
46
in the center of the channel at high water slack. A four-hour frequency
sampling program similar to that used for the intensive surveys was
initiated at the time of release and was to be continued for a period
of five days. Approximately six hours after the dye was released,
a marked increase in turbidity was noted in the harbor in the vicinity
of the dye cloud. Approximately two hours later all traces of the
dye/disappeared.. No: further dye studies were attempted.
-------
47
HYDRAULIC MODEL STUDIES
Two types of studies were conducted on the Corps of Engineers
hydraulic model of Charleston Harbor. The first type consisted of
a lengthy series of dye tracer studies at various conditions of
fresh water inflow; and the second type consisted of a series of
salinity studies to duplicate the last four intensive surveys and
to vary the similitude of the model. The dye studies were scheduled
previously discussed
and conducted before the/verification studies because of time
later
considerations. The verification studies/demonstrated
that the model, insofar as project data were concerned, would not
adequately reproduce the salinity distribution to enable*the oroject
to make full use of all of the model dye data. Nevertheless . both
types of model studies produced useful information and gave additional
insight into the hydraulics of the harbor.
The salinity verification studies were based on the concept that
the chloride ion in both the model and the prototype systems should
have a similar distribution. Since the project-/already processed the
chloride data from the intensive surveys, it would be possible;, by
sampling at the same locations and frequency in the model under the
same conditions of fresh water inflow to reproduce the prototype ,data.
in the model studies.
Table 13 shows a summary of the intensive surveys used/ The model
was programmed to run in one 16 hour period the inflow hydrograph
covered by
that existed during the period / intensive surveys B through E. The
sampling stations were marked.,and the sampling procedure and schedule were
developed to reproduce the prototype data. During the test approx-
samples
imately 2400 samples were taken. These/were analyzed using the
modified chloride procedure with automatic titration, and the data
were compared with the prototype data.
Three separate types of data comparisons were made. The first
involved computing the mean chloride concentration at each station
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49
for each survey. These data are shown in Table 14 . A comparison
7
of the means showed a better similitude at the higher fresh water
inflow rates. The second comparison used was to compute the surface
to bottom ratio of the chloride concentrations to see if a similar
density stratification existed in both systems. These data are
shown in Table 15 The third method of comparison involved
making a cross spectral analysis of the response of the chloride
concentration to the river inflow. This type of analysis showed the
relationship of the variations in one time series record to the
variations in a second time series record. There were two types of
useful information developed from the cross spectral analysis. The
first was a frequency spectrum of the response of the variance of
one record (output) to the variance in a second record (input).
By graphically comparing the response spectrum of chlorides concentration
to river discharged for model and prototype, the similarity of the
two systems could be verified. This was done for all stations for
all surveys and it again showed a decrease in similitude as flows
decreased. The second type of information developed from the cross
spectral analysis was the overall response of the chlorides to fresh
water inflow. These data in grams per liter per cfs are shown in
Table 16 . Again there is an apparent loss of similitude with
decreasing flow. Due to this apparent loss of similitude with
decreasing flows, it was felt that the model dye data would be of
limited use for predicting the proposed future low flow conditions.
The model dye studies did provide some useful information on the
harbor system. A total of 18 dye studies were completed. A summary
of these studies is presented in Table 17 These da-za were used
to compute mean residence times and mean flushing times for the
harbor system.The method of analysis was to plot dye particle distribution
vs. time after dye release, assuming a log normal distribution, and to
use the 50th percentile time as the mean travel time from release
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53
TABLE
17
SUMMARY OF MODEL DYE STUDIES
STUDY NO. LOCATION
OF
RELEASE
1 Cooper River,
Mile 37
TYPE
OF
RELEASE
One Cycle,
Mid-Depth
TYPE
OF
DYE
FRESH WATER
INFLOW
cfs
Uranine 3,500
TIDE
RANGE
ft.
5.1
2
3
4
Cooper River,
Mile 20.3
Continuous
Surface -
Pontacyl
Brilliant
Pink
Bottom -
Uranine
3,500
Cooper River
Mile 20.3
Continuous
Surface -
Pontacyl
Brilliant
Pink
Bottom -
Uranine
15,500
5.1
Continuous
Surface -
Pontacyl
Brilliant
Pink
Bottom -
Uranine
30,500
5.1
10
Town Creek,
Mile 3.5
Continuous
Surface -
Pontacyl
Brilliant
Pink
Bottom -
Uranine
3,500
5.1
11
Town Creek,
Mile 3.5
Continuous
Surface -
Pontacyl
Brilliant
Pink
Bottom -
Uranine
15,500
5.1
-------
TABLE 17 (Cont'd)
54
STUDY NO.
LOCATION
OF
RELEASE
TYPE
OF
RELEASE
TYPE
OF
DYE
FRESH WATER
INFLOW
cfs
TIDE
RANGE
ft.
12
13
14
15
16
17
Town Creek,
Mile 3.5
Continuous
Custom House Continuous
Pier
Custom House
Pier
Custom House
Pier
Ashley River Instantaneous
Mile 7
Wando River,
Mile 4.5
Ashley River,
Mile 7
Wando River, " "
Mile 4.5
Surface -
Pontacyl
Brilliant
Pink
Bottom -
Uranine
Surface -
Pontacyl
Brilliant
Pink
Bottom -
Uranine
Surface -
Pontacyl
Brilliant
Pink
Bottom -
Uranine
Surface -
Pontacyl
Brilliant
Pink
Bottom -
Uranine
Pontacyl
Brilliant
Pink
Uranine
Pontacyl
Brilliant
Pink
Uranine
30,500
3,500
15,500
30,500
3,500
3,500
15,500
15,500
5.1
5.1
5.1
5.1
5.1
5.1
5.1
5.1
-------
TABLE 17 (Cont'd)
55
STUDY NO.
LOCATION
OF
RELEASE
TYPE
OF
RELEASE
TYPE
OF
DYE
FRESH WATER
INFLOW
cfs... -
TIDE
RANGE
ft.
18
20
23
26
Ashley River,
Mile 7
Wando River,
Mile 5
Entrance
Channel,
Mile 3
Entrance
Channel,
Mile 3
Entrance
Channel,
Mile 3
Instantaneous Pontacyl 30,500
Brilliant
Pink
" " Uranine 30,500
Flood Interval, Pontacyl 3,500
Continuous, Brilliant
Bottom Diffuser. Pink
Flood Interval, Pontacyl 15,500
Continuous, Brilliant
Bottom Pink
Diffuser.
Flood Interval, Pontacyl 30,500
Continuous, Brilliant
Bottom Pink
Diffuser.
5.1
5.1
5.1
5.1
5.1
-------
56
point to sampling station. This was done for all three tributary
streams for three different conditions of flow to show the effects
of river flow. The results of these computations are shown in
Table 18
-------
58
SAMPLE PRESERVATION
From March 3, 1965j to September 24, 1965, 6000 samples were
collected for nutrient determinations (total phosphates, nitrate,
ammonia and organic nitrogen). These samples could not be analyzed
on the day of collection due to lack of laboratory space, equipment,
samples
and personnel. Thus/were preserved with 1 ml of cone l^SO^ per
liter of sample and stored in plastic cubitainers. The purpose of
this study was to determine the effects of acid preservation of
nutrient samples on the accuracy of the analytical results.
Sample collection and preservation
Harbor samples were collected with either a submersible pump or
Sargent sampler and delivered to the lab in one gallon plastic
bottles within three hours from time of collection. One liter was
immediately poured into a plastic cubitainer and 1 ml of cone K^SO^
added. For the purposes of the preservation study, nutrient
determinations were immediately made upon delivery of samples to the
£1
lab and then at/time sequence of usually one month, two months, three
months and six months. Nutrient concentrations in Charleston Harbor
were generally less than 0.3 mg/1; thus, to give the effect of
preservation at different concentrations, some of the samples were
spiked with known concentrations of nutrient material. A summary
of the results of this study is shown in Tables 19 - 22.
Total phosphates
The mean total phosphate concentration of 18 samples collected
from the harbor was 0.09 mg/1 PO^ with a range from 0.04 to 0.35
mg/1. The samples were preserved with 1 ml of cone ^SO^ per liter
of sample and stored in plastic cubitainers. At the end of one month
the mean total phosphate concentration of 17 samples was 0.15 mg/1
-------
59
with a range from 0.11 to 0.52 mg/1. At the end of two months
the mean total phosphate concentration of 18 samples was 0.19 mg/1
P04 with a range from 0.11 to 0.54 mg/1.
The mean total phosphate concentration started to decrease at
the end of three months. The mean total phosphate concentration of 18
samples was 0.17 mg/1 PO^ with a range of 0.08 to 0.65 mg/1. The mean
total phosphate concentration continued to decrease and at the end of
six months was down to the level of the raw sample; i.e., 0.09 mg/1
P04 with a range of 0.01 to 0.52 mg/1.
A second set of the raw samples were spiked with 0.25 mg/1 PO^
giving a mean total phosphate concentration of 0.34 mg/1 PO^ with a
range from 0.27 to 0.55. These spiked samples were also preserved
with ^SO^ acid and stored in plastic cubitainers. The mean total
phosphate concentration increased throughout the six month period
reaching a level of 0.56 mg/1 PO^ with a range from 0.25 to 1.00 mg/1,
Based on these data it appears that phosphates are being released
by the plastic cubitainers. The mean total phosphate concentration
increased over 100 percent on the raw preserved sample at the end of
two months and the total phosphates on the spiked preserved sample had
increased 65 per cent at the end of six months. It is concluded that
acid preservation and storage d>£ samples in plastic cubitainers will
lead to erroneous results for total phosphate analysis at these low
concentrations. It is recommended that further work on sample
preservation techniques be undertaken. See Table JL9.
Nitrate nitrogen;
The mean nitrate concentration of 20 samples collected from
the harbor was 0.06 mg/1 N03 - N with a range of 0.03 to 0.13 mg/1.
-------
60
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At the end of six months the mean concentration of acid
preserved samples stored in plastic cubitainers was 0.05 mg/1
N03 - N with a range of 0.03 to 0.10 mg/1.
Analyses of the spiked samples preserved with 1 ml H2S04 showed
equally good results. The mean concentration of the raw sample spiked with
0.2 mg/1 was 0.26 mg/1 N03 -. N with a range from 0.22 to 0.28 mg/1.
At the end of six months the mean concentration was 0.21 mg/1 NO^ - N
with a range from 0.18 to 0.26 mg/1. Based on these data it appears
that acid preservation and storage in plastic cubitainers is a
satisfactory means of preservation for nitrate analysis. See table 29.
Ammonia nitrogen
The mean ammonia concentration of 19 samples collected from the
harbor was 0.27 mg/1 NH3 - N with a range of 0.14 to 0.54 mg/1. The
ammonia concentration in the samples preserved with 1 ml of I^SO
per liter of sample and stored in plastic cubitainers increased
through the second month, resulting in a mean concentration of 0.42
mg/1 NH3 - N with a range of 0.18 to 0.74 mg/1. At the end of
six months the mean ammonia concentration was 0.32 mg/1 NH3 - N
with a range of 0.09 to 0.67 mg/1.
The acid preservation of spiked samples produced about the same
results. The mean concentration of raw samples spiked with 0.3 mg/1
was 0.60 mg/1 NH-j - N with a range from 0.48 to 0.76 mg/1. The mean
concentration at the end of six months was 0.78 mg/1 NHo - N with
a range from 0.49 to 1.10 mg/1.
The only explanation for the high values at the end of 2 months
on the preserved spiked samples is procedure difficulties or laboratory
error.
As has been stated before, the pre-floc ammonia procedure leaves
much to be desired. Even though these data indicate a slight increase
-------
62
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63
in low ammonia concentration using acid preservation, this method
of preservation is as satisfactory as is the analysis of fresh
samples employing the pre-floc procedure. See Table 21.
Organic nitrogen
The mean organic nitrogen concentration of 19 samples collected
from the harbor was 0.38 mg/1 with a range from 0.22 to 0.47 mg/1.
The samples were preserved with 1 ml of cone. l^SO^ per liter
of sample and stored in plastic cubitainers. At the end of one
month the mean organic nitrogen concentration was 0.36 mg/1 with
a range from 0.24 to 0.47 mg/1, and at the end of two months was
0.45 mg/1 with a range from 0.33 to 0.67 mg/1. At the end of
3 months the mean had dropped to 0.30. The preserved samples were
run again in seven days for duplicate 3 months data. The mean was
0.30 again.
The raw samples were spiked with 0.2 mg/1 of organic nitrogen.
The mean concentration was 0.54 mg/1 organic nitrogen with a range
from 0.36 to 0.68 mg/1. The spiked samples were also preserved
with acid and stored in cubitainers. The mean organic nitrogen
concentration remained constant through two months and dropped 0.1
at the end of the third month.
Based on these data it appears that preservation of samples
with l^SO^ and storage in plastic cubitainers will suffice for organic
nitrogen analysis if the samples are analyzed within two months.
See Table 22.
-------
64
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66
FREE CARBON DIOXIDE
Free carbon dioxide in estuarine waters exists as C0£ molecules
and carbonic acid with 99 per cent as CX^. Combined carbon dioxide
exists as carbonates and bicarbonates. The form of carbon dioxide
depends primarily.upon pH, temperature, salinity and pollutional
conditions. The nomographs in Standard Methods will not suffice
in estuarine waters due to the buffer capacity of sea water. The
buffer capacity or total alkalinity is directly related to salinity
and is independent of either total carbon dioxide, free carbon dioxide
or combined carbon dioxide in this estuary.
There is considerable disagreement in the literature about the
it
toxicity threshold of carbon dioxide to fish but'is generally agreed
. .where
d/tlu
that free carbon dioxide can be toxic to fish.
The purpose of this study was to measure free carbon dioxide
in the Ashley River where numerous fish kills have occurred and/the
fisTi population is now very small. The active sludge beds in
the Ashley River produce sufficient free carbon dioxide to create
a deleterious venvironment for the fishery resources.
Apparatus
1) Natelson Microgasometer and associated parts
2) 10 ml disposable hypodermic syringes
3) Mercury
The basic theory of the Natelson microgasometer is the same
as thecdassical Van Slyke manometric method. The gas pressure is
measured under constant volume so that results are independent of
atmospheric pressure.
-------
67
Procedure
1) Samples for free carbon dioxide determinations were
collected under mineral oil and refrigerated until analyzed.
Surface samples were collected with a hypodermic syringe in
the following mannerT
Draw up approximately 2 ml of mineral oil into a 10 ml disposable
syringe. Hold the syringe in upright position and remove all
atmospheric CC>2 by eluting a small amount of mineral oil. With
the syringe approximately one foot under the surface, draw
approximately five ml of sea water into the syringe being careful
to elude atmospheric carbon dioxide. Cap the syringe under
water and place in an ice chest in upright position. The mineral
oil should be at the top of the syringe or over the water sample.
Keep refrigerated until analyzed.
The following glass bottle method can be employed for depth
samplesc !Place mineral oil to a depth of approximately two
inches in a glass bottle. Drop a kemmerer sample to a desired
depth, close the sampler with plunger and bring to surface.
Discard 200 to 300 ml of sample and then place the rubber tubing
on the bottom of sampler to the lower limit of the mineral oil
in the bottle. Allow the bottle to fill but do not overflow.
Place the bottle in upright position in an ice chest and keep
refrigerated until analyzed.
2) Prior to the determination of free carbon dioxide the manometer
employed with the Natelson microgasometer should be checked and
calibrated according to the Natelson Microgasometer Instruction
Booklet #5 as outlined on pages 16, 17 and 18. Advance the
mercury until a small drop is held on the tip of the pipette and
-------
68
then draw 0.10 ml of sample into the pipette, being careful
not to draw in mineral oil. Cap with 0.01 ml of mercury and
then draw in 0.10 ml of 10% low foam detergent. Cap with
mercury to 0.12 ml mark of reaction chamber. Close the
reaction chamber stopcock and retreat with piston until liquid
level is halfway into reaction chamber. Mix one minute and
advance the piston until the top aqueous miniscus is at the
0,12 ml mark. Obtain Pi reading and record along with temperature,
3) Advance piston till mercury is to top of manometer. Place
vial of IN lactic acid solution under the tip of pipette and
draw in 0.03 ml. Cap with mercury to 0.12 ml mark of reaction
chamber. Close the reaction chamber stopcock and retreat with
piston until liquid level is halfway into reaction chamber.
Mix one minute and advance the piston until the top aqueous
miniscus is at the 0.12 ml mark. Obtain Pn reading and record.
4) Advance piston until mercury is to top of manometer. Place
vial of 3N NaOH solution under the tip of pipette and draw
in 0.10 ml. Cap with mercury to 0.12 ml mark of reaction chamber.
Close the reaction chamber stopcock and retreat with piston
until liquid level is to bottom of the reaction chamber. Raise
and lower the piston several times and then advance the piston
till the top aqueous miniscus is at the 0.12 ml mark. Obtain
?3 reading and record along with temperature.
5) Advance piston until mercury is to top of manometer. Open
reaction chamber stopcock and wash reaction chamber with 0.1
ml of distilled water followed with 0.03 ml of 1(1 lactic acid.
Repeat several times with distilled water and then proceed to
next sample.
-------
69
Experimental data
The observed free C02 data are shown in Tables 23 - 28. These
data result from analyses of samples collected from the Ashley River.
-------
70
Calculations
These; calculations are a slightly modified version of those
given in Instruction Booklet #5 on Page 17 for the Natelson
Microgasometer to give COo concentration in mg/1. The equations
j manometer,
used to convert instrument'readings to C02 concentrations are
shown below.
mg/1 of free C02 = (pl - P3 > F 44
3.3
mg/1 of Total CO, = F 44
3.3
mg/1 of combined C02 = ^P2 " Pl^ ' F * 44
3.3
where :
PI = Partial pressure of all gases in sample in mm of mercury.
P2 = Partial pressure of all gases plus the partial pressure of
acid released C02 in mm of mercury
P3 = Partial pressure of all gases less the partial pressure
of the carbon dioxide absorbed in caustic in mm of mercury.
F = factor for converting mmr. of mercury to mmole/1 of
These factors are found in Table #3 on page 27 of the
Natelson Microgasometer Instruction Booklet #5.
44 = is a conversion factor for converting mmole:' to mg of C05
mg _
3.3 = is a factor used to correct formulas given in the Natelson
Microgasometer handbook for the size of sample used in
the analysis.
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77
ORGANIC CARBON
During the summer months the dissolved oxygen depletion in
Charleston Harbor is much greater th^u chat attributable to the
5-day BOD ln the water. This oxygen depletion is apparently
caused by the stabilization procedure occurring in the sludge
deposits. To check this premise a study was conducted to measure the
organic carbon in solution and correlate long term BOD to organic
carbon content utilizing the Beckman Carbonaceous Analyzer.
Sample collection and preservation. The samples were obtained with
the ordinary water sampling equipment and were analyzed immediately
upon collection and return to the laboratory.
The effects of acid preservation techniques on organic carbon
content were investigated, but sufficient data were not collected to
fully evaluate the methods.
Procedure:
1) Add 3 drops of cone HC1 to approximately 20 ml of sample in a
50 ml beaker. Purge with nitrogen gas for 5 minutes to remove inorganic
carbonates. This N£ strip p.^ccdure will not suffice for the removal
of inorganic carbonates if low volatile organics are present.
2) Place the 50 ml beaker containing the sample on a small magnetic
stirrer and allow to stir 30 seconds before drawing an aliquoc for
injection into the analyzer.
3) Draw 40ul of sample using a hypodermic syringe and inject into
the Analyzer according to the Beckman Instruction Manual.
4) Prepare a series of standards in the range of 0.0 to 10.0 mg/1
working standard of Potassium hydrogen phthalate (2.1254g of KHCoH/0/
diluted to one liter = 1000 mg/1 of organic carbon). Treat the
standards identical to the sample and inject 40 microliters of each
into the instrument. Plot peak heights vs. concentration of organic
-------
78
carbon or. graph paper (Note: the distilled water blank will not
pass through zero due to 1^0 interference). Compare the peak
heights of sample to peak height of the curve to compute the organic
carbon content of the sample.
Notes:
1) A gain setting of 264 is recommended by Beckman. We found
(See Figure 1) that a gain setting of 600 in the range of 0.0 - 10=0
mg/1 O.C. is much more sensitive and the increased noise is tolerable.
The peak height of the 5.0 mg/1 standard was doubled by increasing
the gain setting to 600.
2) NaCl in sea water has little or no effect in the determination
of organic carbon. The effect of other salts in sea water, not
including the carbonates, appears to be negligible due to the low
concentrations. All samples must be pretreated to remove carbonates
and acid carbonate salts as these will give erroneous, positive
results.
3) The Beckman instructions suggest an oxygen flow rate of 50 cc/minute,
The best flow rate for our particular instrument is 100 - 125 cc/minute
with a 40 microliter sample. Sample injections faster than one
every two minutes produces "feed back" from the combustion tube.
4) The silt and salts in Charleston Harbor clog the combustion tube
and micron filter. The tube must be repacked and the filter cleaned
after every 125 samples or 375 injections (each sample is injected
at least 3 times as odd peakrs are sometimes encountered).
5) The precision of the analyzer is + 0.3 mg/1 O.C. in the range
of 0.0 - 10.0 mg/1 with a gain setting of 600.
Experimental data:
Tables 2^ and 30 show respectively the 5-day and long-term
BOD - organic carbon comparison.
-------
79
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-------
81
OXYGEN UPTAKE BY SEDIMENTS
The purpose of this study was to quantitatively measure the
potential oxygen utilization by the deposits and to determine what
effect different types of sludge beds in different areas of the
harbor have on the dissolved oxygen resources.
"Vpor 1 -ipn'ral methods:
Sediment samples for this investigation were taken at 61
locations in the Harbor and the major tributaries. Sediment samples
were taken with a Peterson dredge and delivered to the lab in sealed
one-quart plastic containers. The sample was thoroughly mixed and
50.0000 grams were placed in a 5-gallon glass carboy containing sea
water (18,600 - 19,200 mg/1 Cl). The sea water was aged at least
3 days and aerated several hours at 21°C before using. The carboy
was then sealed with a syphon system as shown in Figure 5 .
Another portion of the mixed sample was dried at 103°C overnight
and stored in glass vials for chemical oxygen demand and organic
nitrogen determination. In addition, volatile solids and percent
moisture determinations were made on the sediment samples.
Sediment samples for oxygen uptake determinations were placed
in both a mixing and a non-mix system. Neither of the systems were
exactly similar to the conditions in the harbor but this approach permitted
a determination of extreme ranges of oxygen uptake potential.
Salinity, temperature, light conditions and initial dissolved
levels were maintained as near constant as possible for all tests. Sea
water x^as used as dilution media and was always 18,600 to 19,200 mg/1
chloride. The sea water was delivered to the lab several days ahead
of samples and allowed to come to room temperature (21°C). On several
occasions when the sea water contained turbidity they were allowed
-------
c
82
to
r-i
pt,
-------
83
Lo s,_.tele over fright and syphor.cd the next morning. The temperature
i.'as r.'..v'..n coined at 21°C0 The tcmparr.tures of mixing systems were
slightly higher than non-mixing systems due to the heat from magnetic
stirrers. Light conditions were constant in the laboratory. The
only source of light was from the overhead fluorescent lights which
were turned on every morning and off at Lhe end of the working
day. The dissolved oxygen concentration was also close to saturation
of sea water at 21°C.
A sea water blank was run along with every set of samples. At
first thi;-- was a mixing blank but later was changed to a non-mixing
blank ,r.;j the dissolved oxygen depletion was very small in both the
mixing and non-mixing systems. Dissolved oxygen depletion in the
sea wacer bl.ir.ks '..--.is always less than 0.5 mg/1 at the end of five days
and was usually about 0.1 mg/1.
On sediment samples near the paper mill the size of the sample was
reduced f:v . 50.0000 weight grams to 10,0000 grams so as not to
deplete the oxygen in the carboy to less than 1.0 mg/1 at the end
of five days. The size of the sample was increased to 200.COOOg
for the datum stations in the upper Cooper River above all pollution
sources.
There are many arguments concerning the oxygen demand of disturbed
and undisturbed bottom muds. The purpose of this study was to
measure the potential for dissolved oxygen uptake by resuspended benthic
deposits. The actual oxygen demand of deposits in the harbor probably
is less than that observed in the mixing system and more than that
demonstrated by the non-mixing system. The exact amount of resuspension
of bottom deposits in the harbor is virtually impossible to measure.
-------
1) Eloven 5-gallon glass carboys
2) Eleven 4-liter glass botcles with tuning outlet
3) Six senior mag-mix stirrcrs
4) Eleven size #llJj rubber steppers
5) An assortment of rubber tubing, glass tubing and clamps
(See Drawing #1)
Procedure:
1) Determine the volume of the glass carboys and record.
2) Collect the bottom sampl-Li \\''. >:n a Peterson dredge and seal in
a suitable plastic cor.t,.'..-....:. Vhe sample should be tested as
soon as possible, and not stored more than 2 to 3 hours. The
plastic container must be scaled and completely full to retard
oxidation.
3) The dilation water in the carboys i;, sea water (19,000 mg/1
of chloride) which is several days old and has been aerated
at 20 to 21°C for several hours.
4) Mix the sample and place 50.000C grams of the wet sample into a
carboy containing sec. water co within 3 inches of the top. Add
a stirring bar to chc c..j.,oy and add sea water to bring the
water level to the top. Carefully inset the syphon system into
the carboy being careful not to entrap air bubbles in the system.
Set the carboy upon a mag-mix stirrer and stir 10 to 15 minutes
before drawing a sample for dissolved oxygen determination.
50.0000 grams of wet samples is placed in a carboy without a
stirring bar for the non-mixing system. A blank of the sea
water is set up in identical fashion with the omission of bottom
samples. The initial D.O. of the blank is used as the initial
D.O., of the carboys containing sediment. The oxygen utilization
in DO 1 luted areas is rapid and the D.O^ at the end of 10 to 15
-------
85
m dilutes may be as much as 1.5 to 2.0 mg/1 less than the blank.
5) Determine the percent moisture of a weighted portion of the
regaining sludge in the plastic containers by drying over night
ac 103°C. The volatile solids is then determined at 6GO°C for
15 v.i.r.L, cos.
o) Dry anojhar portion of the remaining sludge in the plastic
containers by placing approximately 20 grams in an evaporation
cILsh and drying at 103°C over night. Grind and mix the dried
sample and store in a glass bottle for chemical oxygen demand
and organic nitrogen utilizing the same method discussed in the
special study section on organic carbon to organic nitrogen ratios
of benthic deposits.
7) Svphon and determine the D.00 daily from the blank, mixing and
non-mixing systems.
1) Determine the grams of dry material in the 50.0000 grams of
the sample.
50.0000 X (ICO - percent moisture)
= grams of dry sample
2) Determine the mg of oxygen utilized per gram of dry sediment
mg oxygen per gram of dry sediment ~
(DO^ - D0t ) X volume of carboy in liters
GRAMS OF DRY SEDIMENT
where:
DO- = Initial dissolved oxygen
DO*. = Dissolved oxygen at time t
Experimental Resales;
All experimental results are presented in Table 31 and a statistical
treatment of ive data is presented in Table 32.
-------
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, . DATA ANALYSTR
BASIC STATISTICAL METHODS
The scheme of data analysis developed herein is one that was
evolved for this specific project for use 'with the intensive
survey data. It is based on fundamental statistical principles of
data handling and analysis to provide an understanding of the
significance of the variations in the data and a reliable starting
point for engineering and scientific evaluation of the results.
The basic steps in this analysis scheme were these:
1) Compute the basic descriptive statistics of each significant
parameter distribution at each sampling station;
2) Compute the Pearson distribution of each significant parameter
at each station;
3) Make an analysis of variance for each significant parameter
between surveys to determine if there was a statistically significant
difference between parameter distribution;
4) Make an analysis of covariance for pairs of significant parameters
for stations and for surveys. This is a combination of an analysis
of variance and a regression analysis; and
5) based on the analyses of variances, significant pairs of parameters
were selected for cross-spectral analysis to determine the parameter
interaction at each station.
Each step of data analysis procedure is discussed below in greater
detail.
Descriptive statistics; All basic water quality and environmental
data were put on punch cards and, except for the nutrient series
(i.e. ammonia nitrogen, nitrate nitrogen, total organic nitrogen,
total phosphates)and pH,were tabulated along with the mean, variance
standard deviation, skewness, kurtosis and frequency distribution in
-------
95
standard deviations on computer print out sheets. The nutrient
and pH data were only tabulated because the nutrient values were
sufficiently low to be of minor concern and the pH values were not
amenable to this statistical treatment. Data processed through
the descriptive statistics program are shown in Table 33
Pearson coefficients; The coefficients of the Pearson theoretical
frequency distribution were calculated and also tabulated on the
descriptive statistic print out sheets. The Pearson distribution,
which is a general analytic representation of a wide variety of
possible observed distributions, is obtained from the solution of
the first order differential equation.
Where the y - axis is the centroid vertical and the values of y
are the number of observations found at corresponding values of x.
The Pearson coefficients are calculated from the relationships
A =
A
b= £
S is the variance, L is the skewness and K is the kurtosis.
The Pearson distributions provided a common mathematical basis for
evaluation of the observed frequency distributions.
Analysis of variance; The analysis of variance is essentially the
separation of variance according to causes and determining by
variance ratios the probability of the samples being tested of
coding from the same populations. The analysis of variance computations
The definition of pH is: pH =-jJ Therefore pH, similarly
to MPN coliforms, should be analyzed statistically in terms of
a geometric mean or a harmonic mean rather than an arithmetic
mean.
-------
96
TABLE 33
DATA PROCESSED THROUGH DESCRIPTIVE STATISTICS
PROGRAM
ENVIRONMENTAL WATER QUALITY
DATA DATA
Rainfall Chloride Concentration from Model Studies
Air Temperature BOD
Tide Height Total Coliforms
Wind Speed Fecal Coliforms
Solar Radiation Water Temperature
River Discharge Chlorides (Prototype)
Dissolved Oxygen
Dissolved Oxygen (percent saturation)
Total Solids4
Volatile Solids4
Turbidity4
NOTES:
1) Intensive survey data measured on four-hour frequency for period
of 5 days.
2) Environmental data recorded every four hours during intensive
surveys.
3) Observed values for nutrients and pH only tabulated.
4) frhese parameters measured only during intensive surveys AA and AB
Khen sufficient laboratory personnel were available to make the
determinations.
-------
97
result in an F ratio or variance ratio which can be compared to
standard statistical tables to ascertain for any given degree of
significance whether the samples came from the same populations.
The analysis of variance procedure was applied to the data
of the two most important quality parameters, chloride concentration
and dissolved oxygen percent saturation. Chloride concentration was
used because it is a conservative constituent and dissolved oxygen
percent saturation was the predominant water quality degradation
factor. The major questions to be answered by the analysis of
variance were these:
(1) Is ther^a significant change in the statistics of each water
quality parameter between surveys at the same stations?
That is, does each of the six surveys represent sampling of a
different physical environment, or may two or more of the surveys
\e used as representing the same environment? A lack of significance
in the F-ratio between surveys would indicate that the surveys
being considered can be regarded as one survey, and that the data
obtained are all samples of the same physical environment.
(2) Is there a significant change in the statistics of each
water quality parameter between stations for each survey? That
is, are the stations chosen sufficiently far apart that the observed
changes in parameters between the stations do represent changes in
the environment between them,or may some of the stations be grouped
together in the data analysis? A lack of significance in the
F-ratio between stations would indicate that the station records
concerned are actually measurements of the same environment and may
be treated as such. -
(3) Are the statistics of difference between the same parameters
at different stations the same for all surveys or sequential parts.
-------
98
of surveys? For example, is the change in Chlorides between
Stations 1 and 2 the same for Survey B as for Survey C? A lack of
significance in the F-ratio for station-survey interaction would
indicate that the relationships between stations are similar for
the surVeys concerned.
(4) For the environmental factors (River Discharge, Tide Height,
Air Temperature, Solar Radiation, etc.), which factors show
significant changes between surveys? A lack of significance in
the F-ratio between surveys would indicate that the environmental
factor analyzed does not change and may be regarded as having
similar effects during each survey.
The results of the analysis of variance were used as a basis for
selecting pairs of environmental and water quality parameters on
which an analysis of covariance was run.
Analysis of cpvariance: The analysis of covariance and cross-spectral
analyses were begun at the same time with the object of reaching
the same goal. This was to develop significant relationships between
pairs of water quality parameters and between water quality parameters
and environmental factors. The major difference in the two approaches
being that the covariance analysis approach does not yield as much
information about the relationships. However, at the time these
approaches were started, it was questionable whether the records were
of sufficient length to yield reasonable results from the cross-spectral
computations, therefore, both methods were tried. The information
yielded by the cross-spectral analysis was far superior to that from
the covariance analysis and further covariance analysis was discontinued,
-------
99
Essentially the analysis of covariance involved a combination
of the methods of regression and analysis of variance where the
regression coefficients were calculated and tested for equality
along with the residual variances. The questions to be answered
from this approach were these:
(1) Is there regression between individual values of y and x
for the entire body of data?
(2) Is the regression of replicates at individual stations the
»
same for all stations in all surveys?
If this F is not significant, then the regression of y on x is
the same for each station in each survey.
If this F is significant, then it is necessary to examine the
variation of the regression coefficients at each station between
stations and between surveys.
(3) Is there a significant difference between the regression of
replicates within one station and the regression of mean values for
each station over all surveys and all values?
If this ratio is not significant, then the regression coefficient
of replicates of y or x within stations is the same as the regression
coefficient of the mean values of y and x at each station for all
stations in all surveys.
If the ratio is significant, then it is necessary to examine the
variation of the mean regression coefficients at each station between
surveys and stations.
(4) Is there a significant difference between the regression of
the mean values at each station between all stations at all surveys
and stations only?
If this F is not significant, then there is no difference in the
regression of the individual station means for all stations and
surveys and for stations only.
-------
\
100
(5) Is there a significant difference between the regression
of the mean values at all stations at all surveys and surveys
only?
Cross-spectral .analysis: Cross-spectral analysis is a technique
whereby a pair of sequential records can be analyzed to ascertain
the statistical relationships between them. Conceptually, cross-
spectral analysis is the harmonic covariant analysis of two time
series records where one record is considered a causative factor
and the other a resultant. The statistics produced show the
significance of the cause-effect relationships as well as a temporal
relationship. The procedures involved in cross-spectral analysis
require a tremendous amount of calculations and are practical only
if a high-speed computer is available. The computational steps
for cross-spectral analysis are (1) compute the individual power
spectrum of each record; (2) compute the cospectrum and quadrature
spectrum from the cross-correlations of the two records; (3) compute
the coherence, the phase lag, and the response spectrum from the four
spectra listed above; and (4) compute the overall response. Each
of these steps is discussed in more detail below.
(1) Individual power spectrum. The term power spectrum refers to
a sorting/the total variance of a time series record into those parts
that recur at a constant time interval or frequency. This sorting
is accomplished by the following procedure. Using a record of
constant sampling interval, tabulate the data sequentially and
determine the mean and the square of the mean. Compute the auto-
correlation function of the record for the desired number of lags.
This function is obtained by multiplying each number of the record
by another number in the eecord, determining a mean of the sum
and subtracting from this mean the square of the arithmetic mean
-------
101
of the entire record. This may be expressed mathematically by
= N~r 2_ Vt
where '
Cr = Autocorrelation at lag r,
Xt = record value at t ,
t = sequential index of values,
r = lag numbers,
m = total number of lags, and
n = total number of values.
The fluctuations in autocorrelations are smoothed by applying a
cosinusoidal weighting factor. This factor is the Fourier cosine
transform and is computed mathematically from the expression
where
Vr = Fourier cosine transform of the autocorrelation of lag r,
q = lag number, having values between 1 and m - 1
k = a constant, k « 1 for r = 1, 2 --- m - 1
k = 1/2 for r = o and m.
The final step is computing the power specrum estimates for each
lag period. This procedure involves another weighting operation
to counteract distortion of spectrum resulting from the small
sample size. Mathematically this is accomplished from
V0 = 0.54V [Vo + Vj] ,
v = 0. as Vr-, -f
Urn = 0.5> V^_, +
Vo, Vr and Urn are the power spectrum at the corresponding lag periods.
-------
102
The temporal period corresponding to each lag can be obtained
from the expression
2-m
Tr is the period corresponding to the lag, and A t is the sampling
interva 1 .
(2) Cospectrum and quadrature spectrum - These two spectra are
the result of a cross-correlation procedure which is an extension
of the autocorrelation process. They are obtained by multiplying
one record by second record, and since either record may be lagged,
there two possible cross-correlations. The cross-spectrum scheme
of data analyses utilizes the sums and differences of the cross-
correlations and may be expressed mathematically
^r=jT,-r)
where x and y are the values of the records, t is a sequential
index of values, r is the lag number, m is total number of lags,
and S denotes whether the computed factor is from the sums or
differences of the cross-correlation.
The Fourier transform of the two cross-correlation functions
is then computed. This again is a weighting operation or smoothing
function. However, it differs from the procedure used for the
individual power spectrum in that a sine transform is used on one
of the cross correlation factors and a cosine transform is used on
the other. This suppresses components of the variance which are not
90° out of phase and permits the computation of the phase lag which
is the angular time lapse between respective maxima and minima in
-------
103
the two records. The Fourier transforms are computed as follows.
For the S+ cross-correlation function the cosine transform is
used. Mathematically this is expressed
*) + ?'*;] , ,
r + C * r$ f Ai
Sg. Los -^f J )
Co , G£ and Cm are the transforms at lags 0, r, and m.
r is the lag number, m the total number of lags, and a the
lag number between 1 and m - 1.
For the S~ function the Fourier sine transform is computed from the
expressions
Qo =o,
,J
/ .\* \ ,
/rrv.
Qm - 0.
A final weighting of the transforms yields the cospectrum and
quadrature spectrum. This is accomplished/tne same procedure used
for the individual power spectrum. Mathematically the relationship are
C^- o.s-4 ( C«-i +C^') ,
Q6 = O.5M- ( Qo' + Q/)->
Qr. 0.33 Or-i t 0.5₯ C?r -f- 0.
9m
Or = ^ > S
the
Co, Cr, Cm, QOj Qr> and Qm are < respectively/oospectra and
quadrature spectra at the subscripted lags.
The period of these spectra can be computed from the same
expression as given for the individual power spectrum.
-------
104
(3) The coherence, phase lag and response spectrum can now be
computed from the individual power spectra of the two records and
the cospectrum and the quadrature spectrum. These statistics are
computed as follows:
The coherence, which is a dimensionless number, is
analogous to the square of a linear correlationship coefficient.
It can be computed for each lag from the relationships
r * JL Qt-*-
fjr = - ^ , where Hr is the coherence.
Urx "Wry
The phase lag, which as stated earlier is an indicator of
the temporal relationship between similar variations in the
records, can be computed from the expression
Lr =
Cp J > where Lr is phase lag at lag r
in units of radians.
The response spectrum, which shows what the resultant
spectrum would be like if the causative record were the only
parameter dominating it, is computed from the expression
Rr = Hr Uro where Rr is the response at
lag r and Uro is the individual power spectrum at lag r of
the causative or output record. The units of the response
spectrum are variance of resultant or output record. This
function is analogous to the individual power spectrum and
is interpreted the same.
(4) The overall response of the cross-spectral analysis is the
final statistic fo be computed. This is a rate statement of
-------
105
the process under investigation and is computed from the
relationship
\
where OR is the
T'O
overall response and Uri indicates the value of the individual
power spectrum of the causative or input record. The units
of the overall response are the unit of resultant record
(output) per unit of causative record (input).
The above discussion of the data analysis scheme used for the
Charleston Harbor Study defines only the mathematical and statistical
manipulations used on the intensive survey data. The evaluation and
interpretation of the results of these manipulations is presented in
the document to which this report is appended.
-------
106
Computer Programs
Calculation of Pearson frequency curves
This is the basic statistical program used in this study. Input
is raw data from the intensive surveys; printed output is the accompany-
ing tabulation of statistics and frequency plot for surface and
bottom records; punched output is one card for the surface record
and one card for the bottom record, each containing the number of
values (SUMA or SUMC), the sum of the experimental values (SUMB or
SUMD), and the sum of the squares of individual experimental values
(SB2 or SD2).
Input consists of a lead card identifying the data, thirty cards
containing the empirical data, and a blank card or termination card.*
Where data are missing, 0.0 is punched in the data field (B(I)) or
D (I) ) and a 0 is punched in the corresponding identification field
(A(I) or C(I) ).
The arithmetic operations are these:
I. Sums of the numbers of values (SUMA or SUMC) and of the experimental
values (SUMB or SUMD) are formed as the data are read in. For
the experimental values sums of squares, cubes, and fourth powers
are also formed (SB2, SB3, SB4, or SD2, SD3, SD4).
II. For surface and bottom records separately, these further calculations
are made:
Let x^ = the i the value of the record
N = the total number of values in a record.
^ X'
a) x = .JjL l ( x BAR)
~u~ w
b) x2 = Jn^ (P2MO)
c) x3 =
£ ft)
* A termination card for any of these programs has a 1 punched in
Column 4.
-------
107
d) x4
e) M
N
Variance x
x2
(P4MO)
(SQUMO)
g)
X*-
(TRIMO)
(QUAMO)
h) S Standard Deviation = (M2)
1/2
(SIGMA)
i) P = Skewness
(SKEW)
j) K = Kurtosis =
M,
(M9 )
(BETA 2)
k) Pearson Coefficients*
A = 10K - 12P2 - 18
B0 = M2 (4K - 3P2)/A
Bj. = SP (K + 3) /A
B (2K - 3P2 - 6)/A
(ABIG)
(PBO)
(FBI)
(PB)
III. The experimental values (B (I) ) or D (I) ) are sorted in ranges
of one standard deviation from the mean and a histogram of the
values is printed out.
Analysis of variance, part one and part two
These programs carry out an analysis of variance of the experimental
values between stations and between surveys for one parameter. The
scheme used is that presented in Bennett, C.A. and N.L. Franklin,
As defined in Smart, W. M. , Combination of Observations, Cambridge
University Press, 1958. pp. 166 - 188.
-------
108
C CALCULATION OF PEARSON FREQUENCY CURVES FROM EMPIRICAL DATA
C REQUIRES BLANK CARD BETWEEN DATA DECKS. PROGRAM IS TERMINATED BY
C CARD PUNCHED 1 IN COLUMN 4 FOLLOWING LAST DECK. FIRST DECK HAS
C NO BLANK CARD PRECEDING IT
DIMENSION A(30), B(30), C(30), D(30)
92 RE.'^D k8
48 FORMAT(15X 49HSAYTHEMAG ICWORDSOFPLEASEANDTHANKYOUANDHOPE ITWORKS )
PRINT 48
SUMA=0.0
SUMB=0.0
S UMC =0.0
S UMD =0.0
S 82 =0.0
SB3=0.0
SB4=0.0
SD2=0.0
SD3=0.0
SD4=0.0
L=30
DO 61 1=1 ,L
F'EAD 53, A(|), D(l), C(l), D(l)
53 FORMAT(34X F3.0.F7.2,2X F3.0,F7.2)
SUMA = SU.MA + A( I)
S UMB = S IJMB + 8(1)
SB2 = SB2+B( l)**2
SB3=SB3+B( l)**3
S UMC = S UMC + C ( I )
S UMD = S UMD + D ( I )
SD2=SD2+D( |)**2
SD3=SD3+D( l)**3
61 SD^=SD4+D( |)**4
PUNCH 50,SUMA,SUMB,SB2
50 FORMAT (F6.0.EI4.8, El 4.8 f15X,7HSURFACE)
PUNCH 51 .SUMC,SUMD,SD2
51 FORMAT(F6.0,E14.8,E14.8,15X,6HBOTTOM)
TOT=SUMA
SUMX=SUMB
SUMX2=SB2
SUMX3=SB3
K=1
PRINT 49
DO 23 1=1 ,L.6
23 PRINT 110,B(l),B(l+1),B(l+2)fB(l+3),B(l+4),B(l+5)
110 FORMAT(14XF7,2,2XF7.2,2XF7.2,2XF7.2,2XF7.2,2XF7.2)
49 FORMAT(/28X 24HVALUES OF SURFACE RECORD)
45 XBAR=SUMX/TOT
P2MO=SUMX2/TOT
P3MO=SUMX3/TOT
P4MO=SUMX4/TOT
SQUMO=P2MO-(XBAR**2)
TRIMO=P3MO-3.*XBAR*P2MO+2.*(XBAR**3)
QUAMO=P4MO-4.*XBAR*P3MO+6.*(XBAR**2)*P2MO-3.*(XBAR**4)
SIGMA=SQRT(SQUMO)
SKEVy=TRIMO/(SIGMA**3)
BETA2=QUAMO/(SOUMO**2)
ABIG =10.*BETA2-12.*(SKEV/**2)-l8.
PBO=SQUMO*(4.*BETA2-3.*(SKEV/**2))/ABIG
PB 1 =S I GMA*S KEV/*( BETA2+3 . ) /AB I G
PB =(2.*BETA2-3.*(SKEV;**2)-6.)/ABIG
PRINT 14. TOT *.
-------
1'4 |{TM-\T(/»X I7IINUMBCR OF VALUES=,F4.0,24X 20HPEARSON COEFFICIENTS)
PRINT 15. XBAR,ABIG
15 FORMATS 8X 5HMZAN=.F8.3, 35X 2HA = F1206) ino
PRINT 16, SQUMO,PBO 109
16 FORMAT( 8X 9HVAR|ANCE=, F14.6, 25X 3HBO=, F12.6)
PRINT 17, SIGMA, FBI
17 FORMAT(8X I9HSTANDARD DEVIATION=, F12.6, 17X 3HB1=, F12.6)
PRINT 18, SKEW, PB, BETA2
18 FOR^AT(8X9HSKEWNESS=,F12.6,27X,2HB=,F12.6/8X9HKURTOSIS=,F12.6)
PRINT 131
131 FORMAT(/ 25X 30HFREOUENCY DISTRIBUTION OF DATA)
PRINT 152
152 FORMAT(/31X 11HUPPER BOUND, 3X 16HNUMBER OF VALUES)
PRINT 153
153 FORMAT(33X 8HOF RANGE, 8X 8HIN RANGE)
PLOT = -6.0
128 UNUM=1.0
MUM = 0
PLOT = PLOT + 1 .0
DOWN = XBAR +(PLOT - 1.0)*SIGMA
UP - XBAR + PLOT*SIGMA
DO 143 1=1 ,L
133 GO T0( 164,163),K
163 IF(D(I)) 121,121,165
165 IF(D(I) - DOWN) 121,121,162
152 IF(D( I) - UP) 123,123,121
164 |F(B( I)) 121 ,121 ,125
125 IF(B( I) - DOWN) 121,121,122
122 IF(B(I) - UP) 123,123,121
123 UNUM = UNUM*10.
MUM = MUM + 1
121 IF( I-L) 127,132,132
127 1=1+1
GO TO 133
143 CONTINUE
132 PRINT 126, UNUM, PLOT, MUM
126 FORMAT(F30.0, 3XF4.0, 5HSIGMA, 9X 13)
IF(PLOT - 5.0) 128,129,129
129 GO TO(75,85),K
75 TOT=SUMC
SUMX=SUMD
SUMX2=SD2
SUMX3-SD3
SUMX4=SD4
K=2
LAST = -1
PR I NT 44
44 FORMAT(/28X 23HVALUES OF BOTTOM RECORD)
DO 24 1=1,L.6
24 PRINT 110,D( l),D(l + 1),D(l+2),D(l+3),D(H-4),D(l+5)
GO TO 45
85 PRINT 172
172 FORMAT(////)
READ 91, LAST
91 FORMAT(|4)
IF(LAST) 87,87,111
87 LAST = 0
GO TO 92
111 STOP
END
RELOCATABLE SUBROUTINES CALLED
SQRT
OBJECT PROGRAM DATA TABLE
-------
110
ENTER SOURCE PROGRAM
THEN PUSH START
C ENVIRONMENTAL DATA) PEARSON PROGRAM
CALCULATION OF PEARSON FREQUENCY CURVES FROM EMPIRICAL DATA
REQUIRES BIANK CARD BETV/EEN DATA DECKS. PROGRAM IS TERMINATED BY
"C CARD PUNCHED 1 IN COLUMN 4 FOLLOWING LAST DECK. FIRST DECK HAS
C NO BLANK CARD PRECEDING IT
DIMENSION B(30)
92 READ 48
48 FORMAT(15X 49HSAYTHEMAG ICWORDSOFPLEASEANDTHANKYOUANDHOPE ITWORKS)
PR I NT 48
SUMA=30.0
SUMP =0.0
SR2-0.0
SB3=0.0
SB4=0.0
L=30
DO 61 1=1,L
READ 53, B(l)
53 FORMAT(F9.2)
SUMB = SUMR + B(l)
S32 = SB2+B(l)**2
SB3=SB3+B(|)**3
61 SB4=SB4+B(I)**4
PUNCH 50tSUMA,SUMB,SB2
50 FORMAT(F6.0,E14.8,E14.8)
TOT=SUMA
SUMX=SUMB
SUMX2=SB2
SUMX3=SB3
SUMX4=SB4
K=1
PRINT 49
49 FORMAT(/24X 24HVALUES OF OBSERVED DATA /)
DO 23 1=1,L,6
23 PRINT 110,B(l).B(l+?),B(l+2),B(l+3),B(l+4),B(l+5)
110 FORMAT(8XF9.2,3XF9.2,3XF9.2,3XF9.2,3XF9.2,3XF9.2)
XBAR=SUMX/TOT
P2MO=SUMX2/TOT
P3MO=SUMX3/TOT
P4MO=SUMX4/TOT
SQUMO=P2MO-(XBAR**2)
TPIMO=P3MO-3.*XBAR*P2MO+2.*(XBAR**3)
QUAMO=P4MO-4.*XBAR*P3MO+6.*(XBAP**2)*P2MO-3.*(XBAR**4)
SIGMA=SQRT(SQUMO)
S KEV,'=TR I MO/ (S I GMA**3)
BETA2=QUAMO/(SQUMO**2)
ABIG =10.*BETA2-12.*(SKEV'**2)-18.
PBO=SQUMO*(4.*BETA2-3.*(SKEV/**2))/ABIG
PB1 =S I GMA*SKEV/*( BETA2+3 .) /AB I G
PB =(2.*BETA?.-3.*(SKEW**2)-6.)/ABIG
PRINT 14 TOT .
14 FORMAT(/8X 17HNUMBER OF VALUF.? = ,F4.0,24X 20HPEARSON COEFFICIENTS)
PRINT 15. XBAR.ABIG
15 FORMAT( 8X 5HMEAN=,F9.2, 35X 2HA=, F12.6)
PRINT 16 SQUMO,PBO
16 FORMAT( 8X 9HVAR IANCF. = , E14.8, 25X 3HBO=, E14.8)
PRINT 17, SIGMA, PB1
17 FORMATfSX 19HSTANDARD DEVIATION-. E14.8, 17X ?HB1». F14.8)
-------
,-;; = 0
:7 - PLOT -r '\ .0
1 ' .> '"
- " ' ' ' ", " 791 19'
. ; , ''''., i ^ i j ; /. I , i /..
' - \ i'-A " f\ '-: 1O^ 1O1
. ,; - s.',-,. j 2;. , ! 2,-i, i 2 1
' . > -07 - -. o 1 ? ?
, - - / it- ! , j - , J -
L ," ! I, '
,U. .
^ *
92
:ALL:I
* '- r~ f< ^ . f f - T~ ^S f~-- >~-
A ^ u b i u -<, . C. c r" U:
!S = ,F12.6)
111
::' Cr VALuZS)
-------
112
Statistical Analysis in Chemistry and the Chemical Industry.
Wiley, 1954. pp. 368 - 379. The program was debugged using the
data presented in the example in this reference.
B.I. Part one. Input consists of these cards:
(1) Lead card identifying the data
(2) Lead card stating number of stations, surveys, .and
replicates for the analysis of variance
(3-n)A data card (the output from program A) for each station
of each survey to be used. Data cards are arranged in
order of stations, then in order of surveys.
The output is (1) printed cross check of summations, (2) punched
cards for input to part two, consisting of (a) lead card identifying
the data, (b) lead card stating number of stations, surveys, and
replicates, (c) one data card containing summations of data by
stations, surveys, and replicates.
The arithmetic computations consist of summing the data and
squares of the individual data points by stations, surveys, and
replicates.
BIGN = Total Number of Values (N)
GSX = Sum of Individual Data Values (5. x)
GSXS = Sum of Squared Individual Values ( j? x2)
TS = Sum of Squared Sums of Values for each station
in each Survey
The notations used are these:
i = station index (i = 1, 2, 3 p)
j = survey index (j = 1, 2, 3 q)
n = individual value index (n = 1,2,3 30)
-------
113
STI = Summation of squared sums of individual values in each
survey at each station over all surveys "
J = i
STJ = Summation of squared sums o£ individual values in all
surveys at each station over all stations
.2. Input consists of the three output cards from Part I.
Output consists of a printed analysis of variance table and
one punched card which is input to the analysis of covariance
program.
Variable names used in the FORTRAN program are equivalent to
these symbols used in Bennett and Franklin
SIGN = N
GSX = T
GSXS = Z;j/n.*»J
= So 7i|
STI = .-a
PEE = p
CUE = q
COMP = n
The calculations made are these:
a. Variance breakdowns within c las ses
ESI =
^f *
F^ T = ^. = ^T" *!" ~"r
i ^ ' / /
" nj^ TT
-------
114
ESAU = Sdij =
ES - S
ESSIJ = svr =
b. Degrees of Freedom
DEFR « p - 1
DEFC = q - 1
DFINT = (p -l)(q - 1)
DFREP = N - pq
DFT = N - 1
c. Mean Values of Variance estimates
AMEAN = Si A
BMEAN = Sj = B
q - 1
CMEAN = S... = C
(p -~l(q - 1)
DMEAN = Sati = D
N - pq
d. Hypothesis Testing (F - ratios)
AFD = A/D
BFC = B/C
CFD = C/D
VARA = A - D
nq
VARB = B - C
np
VARC = C - D
n
-------
115
, v/f- , {-, p i- , , f -, , . ,,* (- r-;., j-y-. -
T ". ;::ST COLUMNS
\ " SQUARES FOR ROV'S, COLUMNS
" " OUT AND PUNCHED FOR
:i!ECK OF SUMS FROM ROV'S
......ATION.
.T'T'T.X 36HCHLORIDE DATA FROM INTENSIVE SURVEYS)
;>:;,;! R!GJN(20) TJX(20), TJXS{20), TS!(20)
VS:~N u.,"jr/20,6j, su:;xf20,o) .:.-.:'T>'20,6), xcUMS(20,6)
'lF!..;,. oIGIN(6), T!X(6), T!XS(6). TSJ(6)
. . --
r.sx£=o.o
RGSXS^O .0
7".-0.0
I 0 2
i--=O.C
:' 10?..
::\T(K;x !^,!OH STATIONS,. 1^,9:-: £u^vFvs,,F6.o,iiH REPLICATES)
; :T m?., iP.-I, JCUE, COM?'
:-:.£, JCUE,COMP
JCUc
! ^ '"'i O
J ; - U . o
I =* 1
Jj =
PEE
103
113
t\ C I I"v' / ' : ' C i".'1'' l\
J; , SUr/ v i ,^} , -^ ,JJ
N'iATlFft.O, EHi-,8, E14.6)
'CCMP-!JNun(! ,J)) 106, 107, 108
VT 102, !, J
" :AT(fA32X i4 2X 25HN[;::"ER OF VALUES TOO HIGH)
. - su:-;x(i ,J)/UMUM( i ,j)
'S( f^J) =~ SUMXsf I , J) + ( X3AR**2}->(CCfiP-UNUM( I , J) )
./.{: ,.;i --- COMP
:.':!/' J' - r.!CiN( J) + UNiJ/ ' .. , J)
:.; j) - T;X(J) 4- SUMX( i,j)
'-( J' - 7IXS( J) -i- SUMXS( ; . .,}
::r,,,s( -. .j' = (SUMX( i,j))**2
TSJ:J) = TSJ(J) + XSUMS(I,J)
?, 1GN = "'!GN + BIGIN(J)
re'' <~ ' i T \\f ( \\
L- 3 A = i - , -!- I I A ^ J )
GSXS = ^CXS + TIXS(J)
-S - TS -;- TSJ(J)
FT: = ST; + ((TIX(j))**2)
r:. in i - i, IPEE
-: ^j.\" s) =oeo
7JX( !) =0.0
TJXC.( ! ) =0.0
--r < r < \ _ n n
l j i v ! = U . U
DO M3 J = 1 , XUE
H1GJN' J) = P1GJNC!) + UMUM(I,J)
TJX: I) = TJX(I) + SUMX( |,J)
TJXC(I) = TvJXS(l) + SUMXS(I.J)
TSI( I) = TSI( I) + XSUMS(!,J)
BBIGM = BBIGN + BIGJN(I)
-------
H- TJXSf !)
:.rs = rrrr. -;- TSI( i)
~7J - T"J -- ((TJX( !))**2)
1]
STJ
;i( 11 2.6 , E 12 Oo ,E 1 2 .6 >r: 12 .& ,E 1 2 06 ,E1 2 .6)
::-! 1 90 ,B ! GM ,GSX , GSXS ,TS ,ST I ,STJ
; ' ' T 100 P. T I (t '! P, !7 C Y R ft "^ V C Q T C
TO 92
""OGFIAM CATA TABLE
".T^ACE POSITIONS
c; ' ;. i ^ r pi * p ! c ~r
-------
117
3K:CG0300&02b
CARD OJ7 OF SEQUENCES 10000300002R"
ENTER CnijRCE PROGRAM
THE?. ?j£;-: START
C A'-'-ALYSIS OF VARIANCE PROGRAM. PART TV.'O.
c /';:CUIRES AS INPUT THE PUNCHED OUTPUT FROM PART ONE. RESULTS ARE
c --:::TED OUT IN AM ANALYSIS OF VARIANCE TABLE AND THE SUMS OF
C .-. i-'.RES ARE PUNCHED OUT FOP. INPUT TO COVARIANCE PROGRAM.
"?. i'!T 101
'-'. ". ..:AT(//// 3ox ZOHANALYSIS OF VARIANCE //)
,: : 100
]':' -;\-;AT(22X 35HCHLORIDE DATA FROM INTENSIVE SURVEYS)
r
1 '! 1
(16X 30HSURVEYS AA, AB, B, C, D
\T(16X40!!STATIO^S. SURFACE, 1 2 3 *: 5 o 7 S 9 1 3 )
READ 102, I PEE, JCUE, COMP
102 FCRMAT(13X |4,10H STAT IONS , , !^,9H SURVEYS , ,F6. 0,11 1! REPLICATES)
PRi;\T 102, I PEE, JCUE, COMP
-------
,"£AD U-)0,BIGN, GSX, GSXS, TS, STI, STJ
190 FORMAT(E12.6, E12.6,E12.6,E12.6,E12.6,E12.6)
PEE = I PEE 118
CUE = JCUE
ESI = (STJ/(COMP*CUE))-(GSX**2)/BIGN
ESJ = (STI/(COMP*PEE))-(GSX**2)/BIGN
ESAU = GSXS - (TS/COMP)
ES = GSXS - (GSX**2)/BIGN
ESSIJ = (TS/COMP) -(STJ/(COMP*CUE)) - ESJ
DEFR = PEE - 1.
DEFC = CUE - 1 .
DPI NT = DEFR*DEFC
DFREP = BIGN -(PEE*CUE)
OFT = RIGN - 1o
AMEAN = ES I/DEFR
BMEAN = ESJ/DEFC
CiMEAN = ESSIJ/DFINT
DMEAM = ESAIJ/DFREP
AFD = AMEAN/DMEAN
BFC = BMEAN/CMEAN
CFD = CMEAN/DMEAN
VARA = (AMEAN-DMEAN)/(COiMP*CUE)
VARB = (BMEAN-CMEAM)/(COMP*PEE)
VAPC = (CMEAN-DMEANJ/COMP
PRINT 121
121 FORMAT(// 32X 31HSOURCE OF ESTIMATED VARIANCE/)
PRINT 122
122 FORMAT(20X7HBETOEEN,3X7HBETV/EEM,5XH'HSTAT!ON-SURVEY,16X5HTOTAL)
PR INT 123
123 FORMAT(20X8HSTATIONS,2X7HSURVEYS,4X11 HINTERACTION,5X10HREPLICATES)
PRINT 124.ESI,ESSIJ,ES
12k FORMAT(//6HSUM OF,10XE12.6,12XE12.6,14XE12.6)
PRINT 125,ESJ, ESAU
1 25 FORMAT( 7HSQUARES ,21 XE 12 .6,1 7XE1 2 ,6//)
PRINT 126, DEFR,DEFC,DF I NT.DFREP,DPI
126 FORMAT(10HDEGREES OF , 10XF4.0,8>(P4.0 ,8XF6eO , 10XF6.0 ,6XF600)
PRINT 12?
127 FORMATC7MFREEDOM//)
PR INT 128,AMEAN,BMEAN,CMEAN,DKEAN
128 FORMAT(ifHMEAN, 12X E12.6, 2X E1206, 2X E1206, 2X E1286)
PRINT 129
129 FORMAT(6HSQUARE //13HAVEP.AG,r ' J£ '
PRINT 130,VARA,VARB,VARC
130 FORMAT(11HOF VAR IANCE ,5XE12 . :_ .lXc.12.6/8HEST IKA-L//)
PRINT 131,AFD,CFC,CFD
131 FORF;AT(10HCALCULATED,6X F12.5.2X F12.5, 2X F12.5/zfX 1 HP //)
PRINT 132, DEFR,DEFC,DPI NT
132 FORMAT(9HTABULATED/8HFUNCTIOK/^X2HN1 , U;-XF4.0 ,8XF400 ,8XF5.0)
PRINT 133, DFREP,DFINT,DFREP
133 FORMAT('fX 2HN2, 12X F6.0,6XF600,8X F6.0/4X IMF///)
PUNCH 134, ESAU,ESSIJ.ESI.ESJ,ES
PRINT 406
40 6 FORMA
GO TO 92
END
":JECT Pr.CSr:AM DATA TABLE
0 STORAGE POSITIONS
PROCESSING COMPLETE
-------
119
Spectral analysis
These computations required to use of four programs because
of the limited memory of the IBM 1620 being used. The general
procedure followed this scheme:
DATA DECK
INPUT RECORD
T
SPECTRUM
PREPROCESSOR
^
POWER
SPECTRUM
CROSS SPECTRUM
PART 1
CROSS SPECTRUM
PART 2
DATA DECK
OUTPUT RECORD
SPECTRUM
PREPROCESSOR
POWER
SPECTRUM
PRINTED OUTPUT
-------
120
I. Spectrum preprocessor program
Either of two separate programs are used for this operation,
one for environmental parameters and one for all other data.
Input consists of one lead card identifying the record,
thirty data cards, and a termination card.
Output consisted of punched cards, two lead cards, six
data cards, and one termination card for each record, (i.e.,
one set for surface values and one set for bottom values.
Arithmetic operations consisted of finding the arithmetic
mean and the deviation of each value from the mean. Output is
the deviation from the mean for each value of the record.
II. Power spectrum program
This program computes the power spectrum of a single record
to a maximum of 10 lags at 100 record values.
Irput is (1) one lead card stating number of values (IPEE),
number of lags (LAG), and sampling interval (BELT), and (2) output
from the spectrum preprocessor program,,
Output is printed and punched. Printed output is (1) record
identification; (2) autocovariance at Lag 0 and a sum of the
'spectral values, which are equal. This operation is provided
as an internal check on the arithmetic operation of the computer.
(3) a listing of each spectral estimate computed and the lag
number at which it is valid. Punched output consists of
two lead cards identifying the record, a set of cards each
containing one lag number and corresponding spectral estimate,
and a termination card.
Several standard spectral analysis schemes were followed in
developing this program. The programs developed at New York
University and at U.C.L.A. for larger computers were the basis
for many of the procedures.
-------
121
310000300002RS
ENTER SOURCE PROGRAM
THEN PUSH START
C PREPROCESSOR FOR SPECTRUM PROGRAM.
DIMENSION A(30),B(30),C(30),D(30),X(30),Y(30)
92 READ 43
48 FORMAT(15X 49HSAYTHEMAGICWORDSOFPLEASEANDTHANKYOUANDHOPE ITWORKS)
PUNCH 48
L=30
SUMAaO.O
SUMB=0.0
SUKC-0.0
SUMD^O.O
DO 28 1=1 L
READ 53,A(I),R(I),C(I),D(I)
53 FORMAT(3*tX F3.0,1X F6.2,2X F3«0,1X F6.2)
SUHA*SUMA+A( I)
SUiMB = SUMB+B(|)
SUMC=SUMC+C( I)
28 SUMD=SUMD+D( I)
BBAR= SUMB/SUMA
DBAR= SUMD/SUMC
1 = 1
96 IF(A(|)) 101,101,102
101 B(I)=BBAR
102 IF(L-i) 98,98,97
97 1=1+1
GO TO 96
98 1=1
107 IF(C( I)) 103,103,104
103 D(I)=DBAR
104 IF(L-I) 105,105,106
106 | = | + 1
GO TO 107
105 DO 118 1=1 L
118 X(l) = B(I)-BBAR
PUNCH 9
9 FORMAT(15X 29HSURFACE RECORD SPECTRUM INPUT)
DO 108 1=1,L,5
108 PUNCH 10,X(I),X(1+1),X(1+2),X(1+3),X(1+4)
LAS = 0
PUNCH 91 .LAS
10 FORMAT(E14.8,E1408,E14.8,E14.8,E14.8)
PUNCH 48
PUNCH 8
8 FORMATdSX 28HBOTTOM RECORD SPECTRUM INPUT)
DO 119 1=1,L
119 Y(l) = D( D-DBAR
DO 109 1=1.1.5
109 PUNCH 10,Y(I),Y( I + D,Y( 1+2),Y( 1+3),Y( 1+4)
READ 91,LAST
91 FORMAT(l4)
IF(LAST) 87,87,111
87 LAST=0
PUNCH 918LAST
GO TO 92
111 PUNCH 91,LAST
STOP
OBJE'. ' PROGRAM DATA TABLE
0231C STORAGE POSITIONS
-------
122
ENTER SOURCE PROGRAM
THEN PUSH START
C PREPROCESSOR FOR SPECTRUM PROGRAM. ENVIRONMENTAL DATA ONLY
DIMENSION B(30),X(30)
92 READ 48
48 FORMAT(15X 49HSAYTHEMAGICWORDSOFPLEASEANDTHANKYOUANDHOPE I TV/ORKS)
PUNCH 48
L=30
SUMB=0.0
SUMA=L
DO 28 1=1,L
READ 53. B( I)
53 FORMAT(F9.2)
28 SUMB=SUMR-fB(l)
BBAR=SUMB/SUMA
DO 118 |=1,L
118 X(I)=B(|)-BBAR
PUNCH 9
9 FGRMAT(15X 29HENVIRON. DATA SPECTRUM INPUT)
DO 108 1=1.L,5
108 PUNCH 10,XU),X( I + 1),X( I+2),X( I+3).X( 1+4)
10 FORMAT(El4.8,E14.8,El4.8,E14.8,El4
READ 91,LAST
91 FORMAT(|4)
IF (LAST) 87,87,111
87 LAST=0
PUNCH 91,LAST
GO TO 92
111 PUNCH 91,LAST
STOP
END
QBJECT PROGRAM DATA TABLE
00940 STORAGE POSITIONS
PROCESSING COMPLETE
-------
123
The arithmetic operations performed are these:
(a) The auto-covariance is computed;
r = 0, 1 , 2, 3, .... m (lags, m - LAG)
Xq = X]_, X2, X3, .... Xjjj (data values, n = IPEE)
fl » sampling interval = DELT
PROD(L) = ,
/ \ ' 5"
y/H a rr, <£. '
K*- / N-l Q'l
(b) The raw estimate of the power spectrum is computed.
VEE(L) = ftW "^
where k = 0, 1,2, 3 m (lags, K = ARQ(K) )
Ef = I for 0 < 1 < m
1/2 for 1 = 0, m
(c) The smoothed spectral estimates are computed.
"Hamming is used; i.e., the factors are 0.54 and 0.46.
SPEC(l) = SPX (0)
SPEC(L) - 5* M - flM % r
SPEC (HUG) - SP(">)= °'^ ^ H
(d) The sum of spectral estimates used for a check is
computed.
s- SPX
-------
124
III. Cross-spectra p'rogram. Part one.
This program computes the cross-spectral estimates from a
pair of records.
Input is (1) a punched card stating number of values, number
of lags, and sampling interval, (2) punched output from the
spectrum preprocessor for the input record, (3) punched output
from the spectrum preprocessor for the output record.
Output is entirely punched cards, and consists of these:
(1) one card stating number of values, number of lags, and
sampling intervals, (2) four cards identifying the input and
output records, (3) a deck of cards each containing a lag number
and the two cross-spectral estimates corresponding to that lag
number, (4) a termination card.
The arithmetic operations are entirely analogous to those in
the power spectrum program.
(a) The cross-covariance is computed.
Xq = input record values
Y = output record values
SPOS - -y v,
/H-r
SNEG (L) =
(b) The raw cross-spectral estimates are computed.
CTRAN(L) = Pt
, 2-a>
QTRAN - P^ IKJ- -pTS"
-------
125
(c) The smoothed cross-spectral estimates are computed.
C(l) - G! = 0.54 Pxy(0) + 0.46 PXJ (1)
C(L) = Cr = 0.23 P+(r - 1) + 0.54 PX+ (D + 0.23 PX+ (P + 1)
y . X . X
C(NIAG) - Cm = 0.54 Pxy (m) + 0.46 P^y (m - 1)
Q(l) = Qi = 0.54 Pxy (0) + 0.46 Pxy (1)
Q(L) = Qr = 0.23 Pxy (f - 1) + 0.54 Pxy (fr) + 0.23 Pxy (f + 1)
Q(NLAG) = Qm = 0.54 Pxy (m) + 0.46 P'y (m - 1)
IV. Cross- spectrum program. Part two.
This program computes supplementary statistics from the power
spectra of the two records and from their cross spectra.
Input consists of these punched cards: (1) Output from the
Cross-spectrum program Part One, (2) Output from the Power Spectrum
Program for the input record, (3) Output from the Power Spectrum
Program for the output record.
Output is entirely printed out. The printout contains this
information:
(1) Record identification
(2) Numbers of values, lags, and sampling interval
(3) Power spectra of input and output records
(4) Cospectrum
(5) Quadrature spectrum
(6) Period corresponding to each lag
(7) Coherence
(8) Response spectrum
-------
126
ENTER SOURCE PROGRAM
THEN PUSH START
C POWER SPECTRUM PROGRAM.
READ 18,|PEE,LAG,DELJ
18 FORMAT(l4,|4,F6.0)
DIMENS'OM X(100) .PROD(10) .CF.(10) nAR
Q(10),SPEC(10),VEE(10)
92 READ 48
48 FORMAT(15X 49HSAYTHEMAGICVORDSOFPLEASEANDTHANKYOUANDHOPE ITVORKS)
PR I NT 48
PUNCH 48
READ 9
9 FORMAT(15X 23HSURFACF. RECORD SPECTRUM)
PRINT 9
PUNCH 9
PEE = I PEE
SUMX=0.0
DO 101 |=1,|PEE,5
READ 21 X(l).X(J+1),X(l+2),X(!+3),X(l+4)
21 FORMAT (E14.8,E14.8,E14.8,E14.8,E14.8)
101 SUMX=SUMX+X(I)+X(I+1)+X(l+2)+X(l+3)+X(1+4)
NLAG=LAG+1
DO 103 L=1,MLAG
PROD (L) =0.0
I LAG =IPEE-L+1
DO 102 1=1,ILAG
M=!+L-1
102 PROD(L)=PROD(L)+X( I)*X(M)
DIV= ILAG
103 PROD(U=(PROD(L)/DIV)
EM=LAG
DO 192 L=1.NLAG
192 CE(L)=PROD(L)
DO 105 L=1,LAG
108 TEE=L-1
T!NT= DELT/3.1416
SUMC=0.0
DO 104 K=2,LAG
ARQ(K)=K-1
104 S UMC =SUMC+CE(K)*COS(3.1416*TEE*ARQ(K)/EM)
105 VEE(L)=TINT*(PROD( 1 )+PROD(NLAG)*COS(3i1*tl6*TEE)+2 ,0*SUMC)
IF(EM-TEE) 106,106,107
10? L=NLAG
GO TO 108
106 SPEC(1)=0.54*VEE(1)+0846*VEE(2)
DO 109 L=2,LAG
109 SPECfL)=(0.23*VEE(L-1))+(0.5^*VEE(L))+(0.23*VEE(L+O)
SPEC(NLAG)=0.54*VEE(NLAG)+0.46*VEE(LAG)
SUM) =0.0
DO 115 L=2,! AG
115 Si:.'D=SUMD+Sr'EC(L)
CI(?;M=(3J4l6/( EM*DELT))*(0.5*(SPEC(1)+S PEC ( NLAG) )+SUMD)
PRINT n6,CK?M,PROD(1)
116 FORMAT(16HSUM OF SPECTRUM=,E14.8/18HAUTOCOV. AT LAG 0=,E14 8/)
DO 110 L=1,ril.AG '
NO=L-1
-------
PRINT 111,NO,SPEC(L)
111 FORMAT(5X I4.5X E14.8)
110 PUNCH 111. NO, SPEC(L) 127
READ 91, tAST
91 FORMAT(!4)
IF(LAST) 87,87,112
7 PUNCH 91 ,LAST
GO TO 92
112 STOP
END
RELOCATABLE SUBROUTINES CALLED
COS
OBJECT PROGRAM DATA TABLE
02140 STORAGE POSITIONS
PROCESSING COMPLETE
-------
128
ENTER SOURCE PROGRAM
THEN PUSH START
C CROSS SPECTRUM PROGRAM. PARTONE
92 READ 15,JPEE,LAG,DELT
15 FORMAT(|4,|4,F6.0)
DIMENSION X( 100), Y( 100), QPOS( 10) ,C ( 10) ,Q( 10) ,ARQ( 10)
DIMENSION SPOS(10),SNEG(10),CTRAN(10),QTRAN(10),QNEG(10)
PUNCH 14,|PEE,LAG,DELT
14 FORMAT(10Xl4,7H VALUES, 10X14, 5H LAGS ,JOXF6. 0,1 4H HOUR INTERVAL)
READ 48
48 FORMAT(15X 49HSAYTHEMAGICWORDSOFPLEASEANDTHANKYOUANDHOPEITV/ORKS)
PUNCH 48
READ 9
9 FORMAT(15X 14HSURFACE RECORD)
PUNCH 9
DO 101 1=1 ,IPEE,5
101 READ 10,X( |),X( I + 1),X(I+2),X( l+3).XH+4)
10 FORMAT(E14.8,E14.8,E14.8,E14.8,EJ4.8)
READ 91
NLAG=LAG+1
READ 48
PUNCH 48
READ 9
PUNCH 9
PEE=IPEE
DO 102 1=1 , 1 PEE, 5
102 READ 10,Y(l),Y(l + l),Y(H-2),Y(l+3),Y(l+4)
DO 121 L=1 ,NLAG
SPOS(L)=0.0
SNEG(L)=000
TEE= L-1
ILAG=IPEE-L-1
DO 121 I =1,1 LAG
SPOS(L)=SPOS(L)+(1./(2.*(PEE-TEE)))*(X(I)*Y(M)+X(M)*Y(I))
121 SNEG(L)=SNEG(L) + (1 ,/(2.*(PEE-TEE) ))*(X( I )*Y(M)-X(M)*Y( I ) )
SUMD=0."0
DO 122 L=2,LAG
122 SUMD=SUMD+SPOS(L)
TINT=DELT/6.2832
EM=LAG
DO 192 L=1 ,MLAG
QNEG(L)=SNEG(L)
192 QPOS(L)=SPOS(L)
CTRAM(1)=(TINT)*(0.5*(SPOS(1)+SPOS(NLAG))+SUMD)
DO 124 L=2,LAG
TEE=L-J
FCOR=0.0
DO 123 K=2,LAG
ARQ(K)=K-1
123 FCOR=FCOR+QPOS(K)*COS(3.1416*TEE*ARQ(K)/EM)
124 CTRAN(L)=( 2. *T I NT)*(.5*(SPOS(1 )+((-!.)**( L-1 ))*SPOS(NLAG))+FCOR)
SUMD=0.0
DO 125 L=2.LAG
125 SUMD=SUMD+(((-1 ,0)**( L-1 ) )*SPOS( L) )
CTRAN(NLAG)=( Tl NT)*(0.5*(SPOS( 1 )+( (-1 ,0)**LAG)*SPOS( NLAG) )+SUMD)
QTRAN(1)=0.0
Q TRAM (NLAG) =0.0
DO 126 L=2,LAG
TEE=L-1
FCOR=0.0
DO 1?7 K=2.l AG
-------
ARQ(K)= K.~1
127 FCOR=FCOR+QMF.G(K)*S IN(3.1416*TFE*ARQ( K)/EM)
126 QTRAN(L)=(2. ,*TINT)*FCOP. 129
C ( 1 ) =0 . 54*C TR A N ( 1 ) +0 . 46*C TRA M ( 2 }
DO 128 [_=2,LAG
C(L)=0.23*CTRAN(L-1)+0.54*CTRAN(L)+0.23*CTRAN(L+1)
128 Q(L)=0.23*QTRAN(L-1)+0.54*QTRAM(L)+0.23*QTRAN(L+1)
C(NLAG)=0.5^*CTRAN(NLAG)+0.46*CTRAN(LAG) ......
Q( NLAG)=0 ,54*QTRAN( MLAG)+0 046*QTRAN( LAG)
Q(1)=0.54*QTRAN(1)+0.46*QTRAN(2)
DO 129 L=1 ,NLAG
? N! o = L- 1
129 PUNCH 161 ,MO,C(L).Q(L)
161 -QRMAT(4X |4,E14.8,E14.8)
READ 91 ,LAST
91 FORKAT(|4)
!c (LAST) 87,87,112
87 LAST=0
PL'MCH 91, LAST
CO TO 92
112 PUNCH 91 ,LAST
STOP
EMD
RELOCATABLE SUBROUTINES CALLED
SIM
COS
BJECT PROGRAM DATA TABLE
STORAGE POSITIONS
PROCESSING COMPLETE
-------
130
(9) Phase la^ in hours in = Hr "r" + Qt: 2
Phase la.
/ \
PH(L) = Br = arc tan / Qr x,
~~
\
(c t Transfer inact I..T
TRANS (L) = /
V
(.d) . Response Spectrur
R(L) = Rr = H^ SPV tD
(e) Period
PE(L) = Tf: = : - A>-
(f) Phase lag (hours,'*
HRS(L) = Br Tr
27T
NOTE: Adjustments IP. tho J T factor aro necessary ir the
phase La^ is i" other than c'nc :irst quadrant.
-------
131
(g) Overall Response
RESP =
z
r--o
.Linear regression * v
This program calculates a least squares linear regression
line of the form
Y = A 4- BX
Input consists of (1) one lead card containing the number
of pairs of values to be used (2) one lead card identifying the
data being used, (3) a deck of data cards with three fields:
(a) numeral 1, (b) y value, (c) corresponding x value, (4) term-
ination card.
NOTE: Because of read in and printout limitations on the IBM
1620, the number of data cards must be a multiple of six. Fill
wall data fields with zeros in filler cards. The program does"not
use these data in the computation.
Output is a printout of the data, and a listing of the slope
(B), intercept (A), and variance of y on x.
The arithmetic operations are these:
(a) Formation of sums.
SUMN = n = total number of data pairs
SUMX ^ <-
c =/
SUMY =
, - s
-------
ACCESS ING COMPLETE .- '
132
310000300002R-S
ENTER SOURCE PROGRAM
THEN PUSH START
C CROSS SPECTRUM PROGRAM. PART TWO
DIMENSION C(10),Q(10),H(10),PH(10),R(10),PE(10),HRS(10),ARQ(10)
D IMENSION XSPEC(IO) ,YSPEC(10) ,TRANS( 10) ,RTH( 10)
92 PR i NT 1 6
16 rrORMAT(27X26HCROSS SPECTRUM CALCULAT I ON// 10X 5HINPUT/)
."EAD 13,IPEE,LAG,DELT
13 FORMAT(10XI4,7H VALUES , 10X I 4,5H LAGS , 10XF6.0 ,14H HOUR INTERVAL)
READ 48
48 FORMAT(15X 49HSAYTHEMAG ICWORDSOFPLEASEANDTHANKYOUANDHOPE ITWORKS)
PRINT 48
READ 9
9 FORMATdSX 14HSURFACE RECORD)
PRINT 9
PRINT 17
17 FORMAT(/10X 6HOUTPUT/)
READ 48
PRINT 48
READ 9
PRINT 9
PRINT 14,!PEE,LAG,DELT
14 FORMAT(/10X|4,7H VALUES , 10X |4,5H LAGS,10XF6.0,14H HOUR INTERVAL//)
NLAG =LAG + 1
DO 118 L=1 ,NLAG
118 READ 162,C(L).Q(L) :'
162 FORMAT( 8X E14.8, E14.8)
READ 91
READ 4"8
R:AD 9
DO 103 L=1 ,NLAG
103 READ Hl.XSPEC(L)
111 FORMAT(14X E14.8)
READ 91
READ 48
READ 9
DO 104 L=1 ,NLAG
104 READ 111 , YSPEC(L)
EM = LAG
DO 129 L=1 ,NLAG
H(L)=((C(L)**2) + (Q(L)**2))/ (XSPEC( L)*YSPEC( L)
PH(L)= ATAN(Q(L)/C(L))
TRAflS(L)=SQRT((C(L)**2) + (Q(L)**2))/XSPEC(L)
RTH(L)=SQRT(H(L))
129 R(L)=H(L)*YSPEC(L)
L=2
134 TEE-L-1
P£(L)=(2.0)*EM*DELT/TEE
IF(Q(L)) 130,131,131
131 IF(C(L)) 132.133,133
133 MRS (L)=(PH(L)/6. 2832 )*PE(L)
135 IF(NLAG-L) 138,138,139
139 L=L+1
GO TO 134
132 HRSm=((PH(L) + 1.5708)/6.2832)*PE(L)
-------
GO TO 135
130 !F(C(L)) 136,136,137
136 HRS(L)=((PH(L) + 1.5708)/6.2832)*PE(L) 133
GO TO 135
137 HRS(LH(6.2832+PH(L))/6.2832)*PE(L)
GO TO 135
138 PRINT 140
140 FORMAT(19X18HINDIVIDUAL SPECTRA, 1 JX27HCOMPONE NTS OF CROSS SPECTRA)
PRINT 141
141 FORMAT(5X3HLAG,9X5HINPUT,12X6HOUTPUT,9X8HCOSPECT.,9X10HQUADSPECT.)
PRINT 143
143 FORMAT(/)
DO 144 L=1,NLAG
NO=L-J
144 PRINT 142,NO.XSPEC(L),YSPEC(L),C(L),Q(L)
14 2 F 0 R MA T (4X 14,4 X E14.8, 4X E14.8,1X E 14.8,3 X E14.8)
PRINT 143
PRINT 145
145 FORMAT(5X3HLAG,6X6HPERIOD,5X9HCOHERENCE,11X8HRESPONSE,12X5HPHASE)
PRINT 146
146 FORMAT(14X7H(HOURS),24X8HSPECTRUM,6X5HHOURS,6X7HRADJANS/)
PRINT 147, H(1),R(1),PH(1)
147 FORFAT(7X1HO,6X4HLONG,6XF10.6,5XE14.8,16XF8.5)
DO 148 L=2,NLAG
NO=L-1
148 PRINT 149, NO,PE(L),H(L),R(L),HRS(L),PH(L)
149 FORMAT(5XI3,5XF6.2,5XF10.6,5XE1408,5XF6.2,5XF8.5)
PRINT 152
152 FORMAT(/5X3HLAG,6X17HTRANSFER FUNCTION,6X14HCOHERENCE ROOT/)
DO 153 L=1,MLAG
NO=L-1
153 PR!NT 154,NO,TRANS(L).RTH(L)
154 FORMAT(5X 13, 9X El4.8, 6X F10.6)
SUM!=0.0
SU,".A=0.0
DO 150 L=1,NLAG
SUM!=SUM!+XSPEC(L)
150 SUKR=SU.XR+R(L)
RESP=SQRT(SUMR/SUMI)
PRINT 1'51 , RESP
151 FOR;iAT(//5X 17HOVERALL RESPONSE = ,F10,
READ 91 ,LAST
91 FORMAT(14)
IF(LAST) 87,87,112
87 PRINT 6
6 FORHAT(///)
GO TO 92
112 STOP
END
RELOCATABLE SUBROUTINES CALLED
A TAN
SQRT
OBJECT PROGRAM DATA TABLE
.01920 STORAGE POSITIONS
PROCESSING COMPLETE
-------
134
SMEX =
i" I
- 5,
(b) Calculation of Slope (B) and Intercept (A),
g _
A = Sv - B S
n
(c) Calculation of Variance
fs 2) - AS - B S
VAR = V y / ^ xy _._
n - 2
Theoretical oxygen demand
This program computes a theoretical oxygen demand according
to the equation
U = 2.67 A + 4.57 B
Input is one card containing A and B.
Output is both printed and punched values of U.
Ratios of surface to bottom values
This program computes the ratios of surface to bottom data
for a single pair of observations and the mean ratios and variance
for one survey of a station.
Input is the data deck used for Program A.
Output is printed values of the ratios for each pair of
surface and bottom observations, the mean value of all ratios,
-------
135
C FEED DATA CARD? ONLY IN NUMBERS DIVISIBLE 3Y SIX. IF NECESSARY,
C FILL SUFFICIF.NT ADDITIONAL CARD? V.'ITH ~~~OS IN ALL DATA FIELDS
TO COMPLETE NEAREST MULTIPLE. PUf.'CH THIS NUMBER IN ( 14} FORMAT
AND USE AS LEAD CARD. PUNCH DEPENDENT VARIABLE (Y AXIS) IN FIRST
FULL DATA FIELD.
05 PRINT 10
10 FORMAT(30X20HREGRESSION OF Y ON X//)
PPI NT 12
12 FOPMAT(35X 10MY = A + BX///)
READ 700,M
READ 25
25 FORM*J(15X,49HSAYTHEMAG!CV OFTSOFPLEASEA't'THANKYOUANDHOPE ITV'ORKS)
PRINT 25
DIMENSION X(100),Y(100),R(100)
SUMN=0.0
SUMX=C.O
SUMY=0.0
S;;EX=O.O
SXY=0.0
DC 41 J=1 M
READ 40,R(J) X(J),Y(J)
40 FOnMAT(30XF3.0f2XF10.3,2XF1003)
SUMN=SUMN+R( J)
SL'MX=SUMX+X( J)
?U,MY=SUMY+Y( J)
SMEX=SMEX+X(J)**2
41 S",:Y=SXY+X(J)*Y(J)
PR!NT 55
DO 45 J=l,M,6
45 PRINT 50,X(J),X(J+1),X(J+2),X(J+3),X(J+4),X(J+5)
50 FORMAT(4XF10I>3,1XF1003,JXF1003,JXF1003,1XFJ003.1XF1093)
55 FORMAT(//25X,30HVALUES OF INDEPENDENT VARIABLE)
PRINT 70
70 FORMAT(//26X28h'VALUE? OF DEPENDENT VARIABLE)
DO 60 J=l,M,6
60 PRINT 50,Y(J),Y(J+1),Y(J+2),Y(J+3),Y(J+4),Y(J+5)
B = ((SUMM*SXY)-(SUMX*SUMY))/((S UMM*SMEX)-(SUMX**2))
A = ((S UMY*SMEX)-(SUMX*SXY))/((?UMM*SMEX)-(SUMX**2))
VAR = (SUMY**2-(A*SUMY)-(B*SXY))/(?.UMN-2.)
PRINT 90,8
90 FORMAT(//6X7HSLOPE =7XEJ4.8)
PP INT 95,A
95 FORMAT(//6X11HINTERCFPT =1XE14.8)
PRINT 96,VAR
96 FORMAT(//6X10HVAR|ANCE =1XE14
READ 100, LAST
100 FORMAT(|4)
IF(1-LAST)705.105805
105 STOP
END
OBJECT PROGRAM DATA TABLE
_03440 STORAGE POSITIONS
"ROCESSING COMPLETE
-------
136
ENTER SOURCE PROGRAM
THEN PUSH START
JOO PRINT 1
1 FCRMAT(21X36HRATIO OF SURFACE TO BOTTOM CHLORIDES/)
READ 90
90 FORrlAT(15Xif9HSAYT!-!EMAG!CV/OPDSOFPLEASEANDT!-!ANKYOUANDHOPEITV/ORKS)
PR ! NT 90
D i KENS ION R( 30 ) ,SQ(30 ) ,A( 30 ) ,B( 30) ,C ( 30 ) ,D (30 )
S MA =0.0
S MR =0.0
SMSQ=0.0
L=30
DO 17 1=1 ,L
READ 53,A(I),B(I)>C(I),D(!)
53 FGRMAT(3^XF3.0,1XF6.2,2XF3.0,1XF6.2)
IF(A(I)+C( J)-J.)3,3,6
3 R( l)=0.0
GO TO 17
6 SMA=SKA+A(|)
SKR=SMR+R(I)
SC( I)=R( !)**?.
SMSQ=SMSC+?Q( I)
17 CONTINUE
SQSM=SMR**2
RM=SMR/SMA
DO 55 1=1,L,6
55 PR^NT 7),R( !),R(!+!),R(I+2),R( 1+3),R( 1+4),R(1+5)
PR I NT 10 RM
10 FORMAT(//10X12HMEAM RATIO =IXF604/)
PRINT 11 ,VAR
11 FORMAT(12X10HVARIANCE =1XEJ4.8////)
READ 12,T>I
12 FORMAT(|4)
IF(N)100,100,13
13 STOP
END
OBJECT PROGRAM DATA TABLE
02200 STORAGE POSITIONS
PROCESSING COMPLETE
-------
137
and the variance of the ratios from the mean.
The arithmetic operations are these:
B^ = surface value
D- = bottom value
(a) Computation of ratios
R(I) = RI Bj
(b) Formation of sums
N = total number of values
SMR = So. = ""
SMSQ = S** ~ ? £"*
(c) Calculation of Mean and Variance
RM = Mean Ratio =
VAR
Other programs
Several other programs in addition to these were written and
debugged. Calculations were made using them, but the results have
not been used in the report except as guides for further or different
types of calculation. For this reason a detailed discussion of
of these programs is omitted, and only some general comments are
offered.
-------
138
I. Analysis of covariance
The scheme followed is that in Bennett and Franklin, pp. 451 -
461. This evaluates the variance ratios between two variables
when allowance is made for regression of one on the other.
This was not used because it is a much clumsier method than
spectral computation and does not lend itself to interpretation of
a dynamic system. (We originally believed spectral analysis could
not be used on the short records obtained her. Comparison of
initial covariance results with cross-spectral computations on
comparable sets of data showed that the shortness of the spectral
records did not markedly affect the stability of the results in
this particular case. This is probably due to the basically
deterministic nature of the environmental parameters being used,
as opposed to the purely stochastic processes on which criteria
for spectral analysis are ordinarily based.)
This is a four-part program, and the final result is a
printed out table of variance estimates similar to that produced
in the analysis of variance.
II. Pearson Coordinate Programs (Three)
These programs were written to plot curves based on the
Pearson coefficients as calculated in the basic statistical program.
They were not used because the wide range of Pearson coefficients
calculated made quantitative estimates based on these values
subject to considerable ambiguity.
III. Calculation of Diffusion Factors and Salinity Gradients
This program is based on a theoretical statistical evaluation
of diffusion factors and salinity gradients from the stream survey
data. The program showed considerable promise, but a simpler
approach gave the results necessary for this study, so the
usefulness of the program has not been thoroughly examined.
-------
139
3 1 0000300002^3 1 0000300002*13
ENTER SOURCE PROGRAM
THEN PUSH START
C PREPROCESSOR FOR COVAR IANCE PROGRAM, PART ONE.
C INPUT IS RAV/ DATA DECKS FOR STATION PARAMETERS, WITH LEAD-TAIL CDS
DIVISION A(30),B(30),C(30),D(30)
92 READ 48
48 FGRiMAT(!5X 49HSAYTHEMAG ICVORDSOFPLEASEANDTHANKYOUANDHOPE I TV/OR KS)
?U::CH 48
su,v,n=o.o
SUMC=0.0
SUMO =0.0
r r> o O i _ 1 I
^ U Zo i = I L
53 :rORMAT(34X F3.0.1X F602,2X F3.0,1X F602)
: U;iD=SUMD+D( I)
:/^AR= SUMB/SUMA
C?AR= SUMD/SUMC
F(A(|)) 101,101,102
(|)=BBAR
F(L-l) 98,93,97
=1+1
GO TO 36
=1
F(C(I)) 103,103,104
D( I)=DBAR
IF(L-I) 105,105,106
1=1+1
GO TO 107
PUNCH 9
FORMAT(15X 14HSURFACE RECORD)
DO 108 1=1, L, 5
PUNCH 10,BM).B( 1 + 1) ,B( 1+2) ,B( 1+3) .B( 1+4)
95
101
102
97
98
107
103
104
106
105
9
108
10 F
LAS=0 '
PUNCH 91,LAS
PUNCH 48
PUNCH 8
8 FORMAT(15X 14HBOTTOM RECORD )
DO 109 1=1,L,5
109 PUNCH 10,D(I),D(I + 1),D( I + 2),D( !+3),D( 1+4)
READ 91,LAST
91 FORMAT(i4)
!F(LAST) 87,87,111
£7 LPST=O
?UNCH 91,LAST
GO TO 92
~. * PUNCH 91 ,LAST
-------
STOP
END
OBJECT PROGRAM DATA TABLE 14°
|01690 STORAGE POSITIONS
PROCESSING COMPLETE
-------
310000300002RS
ENTER SOURCE PROGRAM
THEN PUSH START
C ANALYSIS OF COVARIANCE. PART ONE. FORMATION OF XY SUMS.
DIMENSION TIX(6). TIXY(6). TRD(6). TJXY(18)
DIMENSION SY(18 6), SXY(l8,6)» SX(18,6) X(30).Y(30)
DIMENSION TSJ(6),SXP(18,6),TRX(6),XTI(18),YTI(18)
92 READ 2, IPEE,JCUE,COMP
2 FORMAT(18X |4,10H STATIONS ,, |4,9HSURVEYS, ,F6.0,11H REPLICATES)
KCOMP = COMP
TS=0.0
GSXS=0.0
STI=0.0
STIXY=0.0
STRD=0.0
DO 118 J=1,XUE
TRD(J)=0.0
TIX(J)=0.0
TIXY(J)=0.0
TSJ(J)=0.0
DO 117 1= 1. IPEE
READ 48
READ 9
DO 102 K=1,KCOMP,5
102 READ 10,X(K),X(K+1),X(K+2),X(Kvi3).X(K+4)
READ 91
91 FORMAT(I4)
48 FORMATM5X 49HSAYTHEMAGICWORDSOFPLEASEANDTHANKYOUANDHOPE ITWORKS)
9 FORMAT(15X 14HSURFACE RECORD)
READ 48
READ 9
DO 202 K=J,KCOMP,5
202 READ 10,Y(K),Y(K+1),Y(K+2),Y(K+3),Y(K+4)
READ 91
SXY(I,J)=0.0
SX(I,J)=0.0
SY(I,J)=000
DO 106 K = 1, KCOMP
SX( I,J)=SX(|,J)+X(K)
SY(I.J)=SY(I.J)+Y(K)
106 SXY(f,J)=SXY(l,J)+X(K)*Y(K)
SXP(|,J)=SX(|,J)*SY(I,J)
TIX(J)=TIX(J ' '
TRD(J)=TRD(J
TSJ(J)=TSJ(J
+SY(I.J)
+SXP( I.J)
i^w\wy i «.' w \ vr i «* *\ i \ v /
117 TIXY(J)«TIXY(J)+SXY(I,J)
TRX(J)=T|X(J)*TRD(J) .
STI=STI+TIX(J)
STIXY=STIXY+TRX(J)
TS=TS+TSJ(J)
GSXS=GSXS+TIXY(J)
118 STRD=STRD+TRD(J)
STJXY=0.0
DO 120 I =1,1 PEE
TJXY( l)=0.0
XTI( l)=0.0
YTI(I)=0.0
DO 119 J=1 .JCUE
XTI(0=XTI(0+SX(I,J)
119 YTI(I)=YTI(I)+SY(I.J)
TJXY(I).XTI(.|)*YTI(I)
120 STJXY=STJXY+TJXY(I)
PEE=IPEE
-------
CUE = JCUE
BIGN=COMP*PEE*CUE
PUNCH 200,PEE,CUE,COMP,BIGN,STRD __ 142
200 FORMAT(F6.0,F6.0,F6.0,F6.0,E1*t.8)
PUNCH 121,GSXS,TS.STJXY.STIXY.STI
121 FORMAT(2HXY.E11t.8.E14.8,E11f.8fE1^.8, E14.8)
PRINT 121 .GSXS.TS^STJXY^TIXY.STI
PAUSE
GO TO 92
END
OBJECT PROGRAM DATA TABLE
56220 STORAGE POSITIONS
PROCESSING COMPLETE
-------
143
310000300002RS
ENTER SOURCE PROGRAM
THEN PUSH START
ANALYSIS OF COVARIANCE. PART TWO
92 READ 101,PEE.CUE,COMP,BIGN,STRD
101 FORMAT(F6.0,F6.0,F6.0,F6.0,E14.8)
READ 102 ,GSXS,TS,STJXY,STIXY.STI
102 FORMAT(2HX2.E14.8, El^.8, E14.8, E14.8, E1^.8)
XYSA =GSXS-(TS/COMP)
XYSI=(STJXY/(COMP*CUE))-(STI*STRD)/BIGN
XYSJ=(STIXY/(COMP*PEE))-(STI*STRD)/BIGN
XYSS=GSXS-(STI*STRD)/BIGN
XYSIJ=TS/COMP-STJXY/(COMP*CUE)~XYSJ
READ 102, YSA, YSIJ, YSI, YSJ, YSS
READ 102, XSA, XSIJ, XSI, XSJ, XSS
BA = XYSA/XSA
BMIJ = XYSIJ/XSIJ
BMJ = XYSJ/XSJ
BMI = XYS1/XSI
BO = XYSS/XSS
SF = YSA - BA*XYSA
ST = YSIJ - BMIJ*XYSIJ
STV/ = YSJ - BMJ*XYSJ
SO = YSI - BMI*XYSI
SFV=YSS-BO*XYSS
STP =((BMIJ-BA)**2)*((XSIJ*XSA)/(XSIJ+XSA))
STWP =((BMJ-BA)**2)*((XSJ*XSA)/(XSJ+XSA))
SOP = ((BMI-BA)**2)*((XSI*XSA)/(XSI+XSA))
DFN = BIGN-PEE-CUE
DSF = BIGN -(PEE*CUE) -1.0
DST=(PEE-1.0)*(CUE-1.0) -1.0
DSTV/= CUE - 2.0
DSO = PEE-2..0
DSFV=BIGN-2.0
DFC=CUE-1.0
DPC=DFP*DFC
DONE=1.0
FOA=(BA*XYSA*DSF)/SF
FMA=((ST+STP)*DSF)/(DPC*SF)
FMI =((SO+SOP)/DFP)*(DFN/(ST+STP+SF))
FMJ=((STV/+STWP)/DFC)*(DFN/(ST+STP+SF))
PUNCH 718 YSA,XSA XYSA,BA,YSIJ
PUNCH 7l8,XSfj,XYSIJ,BMIJ,YSJ,XSJ
PUNCH 718,XYSJ,BMJ,YSI,XSI,XYSI
PUNCH 718,BMI,YSS,XSS,XYSS,BO
PUNCH 718,SF,DSF,STP,DONE,ST
PUNCH 718,DST,STWP,STW,DSTW,SOP
PUNCH 718,SO,DSO,SFV,DSFV.FOA
PUNCH 718,DPC,FMA,DFP,DFN.FMI
PUNCH 719.DFC.FMJ
719 FORMAT(EJ4.8,£1^.8)
PAUSE
GO TO 92
END
BJECT PROGRAM DATA TABLE
0720 STORAGE POSITIONS
PROCESSING COMPLETE
-------
144
310000300002RS
ENTER SOURCE PROGRAM
THEN PUSH START
C ANALYSIS OF COVARIANCE. PART THREE
92 PRINT 103
103 FORMAT(29X 22HANALYSIS OF COVARIANCE,20X 8HPAGE ONE//)
PRINT 105
105 FORMAT(22X 35HASSUMED LINEAR REGRESSION OF Y ON X/)
PRINT 202
202 FORMAT(I8HDEPENDENT VARIABLE)
READ 100
100 FORMAT(22X 36HCHLORIDE DATA FROM INTENSIVE SURVEYS)
PRINT 100
PRINT 201
201 FORMAT(20HINDEPENDENT VARIABLE)
READ 100
PRINT 100
PRINT 99
99 FORMAT(//) '
READ 141
HI FORMAT(16X 30HSURVEYS AA, AB, B, C, D, E )
PRINT 141
READ 142
142 FORMAT(16X4QHSTATIONS,SURFACE, 12345678913 )
PRINT 142
READ 142
PRINT 142
PRINT 99
READ 718,YSA,XSA,XYSA,BA,YSIJ
718 FORMAT(E14.8,E1408,E14.8,E14.8,E14.8)
READ 718,XSIJ,XYSIJ,BMIJ,YSJ,XSJ
READ 718,XYSJ,BMJ,YSI,XSI,XYSI
READ 718,BMI,YSS,XSS,XYSS,BO
READ 718,SF,DSF,STP,DONE,ST
READ 718,DST,STWP,STW,DSTW,SOP
READ 718,SO,DSO,SFV,DSFV,FOA
READ 718,DPC,FMA,DFP,DFN,FMI
READ 719.DFC,FMJ
719 FORMAT(El4.8,E14a8)
PRINT 96
96 FORMAT(/35X15HSUMS OF SQUARES,17X10HREGRESSION/49X21X6HCOEFF.)
PRINT 106
106 FORMAT(8X9HSOURCE OF,5X8HY SQUARE,6X8HX SQUARE,5X9HX TIMES Y)
PRINT 107
107 FORMAT(8X 8HESTIMATE//4X 1HA,3X 7HBETWEEN)
PRINT 108,YSA,XSA,XYSA,BA
108 FORMAT(8X 10HREPLICATES,E14.8,1XE14.8,1XE14.8,2XE14.8)
PRINT 109
109 FORMAT(8X 11HIN STATIONS//4X 1HB,3X 7HBETWEEN)
PRINT 110,YSIJ,XSIJ,XYSIJ,BMIJ
110 FORMAT(8X 11HSTATIONS,IN,El4.8,1XE14.8,1XE14.8,2XE14.8)
PRINT 111
111 FORMAT(8X11HSURVEYS AND/8X8HSTATIONS//4X1HC.3X7HBETWEEN)
PRINT 112,YSJ,XSJ,XYSJ,BMJ
112 FORMAT(8X 7HSURVEYS,4XEl4.8,1XE14.8,1XEl4.8f2XE14.8//)
PRINT 113,YSI,XS|,XYSI,BMI
113 FORMAT(4X1HD,3X7HBETWEEN,4XE14.8,1XE14.8,1XE14.8,2XE14.8)
PRINT 114
114 FORMAT(8X 8HSTATIONS//)
PRINT 115. YSS,XSS,XYSStBO
115 FORMAT(4X1HE,3X5HTOTAL,6XE14.8,1XE14.8,1XE14.8,2XE14.8//)
PRINT 302
302
-------
PRINT 303
303 FORMAT(29X 22HANALYSIS OF COVARIANCE, 20X 8HPAGE TWO//)
PRINT 116 145
116 FORMAT(20X 40HSUMS OF SQUARES CORRECTED FOR REGRESSION/)
PRINT 117
117 FORMAT(28X 14HSUM OF SQUARES, 10X 18HDEGREES OF FREEDOM)
PRINT 118, SF,DSF
118 FORMAT(8X11HA CORRECTED/8X14HFOR IN STATION,6XE14.8,14XF7.0)
PRINT 119
119 FORMAT(8X10HREGRESSION//8X10HDIFFERENCE/8X19HBETWEEN REGRESSIONS)
PRINT 120,STP,DONE
120 FORMAT(8X 11HFOR A AND B, 9X EH.8, 1 4X F7.0/)
PRINT 121, ST,DST
121 FORMAT(8X 17HB CORRECTED FOR A, 3X E14.8, 14X F7.0)
PRINT 119
PRINT 122 ,STWP,DONE
122 FORMAT(8X 11HFOR C AND A,9X E14.8, 14X F7.0/)
PRINT 123, STW,DSTW
123 FORMAT(8X 17HC CORRECTED FOR A, 3X E14.8, 14XF7.0)
PRINT 119
PRINT 124, SOP,DONE
124 FORMAT(8X 11HFOR D AND A, 9X E14.8, 14X F7.0/)
PRINT 125, SO, DSO
125 FORMAT(8X17HD CORRECTED FOR A,3XE14.8,14XF7.0 /8X10HREGRESSION/)
PRINT 126
126 FORMAT(8X 20HTOTAL SUM OF SQUARES/8X 13HCORRECTED FOR)
PRINT 127,SFV,DSFV
127 FORMAT(8X 18HOVERALL REGRESS ION,2X E14.8,14X F7.0/)
PRINT 128
128 FORMAT(23X34HSIGNIFICANCE OF VARIANCE ESTIMATES,5X10HLEVEL=.025//)
PRINT 129
129 FORMAT(8X10HHYPOTHESIS,8X2HN1,8X2HN2,10X11 RVALUES OF F.9X6HRESULT)
PRINT 130
130 FORMAT(43X 10HCALCUI_ATED,5X 9HTABULATED/)
PRINT 131 ,DONE,DSF,FOA
131 FORMAT(8X 7HBO = BA, 8XF7.0,2XF7.0,2XF11,2/)
PRINT 132,DPC,DSF,FMA
132 FORMAT(8X 9HBMIJ = BA, 6X F7.0,2XF7.0,2XF11.2/)
PRINT 133,DFP,DFN,FMI
133 FORMAT(8X 8HBMI = BA, 7X F7.0,2XF7.0,2XF11,2/)
PRINT 134,DFC,DFN,FMJ
134 FORMAT(8X 8HBMJ - BA, 7X F7.0,2XF7.0,2XF11.2)
PAUSE
GO TO 92
END
OBJECT PROGRAM DATA TABLE
50970 STORAGE POSITIONS
PROCESSING COMPLETE
-------
146
,310000300002RS
;NTER SOURCE PROGRAM
THEN PUSH START
C PEARSON FREQUENCY CURVES, COORDINATE PROGRAM 1
C AT LOAD DATA FIRST LOAD GAMMA FUNCTION DECK
DIMENSION NE(100), BIGG(IOO)
DO 201 L=1.100,2
201 READ 202,NE(L),BIGG{L),NE(L+1),B|GG(L+1)
202 FORMAT(I5,F8.4,I5,F8.4).
955 PRINT 11
11 FORMAT(21X 31HPLOT OF PEARSON FREQUENCY CURVE//)
READ 12
12 FORMAT(15X 49HTHIS IS THE RAW DATA LEAD CARD
PUNCH 12
PRINT 12
954 ARIG = 0.0
PBO =0.0
PB1 = 0.0
PB = 0.0
SIGMA = Q.O
SQUMO= 0.0
SKEW =0.0
BETA2 =0.0
TOT = 0.0
XBAR =. 0.0
READ 13
13 FORMAT(26X 28HSTAT1STICS OF XXXXXXX RECORD)
PUNCH 13
PRINT 13
READ 51, TOT, XBAR, SQUMO. SIGMA
51 FORMAT(7X F4.0, 9X F8.3, 6X F14.6, 7X F12.6)
READ 52, SKEW, BETA2
52 FORMAT(13X F12.6, 17X F12.6)
READ 54SABIG,PBO,PB1 ,PB
54 FORMAT(6X F12.6, 6X F12.6,6X F12.6,6X F12.6)
PRINT 55
55 FORMAT(//47HNUMBER OF VALUES AT PRODUCTS OF SIGMA FROM MEAN//)
PRINT 802
802 FORMAT(J5X 1HX, 10X JHY)
GAM2 = 2.*(3.-BETA2)
CUE2 = 4.*BETA2*SQUMO/GAM2
PLOT = -6.0
IF(PBI) 102,101,102
101 PRINT 924
924 FORMAT(24HUSE COORDINATE PROGRAM 2//)
GO TO 923
102 IF(PB) 121,109,121
109 EFT =(4. -(SKEW**2))/(SKEW**2)
IF(EFT) 122,123,122
123 PRINT 124
124 FORMAT(37HASYMPTOTE HAS ACUTE ANGLE WITH X-AXIS)
GO TO 923
122 DINA = U+EFT
DINB = 1 .
KAPPA = 1
GO TO 228
228 LAPSE - 1
250 IF(DINA -.1.) 222,223,224
-------
223 GDINA = 1.0
GO TO 252
147
22*t DO 2k} MOM » 1 ,1000
BINA = NOM
CINA = DINA - BINA
IF(CINA - 2.0) 2k} ,241,243
2k3 CONTINUE
241 IDUNA=CINA*100.
GO TO 225
222 IDUNA=(D|NA+1.0)*100.
B|NA=-J .0
225 DO 226 L=1,100
IF( IDUNA-NE(L)) 226,227,226
226 CONTINUE
227 GD1A=EXP(BIGG(L)-10.)
IF(BINA)244,245,246
2kk GDINA=GD1A/DINA
GO TO 252
2^5 GDINA=GD1A
GO TO 252
246 DO NAN=1,1000
GD1A=CINA*GD1A
CINA = CINA + 1.0
IF(DINA-CINA) 247,247,248
248 CONTINUE
247 GDINA=GD1A
252 GO TO (253,254),LAPSE
253 LAPSE =2
DINA=DINB
GO TO 250
254 GDINB=GD|NA
GO 70(114,115),KAPPA
114 GAM = SQRT(GAM2)
WYEO =1./(PB1*((PB1/GAM)**EFT)*(2.71828**(GAM/PB1))*GDINA)
GO TO 397
397 IF(PLOT - 5.0) 398,923,923
398 PL07=PLOT+1.0
ABSX = PLOT*SIGMA
GO 70(311,312), KAPPA
311 NORY =WYEO*((1.+(ABSX/GAM))**EFT)/(2.71828**(ABSX/PB1))
GO TO 399
121 SEE =PB1/(2.*PB)
DEE = PBO/PB
GEE2 = DEE -(SEE**2)
AKAY = (-PB1 + SEE)/PB
IF((PB1**2) -(4.*PB*PBO)) 125,126,125
125 PRINT 806 -
806 FORMAT(24HUSE COORDINATE PROGRAM 3//)
GO TO 923
126 TEE2 =AKAY/(ABSX + SEE)
DINA=((1./PB)-1.)
DINB =1.0
KAPPA = 2
GO TO 228
115 SEEK = 1./(AKAY*GDINA)
V/YEO=SEEK/(((SEE/AKAY)**(1./PB))*(2.71828**(AKAY*SEE)))
TEE = SQRT(TEE2)
GO TO 397
312 NORY = SEEK*(TEE**(2./PB))/(2.71828**TEE2)
GO TO 399
399 PRINT 801, ABSX, NORY
ADCV
-------
801 FORMAT(10X F12.6, 15)
GO TO 397
923 READ 91. LAST
91 FORMAT(l*f)
PUNCH 91, LAST
IF(LAST) 95^,956,1111
956 GO TO 955
1111 STOP
END
RELOCATABLE SUBROUTINES CALLED
EXP
SQRT
OBJECT PROGRAM DATA TABLE
03170 STORAGE POSITIONS
PROCESSING COMPLETE
148
-------
310000300002RS 149
ENTER SOURCE PROGRAM
THEN PUSH START
C PEARSON FREQUENCY CURVES. COORDINATE PROGRAM 2
C AT LOAD DATA. FIRST LOAD GAMMA FUNCTION DECK
DIMENSION NE(IOO), BIGG(IOO)
DO 201 L= 1 .100,2
201 READ 202,NE(L),BIGG(L),NE(L+1),BIGG(L+1)
202 FORMAT(I5,F8.4,I5,F8.4)
955 PRINT 1!
11 FORMAT(21X 31HPLOT OF PEARSON FREQUENCY CURVE//)
READ 12
12 FORMAT(15X 49HTHIS IS THE RAW DATA LEAD CARD )
PRINT 12
PUNCH '12
954 ABIG = 0.0
PBO =0.0
PB1 =0.0
PB =0.0
SIGMA = 0.0
SOUMO= 0.0
SKEW = 0.0
BETA2 =0.0
TOT = 0.0
XBAR =0.0
READ 13
13 FORMAT(26X 28HSTAT1STICS OF XXXXXXX RECORD)
PUNCH 13
PRINT 13
READ 51, TOT, XBAR, SQUMO. SIGMA
51 FORMAT(7X F4.0, 9X F8.3, bX F14.6, 7X F12.6)
READ 52, SKEW, BETA2
52 FORMAT(13X F12.6, 1?X F12.6)
READ 54,ABIG,PBO,PB1 ,PB
54 FORMAT(6X F12.6, 6X F12.6,6X FJ2.6,6X F12.6)
PRINT 55
55 FORMAT(//47HNUMBER- OF VALUES AT PRODUCTS OF SIGMA FROM MEAN//)
PRINT 802
802 FORMAT(15X 1HX, 10X 1HY)
GAM2 = 20*(3.-BETA2)
CUE2 = 4.*BETA2*SQUMO/GAM2
PLOT = -6.0
IF(PBI) 102,101 ,"102
102 PRINT 925
925 FORMAT(29HUSE COORDINATE PROGRAM 1 OR 3//)
701 IF(PB) 103,104,105
103 DINB = 1. + ABIG/(2.*GAM2)
DINA = 1.5 + AB|G/(2.*GAM2)
GDINC = 1.77245
KAPPA = 3
GO TO 228
228 LAPSE = 1
250 IF(DINA - 1.) 222,223,224
223 GDINA = 1.0
GO TO 252
224 DO 241 NOM = 1,1000
BINA = NOM
C I NA = D INA - B INA
IF(CINA - 2.0) 241 ,241,243
243 CONTINUE
241 IDUNA=C|NA*100.
-------
GO TO 225
222 IDUNA=(D|NA+1.0)*100.
BINA=-1.0 ' 150
225 DO 226 L=1,100
IF(IDUNA-NE(L)) 226,227,226
226 CONTINUE
227 GD1A=EXP(BIGG(L)-10.)
IF(BINA)244,245,246
244 GDINA=GD1A/D|NA
GO TO 252
245 GDINA=GDJA
GO TO 252
246 DO NAN=1 ,1000
GD1A=CINA*GD1A
C INA = C INA + 1 .0
IF(DINA-CINA) 247,247,248
248 CONTINUE
247 GD|NA=GDJA -
252 GO TO (253,254),LAPSE
253 LAPSE = 2
DINA=DINB
GO TO 250
254 GDINB=GD|NA
GO 10(111,112,113),KAPPA
113 BETAG = (GDINC*GDINB)/GDINA
CUE = SQRT(CUE2)
WYEO = 1./CUE*BETAG
GO TO 397
397 IF(PLOT - 5.0) 398,923,923
398 PLOT=PLOT+1 .0
ABSX = PLOT*SIGMA
GO T0(311,312,313,314),KAPPA
313 NORY »WYEO*((1. -((ABSX**2)/CUE2))**(ABIG/(2.*GAM2)))
GO TO 399
105 IF( BETA2 - 3.000000) 106,104,108
108 DINA = 1./(2.*PB)
DINB » (1.-PB)/(2.*PB)
KAPPA = 1
GO TO 228
111 ELFA = SQRT(PBO/PB)
WYEO =(1./ELFA*1.77245)*(GDINA/GDINB)
GO TO 397
311 NORY - WYEO*(J.+(PB/PBO)*(ABSX**2))**(-DINA)
GO TO 399
106 DINA = 1.5-J./(2.*PB)
DINB = 1. - 1./(2.*PB)
GDINC = 1.77245
KAPPA = 2
GO TO 228
112 BETAG = (GDINC*GDINB)/GDINA
p = SQRT(-PBO/PB)
V/YEO = l./P*BETAG
GO TO 397
312 NORY= V/YEO*((1.-(ABSX**2)/(P**2))**(~J./2.*PB))
GO TO 399
104 V/YEO = 1./(SIGMA*2.50663)
KAPPA = 4
GO TO 397
314 NORY = WYEO*2.71828**((-ABSX**2)/SQUMO)
399 PRINT 801, ABSX, NORY
PUNCH 801, ABSX. NORY
801 FORMAT(10X F12.6, 15)
GO TO 397
-------
91 FORMAT(I4)
PUNCH 91 , LAST
IF(LAST) 95**,956,1111 151
956 GO TO 955
1111 STOP
END
RELOCATABLE SUBROUTINES CALLED
EXP
SQRT
OBJECT PROGRAM DATA TABLE
03180 STORAGE POSITIONS
PROCESSING COMPLETE *
-------
152
310000300002RS
ENTER SOURCE PROGRAM
THEN PUSH START
C PEARSON FREQUENCY CURVES, COORDINATE PROGRAM 3
955 PRINT 11
11 FORMAT(21X 31HPLOT OF PEARSON FREQUENCY CURVE//)
READ 12
12 FORMAT(15X 49HTHIS IS THE RAW DATA LEAD CARD )
PRINT 12
PUNCH T2
954 ABIG - 0.0
PBO =0.0
PB1 = 0.0
PB =0.0
SIGMA = 0.0
SQUMO= 0.0
SKEW =0.0
BETA2 = 0.0 .'
TOT = 0.0
XBAR =0.0
READ 13
PUNCH 13
13 FORMAT(26X 2SHSTATISTICS OF XXXXXXX RECORD)
PRINT 13
READ 51. TOT, XBAR, SQUMO, SIGMA
PUNCH 51,TOT,XBAR,SQUMO,SIGMA
51 FORMAT(7X F4.0, 9X F8.3, 6X F14.6, 7X F12.6)
READ 52, SKEW, BETA2
PUNCH 52,SKEW,BETA2
52 FORMAT(13X F12.6, 17X F12.6)
READ 54.ABIG,PBO,PB1,PB
PUNCH 54,ABIG,PBO,PB1,PB
54 FORMAT(6X F12.6, 6X F12.6,6X F12.6,6X F12.6)
PRINT 55
55 FORMATC//47HNUMBER OF VALUES AT PRODUCTS OF SIGMA FROM MEAN//)
PRINT 802
802 FORMAT(15X 1HX, 10X 1HY)
GAM2 = 2.*(3.-BETA2)
CUE2 = 4.*RETA2*SQUMO/GAM2
PLOT = -6 0
IF(PBJ) 102,101,102
102 IF(PB) 121,109,121
109 PRINT 825
825 FORMAT(24HUSE COORDINATE PROGRAM I//)
GO TO 923
101 PRINT 924
924 FORMAT(24HUSE COORDINATE PROGRAM 2//)
GO TO 923
121 SEE =PB1/(2.*PB)
DEE = PBO/PB
GEE2 = DEE -(SEE**2)
AKAY = (-PB1 + SEE)/PB
IF((PB1**2) -(4.*PB*PBO)) 125,109,127
125 WYEO =15.
MAP = 1
PRINT 998
998 FORMAT(21HAPBITRARY Y ZERO = 15//)
GO TO 397
397 GO T0(395,401),MAP
395 IF(PLOT - 5.0) 398,923,923
398 PLOT=PLOT+1.0
ABSX = PLOT*S|GMA
PARTI = f fAR?;X-fSF.E^**2+GEF.2WfSFF**2-i-nEF,2^
-------
SGEE « SQRT(GEE2)
PART2 = (-PB1+SEE)/(PB*SGEE)
PART3 = ATAN((SGEE*ARSX)/((SEE*ABSX)+DEE)) 153
NORY=V/YEO*(PART1**(-1./2.*PB))*((2./1828)**(PART2*PART3))
GO TO 399
127 WYEO =15.0
MAP = 2
PRINT 998
IF(PLOT - 5.0) 406,923,923
PLOT = PLOT + 1.0
BEEU = (-PB1)*((2.*PB)-1.)
BEEZ =PBO + ((PB1**2)*(PB - 1.))
RTL = (-BEEU+SQRT((BEEU**2)-(4.*PB*BEEZ)))/(2.*PB)
RTS = (-BEEU-SQRT((BEEU**2)~(4.*PB*BEEZ)))/(2.*PB)
7.ETA=XBAR+PLOT*S IGMA
EPEE = J./(PR*(RTL-RTS))
PAR1=(1.-(7ETA/RTS))**(EPEE*RTS)
PAR2 = (1.-(7ETA/RTL))**(-EPEE*RTL)
NORY = V/YEO*PAR1*PAR2
ABSX=XBAR-ZETA
GO TO 399
399 PRINT 801, ABSX, NORY
PUNCH 801 , ABSX, NORY
801 FORMAT(10X F12.6, 15)
GO TO 397
923 READ 91, LAST
91 FORMAT(l*f)
PUNCH 91 , LAST
IF(LAST) 95^,956,1111
956 GO TO 955
1111 STOP
END
RELOCATABLE SUBROUTINES CALLED
ATAN
SQRT
OBJECT PROGRAM DATA TABLE
50870 STORAGE POSITIONS
PROCESSING COMPLETE
-------
154
310000300002RS
ENTER SOURCE PROGRAM
THEN PUSH START
C CALCULATION OF DIFFUSION FACTORS AND SALINITY GRADIENTS
92 READ 18,TAU,DELT,TEE,AMP
18 FORMAT(3X F6.2,F3.0,F6.2 ,F6.2)
DIMENSION A(30),B(30),C(30),D(30),S(30)
READ Jf8
k& FORMATM5X 49HSAYTHEMAGICWORDSOFPLEASEANDTHANKYOUANDHOPE ITWORKS)
PRINT 48
L=30
Pl=3.14159
EN=30.
SUMA=0.0
SUMB=0.0
SUMC=0.0
SUMD=0.0
DO 28 1=1,L
READ 53,A(I),B(I),C(I),D(I)
53 FORMAT(34X F3.0,1X F6.2,2X F3.0,1X F6.2)
SUMA=SUMA+A(|)
SUMB = SUMB+B(I)
SUMC=SUMC-HC( I)
28 SUMD=SUMD-i-D( I)
BBAR= SUMB/SUMA
DBAR= SUMD/SUMC
1=1
96 IF(A(|)) 101,101,102
101 B(I)=BBAR
102 IF(L-I) 98,98,97
97 1=1+1
GO TO 96
98 1=1
107 IF(C(I)) 103,103,10^
103 D( !)=DBAR
10if IF(L-I) 105,105,106
106 1=1+1
GO TO 107
105 K=1
SONE= B(1)
SBAR=BBAR
DO 118 1=1,L
118 S(I)=B(I)-BBAR
212 SUMI=0.0
DO 201 1=1 ,L
201 SUMI=SUMI+S(l)**2
VAR=SUMI/(EN-1.)
V/=SBAR-SONE*(EN-1 ,)/EN
Z=(((EN**2)-1.)/(2.*EN))-((EN-1.)/EN)
TH=TAU/(PI*DELT)
Y1=-(TH/2.)*COS(PI*TEE/TAU)*SIN(PI*DELT*(2.*EN-3.)/TAU)
Y2=-(EN-1.)*((SIN(PI*DELT/TAU))**2)*SIN(PI*TEE/TAU)
Y3=((TH/2.)+(EN-l.))*COS(PI*TEE/TAU)*SIN(P|*DELT/TAU)
Y=(Y1+Y2+Y3)/EN
U1=SIN(2.*PI*(TEE-DELT*(EN-1.))/TAU)+SIN(2.*PI*DELT*(EN-2.)/TAU)
U2=-SIN(2.*PI*TEE/TAU)+SIN(2.*PI*DELT/TAU)
U=(UJ+U2)*TH/(2.*(EN-1.))
SEE 1 =( (((EN-1 .)**2)*(V/**2))/(3 .*( l**2)) )-VAR
SEE2=(((EN-1.)*(SONE-SBAR))/(2.*7))*V/+((SONE-SBAR)**2)
SEE=SEE1+SEE2
BEE=(2.*Y*((EN-1.)**2))/(3.*(7.**2))+(Y*(FN-1.)*(SONE-SBAR))/(2.*Z)
ACO=((Y**2)*((EN-1.)**2))/(3.*(Z**2))+1.0+U
DISC=(BEE**2)-(4.*ACO*SEE)
-------
IF(DISC) 202,203,203
202 AKAY=-BEE/(ACO*2.)
BKAY=AKAY 155
GO TO 316
203 AKAY=(BEE-fSQRT(DISC))/(2.*ACO)
BKAY=(BEE-SQRT(DISC))/(2.*/CG)
316 FAC=(2.*(PI**2)*DELT)/((TAU**2)*AMP*SIN(P|*DELT/TAU))
GRADA= AKAY*FAC
GRADB=BKAY*FAC
DIFFA=((W-Y*AKAY)/Z)/(GRADA*DELT)
D|FFB=((V,'-Y*BKAY)/Z)/(GRADB*DELT)
GO TO (304, 205), K
205 PRINT 215
215 FORMAT(15X J3HBOTTOM RECORD)
GO TO 216
304 PRINT 206
206 FORMAT(15X 14HSURFACE RECORD)
PRINT 207 .
207 FORMAT(10X J8HPARAMETER GRADIENT, 10X 16HDIFFUSION FACTOR/)
216 PRINT 208,GRADA,DIFFA,GRADB,DIFFB
208 FORMAT(6HROOT 1 ,7XE14.8,12XE 14.8/6HROOT 2 ,7XE14.8,12XE14.8/)
GO TO(209,210),K
209 K=2
SONE=D(1)
SBAR=DBAR
DO 211 1=1 ,L
211 S(I)=D(I)-DBAR
GO TO 212
210 READ 91 , LAST
91 FORMAT(I4)
IF(LAST) 92,92,111
111 STOP
RELOCATABLE SUBROUTINES CALLED
S IN
COS
SQRT
QBJECT PROGRAM DATA TABLE
02480 STORAGE POSITIONS
PROCESSING COMPLETE
-------
156
COMPILATION OF BASIC DATA
The following tabulations present the basic data collected
during the routine monitoring and the intensive surveys. The routine
monitoring data are tabulated by station and by date collected
and are shown in Table 34. The intensive survey data are
presented in Table 35 For those data run through the descriptive
statistics program, the tabulations show the basic data, the descriptive
statistics and the Pearson coefficients for each sampling station
for each survey. The other intensive survey data are presented in
tabular form only. It should be noted that in the intensive survey
data where zero values are listed, the values were missing and the
zeros were used only to facilitate the programming.
Also included in the tabulations of intensive survey data is
the pertinent environmental information that was collected during
each survey. These data are river discharge, tide height, rainfall,
wind velocity, solar radiation and air temperature and are shown in
Table 36.
The last data tabulation is the chloride concentrations observed in
the hydraulic model of Charleston Harbor. These data were collected during
the model verification studies and are listed in Table 37 .
-------
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