WATER POLLUTION CONTROL RESEARCH SERIES 16090 DUH 02/71
Stochastic Modeling for
Water Quality Management
ENVIRONMENTAL PROTECTION AGENCY WATER QUALITY OFFICE
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VIATER POLLUTION CONTROL RESEARCH SERIES
The Water Pollution Control Research Series describes
the results and proaress in the control and abatement
of pollution in our Nation's waters. They provide a
central source of information on the research* develop-
ment, and demonstration activities in the VJater Quality
Office, Environmental Protection Agency, through inhouse
research and grants and contracts with Federal, State,
and local aqencies, research institutions, and industrial
organizations.
Inquiries pertaining to Water Pollution Control Research
Reports should be directed to the Head, Project Reports
System, Office of Research and Development, Water Quality
Office, Environmental Protection Agency, Room 1108,
Washington, D. C. 20242.
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Stochastic Modeling for
Water duality Management
by
Stochastics Incorporated
Westover Drive
Blacksburg, Virginia 24060
for the
ENVIRONMENTAL PROTECTION AGENCY
Project #16090 DUH
Contract *14-12-849
February 1971
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price $3.00
Stock Number 5501-0101
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EPA Review Notice
This report has been reviewed by the Environmental
Protection Agency and approved for publication.
Approval does not signify that the contents neces-
sarily reflect the views and policies of the Environ-
mental Protection Agency, nor does mention of trade
names or commercial products constitute endorsement
or recommendation for use.
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ABSTRACT
The purpose of this work was to extend and generalize
the stochastic models found in: A Stochastic Model for
Streams, by Thayer and Krutchkoff. ASCE J. Sanitary
Engineering Division No. SA3, June 1967, pp. 59-72,
Generalized Initial Conditions for the Stochastic Model
for Pollution and Dissolved Oxygen in Streams, by
Moushegian and Krutchkoff, Water Resources Research Cen-
ter of Virginia, Bulletin 28, August 1969, and Stochas-
tic Model for BOD and DO in Estuaries, by Custer and
Krutchkoff, ASCE J. Sanitary Engineering Division, Octo-
ber 1969, pp. 865-885. In particular there were four
tasks: a) to adapt the models to accept variable or
random input loads, b) to adapt the estuary model to
treat segmented estuaries, c) to verify the the adapted
models with data supplied by WQO, d) to find a method
for using data to estimate and predict the stochastic
parameter A.
The four tasks were successfully completed. Verifica-
tion was done with data from the Ohio River and from
the Potomac Estuary.
This report is submitted in fulfillment of project
number 16090DUH, contract number 14-12-849 under spon-
sorship of the Water Quality Office of the Environmental
Protection Agency.
111
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TABLE OF CONTENTS
Abstract
List of Figures vii
List of Tables xi
Introduction 1
Why a Stochastic Model 1
Deterministic Models 2
Street-Phelps Model 2
Dobbins' Model 3
O'Connor's Model 7
Thomann' s Model 7
Orlob's Model 9
Harleman's Model 9
Previous Stochastic Models 1O
The Model of Thayer and Krutchkoff 1O
The Model of Moushegian and Krutchkoff 13
The Model of Custer and Krutchkoff 14
Purpose of This Project 21
Include a Variable Source 21
Segmented Estuary Model. .. 22
Verify the Model 22
Obtain a Method for Predicting A 22
Summary, Conclusions and Recommendations 23
Variable or Random Inputs 23
Simulated Case Studies 23
Analytical Results 26
Segmenting an Estuary 26
Verification of the Model 28
Verification on an Impounded Stream 28
Verification on a Segmented Estuary 29
Predicting A 35
Conclusion 38
Recommendations 38
Random or Variable Inputs 41
Background 41
Derivation 43
Moments of the Resulting Distribution 45
Continuous Approximations 47
The Segmented Estuary Model 51
Output-Input Model . . 51
Development of the New Stochastic Model 55
The Difference Equation. ; .... 56
Continuous Limit for Difference Equations 60
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Continuous Source. . . . 64
Solution of the Differential Equations
for the Mean 71
Data Requirement 72
Discussion of Model 77
Stochastic Component of the Model. ......... 82
Scale Factor, Stochastic Coefficient, or A .... 82
The Complete Stochastic Model. . 86
Program Documentation 91
Internal Modifications .... 92
A General Partial Differential Equation
Describing the Behavior of Any Soluble
Pollution Component in an Estuary 1O1
Verification of the Stochastic Model 109
Potomac Estuary 1O9
Ohio River 128
Delaware Estuary 136
Using the Model: Case Studies. . 138
A Method For Predicting A 151
Continuous State Space . 151
The Mean and Variance for the Continuous
Markov Process 153
Comparing with Thayer and Krutchkoff 156
The Two Stage Method For Predicting A 161
The First Stage Program 162
Prediction Equation for the Ohio i69
Prediction A for the Potomac 17O
Acknowledgements 173
References 177
Glossary and Abbreviations 185
Appendices 189
VI
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LIST OF FIGURES
1. Biochemical oxygen demand-situation 1 . . . . 24
2. Oxygen deficit-situation 1 25
3. A comparison of the predicted and
observed BOD and OD mean concentration
in the Markland pool 30
4. Comparison of predicted and observed OD
concentration as functions of tidal cycle
for station 1, Potomac Estuary 32
5. Comparison of predicted and observed OD
concentration as functions of tidal cycle
for station 2, Potomac Estuary 33
6. Comparison of predicted and observed OD
concentration as functions of tidal cycle
for station 3, Potomac Estuary 34
7. The probability density of a unit of BOD
a± various times 63
8. BOD and OD profiles in an estuary 78
9. BOD and OD profiles in a river 79
1O. Schematic diagram of the parallel-series
reaction with nitrogen and carbon recycle ... 80
11. Comparison of the BOD and OD profiles
which would be expected with the simple-series
and parallel-series 81
12. Hourly average of DO concentration as
function of the time of day for the
Potomac Estuary 84
13. Poisson probability mass function with
distribution parameter equal to 2.O . . . . .89
14. Corresponding converted poisson probability
density function 89
15. Comparison of poisson and converted
poisson with distribution parameter
equal to zero 90
16. Comparison of poisson and converted
poisson with distribution parameter
equal to zero 9O
17. Differential cross sectional segment
of an estuary 1O2
18. Comparison of predicted and observed OD
concentration as functions of tidal cycle
for station 1, Potomac Estuary 115
Vll
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Page
19. Comparison of predicted and observed OD
concentration as functions of tidal cycle
for station 2, Potomac Estuary 116
2O. Comparison of predicted and observed OD
concentration as functions of tidal cycle
for station 3, Potomac Estuary 117
21. OD profiles through tidal phase for 3
stations in the Potomac Estuary 119
22. OD profiles through the Potomac Estuary
for 4 tidal phases 12O
23. BOD profiles for the Potomac Estuary as
functions of tidal phase (O.O1 tO O.495). . . .121
24. OD profiles for the Potomac Estuary as
functions of tidal phase (O.O1O to O.495) . . .122
25. BOD profiles for the Potomac Estuary as
functions of tidal phase (0.495 to O.979) . . .123
26. OD profiles for the Potomac Estuary as
functions of tidal phase (O.495 to O.979) . . .124
27. Comparison of predicted mean OD
Concentration and confidence limits with
observed OD data as functions of tidal cycle
for station No. 1, Potomac Estuary 125
28. Comparison of predicted mean OD
concentration and confidence limits with
observed OD data as functions of tidal cycle
for station No. 2, Potomac Estuary 126
29. Comparison of predicted mean OD
concentration and confidence limits with
observed OD data as functions of tidal cycle. .127
3O. A comparison of predicted and observed
BOD and OD mean concentration in the
Markland pool of the Ohio River 131
31. BOD profiles resulting from four different
methods of introducing pollution to the
Potomac Estuary .140
32. OD profiles resulting from four different
methods of pollution input to the
Potomac Estuary ... 141
33. BOD profiles resulting from three levels
of reaeration rate for the Potomac Estuary. . .142
34. OD profiles resulting from three levels of
reaeration rate constant for the
Potomac Estuary 143
V3.ll
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Page
35. BOD profiles resulting from three levels
of the rate constant for oxygen and
non-oxygen consuming processes for the
Potomac Estuary 144
36. OD profiles resulting from three levels
of the rate constant for biological
utilization of BOD for the Potomac Estuary. . .145
37. BOD profiles resulting from three
pollution input rates for the Potomac
Estuary 147
38. OD profiles resulting from three
pollution input rates for the Potomac
Estuary 148
39. BOD profiles resulting from three levels
of diffusion rate constant for the
Potomac Estuary 149
4O. OD profiles resulting from three levels
of diffusion rate constant for the
Potomac Estuary ISO
IX
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LIST OF TABLES
Page
1. Observed vs. predicted fraction of
values outside specified concentration
confidence intervals for the Ohio River .... 31
2. Observed vs. predicted fraction of
values outside specified concentration
confidence intervals for the Potomac
Estuary .... ... 35
3. A values for the Potomac by station . . ... 85
4. Table of alpha levels generated by
the computer 91
5. Information required for first data card. ... 93
6. Information required for subsequent data
card 94
7. Information for IPT card 97
8. Example of use of position card 97
9. Example with two parameters in Catagory D ... 98
1O. Example (variable NV=8, 5 pairs of values). ... 98
11. Example with several variance in Catagory ... 99
12. IPT card 99
13. Example of FF 1OO
14. FF in PL/1 1OO
15. Major pollution sources for the Potomac . . . .1O9
16. Various estuary physical parameters
for the Potomac 110
17. Fresh water velocity component for
the Potomac Ill
18. Average values of A by station. 114
19. A values by tidal subclass 114
2O. Observed vs predicted fraction of
values outside specified' concentration /
confidence interval for the Potomac
Estuary 128
21. STP outputs for the Ohio River 129
22. Physical and biological information
for the Ohio River 129
23. Fluid velocity as a function of
position for the Ohio River 130
24. A summary of A values for BOD for the
Ohio River 133
XI
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Page
25. A summary of A values for OD for the
Ohio River 134
26. Observed vs. predicted fraction of
values outside specified concentration
confidence intervals for the Ohio River .... 135
27. Physical and biological data for
the Delaware 136
28. Fresh water flow rate for the Delaware 137
29. Reaeration rate for the Delaware 137
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INTRODUCTION
WHY A STOCHASTIC MODEL
Pollution is a Stochastic Process. That is, one
cannot predict exactly how much pollution there will
be at any given time and place in a stream or estuary.
One has simply to look at stream or estuary data to
observe this unpredictable fluctuation. Unfortunately
stream quality standards are given in absolute terms.
It is, however, unreasonable to expect even a clean
stream to have Dissolved Oxygen (DO) readings above
a preset value all the time. Natural fluctuation
might take the DO reading below any value for brief
periods. This momentary violation of a standard can
cause no ill effects. In an attempt to be realistic
one might interpret the standard to mean that the average
value must be above the standard. This too causes
problems. A high average DO might be the result of an
unnecessarily high DO concentration part of the time
and a dangerously low DO concentration the remainder
of the time. Fish kills often occur when the average
DO is above the prescribed value.
The only solution to this problem is to consider
variability as an important aspect of water pollution
and incorporate it into water quality standards.
A good stochastic model can predict not only the
average concentration of a pollutant and the associated
DO but also the variability of the pollutant or the DO
concentration about its average value. In particular
it should be able to predict accurately the proportion
of the time that the pollutant will be above any given
concentration level or the proportion of the time that
DO will be below any given concentration level. Standards
could then be written in terms more appropriate to their
purpose. If, for example, the purpose were to prevent
fish kills the standard might allow fluctuation in DO
such that there is no less than 4 ppm DO 5O% of the time,
no less than 3 ppm DO 2O% of the time and no less than
2 ppm DO 5% of the time.
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DETERMINISTIC MODELS
STREETER-PHELPS MODEL
Streeter and Phelps [68] assumed that the dissolved
oxygen concentrations in a stream are governed by two
independent reactions. First, the oxygen is depleted
by the bacteria while stabilizing the organic matter.
Secondly, the DO is replenished by absorption at the
surface from the atmosphere. By definition the
Biochemical Oxygen Demand (BOD) is decreased by the
first mechanism at the same rate the DO is depleted.
They assumed both of these reactions to be first order.
The BOD and DO are decreased at a rate proportional to
the remaining BOD, and the DO is increased at a rate
proportional to the oxygen deficit (OD). This leads to
the following differential equations:
dL/dt = -KjL, (1)
and
dD/dt = -KgD+iqL, (2)
where
t is the time of reaction,
L is the BOD level,
D is the oxygen deficit level
Kj is the coefficient defining the rate of deoxygenation,
and
K3 is the coefficient defining the rate of reaeration.
Initial conditions L = LQ and D = D0 at t = 0 are
imposed. The differential equations have solutions
-K t K t
D = K, Lo(e * -e 3 ) + DC
K8-K1
(3)
(4)
The independent variable in (3) and (4) is reaction
time, i.e., these equations characterize a static
situation such as polluted water in a laboratory beaker.
In order to apply the equation to a stream it is necessary
to make certain assumptions about the flow. It is assumed
that the system is uniform and steady state and there is
no longitudinal dispersion. The last assumption implies
that in any cross-section the pollution remains intact,
not spilling over into neighboring cross-sections as it
moves down stream.
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Under these assumptions reaction time is equivalent
to travel time. If the uniform velocity is given by
U = dx/dt, (5)
then
x = Ut (6)
Where x = 0 corresponds to t = O. With this transformation
of the independent variable the pollution and DO levels
can be obtained from equations (3) and (4) for any point
down stream from x = 0.
DOBBINS' MODEL
W. E. Dobbins [18] modified and extended the
Streeter-Phelps equations, taking into account various
additional sources of oxygen supply and demand. Streeter
and Phelps assumed that the only reactions in a stream
were the bacterial deoxygenation and reaeration. Dobbins
states additional processes which may take place in a
particular stretch of the stream.
1. The removal of BOD by sedimentation or absorption.
2. The addition of BOD along the stretch by the scour
of bottom deposits or by the diffusion of partially
decomposed organic products from the benthal layer into
the water above.
3; The addition-of BOD along the stretch by the
local runoff.
4. The removal of oxygen from the water by diffusion
ini-^ +be benthal layer to satisfy the oxygen demand in
the aerobic zone of this layer.
5. The removal of oxygen from the water by purging
action of gases rising from the benthal layer.
6. The addition of oxygen by photosynthetic action
of plankton and fixed plants.
7. The removal of oxygen by the respiration of
plankton and fixed plants.
8. The continuous redistribution of both BOD and
oxygen by the effect of longitudinal dispersion.
Dobbins states equations for BOD and DO concentrations
without derivation. A heuristic development of the
equations is give>n by Pyatt [64]; O'Connor [59] gives
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a somewhat more rigid development. The following is
a non-rigid outline of the derivation.
Suppose that the concentration of a substance is a
function of the spatial parameter x and the temporal
parameter t. Let c(x,t) represent the concentration
function. Then by definition
dc = j^c dx + H>c dt, (7)
ax at
or
dc = a_c dx + ^c. (8)
dt dx dt at
Letting U = dx/dt represent the longitudinal velocity,
one obtains
dc = U^c + Be (9)
dt 9x at
dc/dt represents the total change in concentration
in time. The total change can be divided into two
components; the gain or loss of concentration by diffusion,
and the gain or loss of concentration via the local
sources and sinks. The change in concentration due to
the sources and sinks can be represented by Ss. The
diffusion term is of the Fickian type, which represents
diffusion as proportional to the change in the concentration
gradient, i.e., Ea c/ax3 where E is defined to be the
diffusion coefficient. Therefore equation (9) becomes
^c = sa3 c - u aic + Ss. (io)
at ax3 ax
Dobbins assumes the process for the stretch as a
whole is a steady state process, the conditions in every
cross-section being unchanged with time. Therefore,
c(x,t) = c(x) and ac/at = O. Thus
O = Ed3 c - U dc + Ss. (11)
dx
The characteristics of the sources and sinks are
based on the following assumptions:
1. Bacterial deoxygenation and atmospheric reaeration
are treated identically to the Streeter-Phelps model.
2. The removal of BOD by sedimentation, absorption,
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and all other non-oxygen consuming processes is a
first order reaction; the rate of removal being
proportional to the amount present.
3. The removal of oxygen by the benthal demand and
by plant respiration, the addition of oxygen by
photosynthesis, and the addition of BOD from the benthal
layer or the local runoff are all uniform along the stretch.
Therefore the sources and sinks for BOD are
mathematically described as follows:
1. La ,the uniform rate of which pollution is added
by local runoff.
2. KjLjthe rate at which pollution decreases due
to bacterial action.
3. K3L, the rate at which pollution decreases due
to all non-oxygen consuming processes.
Therefore, the pollution concentration L can be
obtained from equation (11), yielding the following
differential equation
O = E dgL - UdL - (Kx + K3 ) L + L» .
dxg dx (12)
The sources and sinks of oxygen are as follows:
1. K3D, the rate at which oxygen increases due to
reaeration. D is the oxygen deficit.
2. KXL, the rate at which oxygen decreases due to
bacterial action.
3. DB , the decrease in oxygen due to the benthal
demand.
Therefore, the oxygen deficit equation obtained from (11)
is given by:
O = Ed D - U dD - K3D + Ka L + Dg .
dx3" dx (13)
In the interest of clarity it is necessary to
comment on several of the sources and sinks. The numbers
in the following remarks refer to the list of additional
processes Dobbins added to the Streeter and Phelps model.
The K3 term includes terms in 2 as well as 1. K3L, is
the net effect of all of these processes, so K3 may be
positive or negative depending on the relative magnitudes
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o. -he processes . The benthal demand term D encompasses
all the processes in 4 through 7. In order to include
photosynthesis, it is necessary to consider the effect
as uniform in time.
The rate of reduction of DO by the benthal demand
is assumed to be independent of the oxygen level. Clearly
this cannot be the case when DO is near zero, or negative
oxygen concentration would result. In truth this
assumption loses its validity for DO levels below 1 mg/1.
As a precaution the analysis is restricted to situations
where a minimum of 1 mg/1. of oxygen exists.
The longitudinal diffusion coefficient is in many
cases unceratin. Dobbins calculated the amount of error
which would be introduced if it were neglected. Using
extreme values for the stream parameters he shows that
the ratio of the true concentration to the concentration
obtained by neglecting diffusion is O.996. Lynch [54]
later corrected this value to O.96O, i.e., an error of
4%. In any case, this represents the probable maximum
error. Thus, the effect of longitudinal diffusion
in a stream is negligible.
The solutions to (12) and (13) with E = 0 are
-(K1+K3)t -fo+KaJt
L = L0e * + La (1-e )
K1+K3 (14)
(L.-U )(e-i3e
i+K
K3-(K1+K3)
-Kg t -Kg t
+ D0e +(^_ + K,La ) (1-e 3 ). (15)
Kg Kafiq+Ka)
where t is the travel time given by t = x/U, and the
initial conditions are L = L0 and D = D0 at t = O.
If all the parameters except Kx and K3 are set equal
to zero. Equations (14) and (15) reduce to the Streeter-
Phelps Equations (3) and (4) .
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O'CONNOR'S MODEL
Donald O'Connor [57,58,59] considered equations
(12) and (13) for the estuary situation in which
E ^ O, The estuary is subdivided into sections in
which conditions are assumed to be constant. The
model then simulates concentrations averaged over
the length of the individual sections and over the
tidal cycle. Since the effect of tidal advection
is not considered in the model, the value of the
dispersion parameter E is increased to account for
the apparent dispersion of the oscillating tidal
flow as well as the dispersion due to turbulent
diffusion.
THOMANN'S MODEL
Robert Thomann [73,74,76] has presented a systems
analysis extension of the segment model of O'Connor.
Physical, biological, etc., conditions within a seg-
ment of the estuary are assumed to be constant. The
rate of change of concentration for a given component
in the kth segment will depend on (a) the mass of that
component transported from segment k--l into k and from
k into k+1; (b) dispersion from both k-1 and k+1 into
k; (c) the sources and sinks in segment k; and (d) the
volume of segment k.
Thomann expresses this in the form of a first order
difference equation. The equation for segment k is
given by
ck) - Qk
dt
- ck)
+V
kfk(t).
(16)
where ck is the concentration of the component of
interest in the kth segment;
V
E-
k- i
k is the volume of segment k;
k denotes the net flow from segment k-1 to k;
k is "the dispersion coefficient between k-1 and k;
fk(t) net sum of all sources and sinks of the component
in the kth segment .
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A set of equations like (16) is obtained, one for each
segment for both dissolved oxygen and BOD. These equa-
tions have been solved both with and without the assump-
tion of dc/dt = O. If dc/dt = O, the set of equations
can be expressed in matrix notation as
Ac = F
***-* 'w
where: A is a matrix of equation coefficients.
£ is a vector of average segment concentrations.
F is a vector of BOD or OD sources and sinks.
*+^
These equations can be solved simultaneously by invert-
ing A and multiplying through by the matrix A'1, yield-
ing
c = A-IF .
*N^
Since the equation for each segment has terms involving
concentrations in just three segments (the segment of
interest and the segments on either side), matrix A
reduces to an easily invertible tridiagonal matrix.
Thus the vector £ can be easily found but its useful-
ness is limited by assumptions on which the above de-
velopment rests.
Explicitly or implicitly the following assumptions
and therefore limitations have been imposed on the above
model
I. It has been assumed that the concentration
gradients can be accurately approximated by straight
lines .
II. Steady state conditions have been assumed.
Ill Concentration variations within the tidal cycle
cannot be simulated.
IV. Concentrations, estuary characteristics, process
parameters, etc., are constant within a segment.
Pence, Jeglic and Thomann (61b) have numerically
solved equation (16) above for dc/dt ^ O, thus removing
limitation II. However, limitations I, III, and IV
still hold.
8
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ORLOB'S MODEL
G. T. Orlob et. al. [61a,61b] developed a two
dimensional model which permits a more accurate ap-
proximation of the advection effects in a shallow
estuary. Two major computer programs must be used
in the application of this model: a hydraulics
program and a water quality program. The output
from the hydraulics program is used as one of the
inputs to the water quality program.
The hydraulics model approximates a one or two
dimensional bay or estuary with an analogous network
of idealized channels. The program is geared to
specific tide and river flow conditions and must be
reworked for each change in these conditions. The
water quality model is essentually a time dependent
Thomann model. The overall effect of this model is
that the hydraulics of the estuary can be more ac-
curately approximated.
HARLEMAN'S MODEL
Harleman, Lee, and Hall (31A) numerically solved a
coupled set of two, one-dimensional diffusion equations
of the following form.
be = I _d_(AE dc) - U ^c + Ra - Rr (16a)
dt A dx dx dx
where: c ~ average cross sectional concentration as
a function of time and position.
U = average cross sectional fluid velocity.
A = cross sectional area.
E = diffusion coefficient.
R» = rate of input of component c due to all
sources.
Rr = rate of disappearance of c due to all sinks.
One equation described DO and another BOD concentrations
Comparison with equation (16) indicates that (16a)
is a more general form of the diffusion equation and
for this reason would be expected to describe more
accurately the diffusion and dispersion effects of an
estuary. This model does not handle the hydraulic
effects as accurately as does the Orlob model.
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PREVIOUS STOCHASTIC MODELS
THE MODEL OF THAYER AND KRUTCHKOFF
Thayer and Krutchkoff developed a stochastic
model for BOD and DO streams, [71,72], Their work was
based on Dobbin's model, with the mechanisms effecting
BOD and DO concentrations modified so as to be random
in nature.
Thayer and Krutchkoff made one additional assumption.
The pollution and dissolved oxygen were discretized.
The term A was introduced to represent the optimum unit
size. All transitions in BOD and DO were asserted to
be in units of size A. A is a measurable parameter of
the individual stream. Methods of estimating A will be
given later.
A change of size A in the concentration constitutes
a change of one "state". The pollution state m corresponds
to a concentration of LE and the relationship between
the two is
State m = L./A. (17)
Similarly, DO state n corresponds to concentration nA = Dn.
Dobbins' assumption concerning the processes in the
stream were replaced by their stochastic analogues. In
a small time increment h, the pollution or DO can be
increased or decreased by A or a multiple of A by each
of the mechanisms considered by Dobbins. The mechanisms
are assumed to act independently. The order of magnitude
of h will be such that h3 will be negligible in compariso?
to h. The probability of change in state is assumed
proportional to h, thus a change of more than one state
by a single factor in time h has probability o(h). Terms
of probability o(h) can be neglected when terms of order
h are present. The probability of one change in state
for each of the factors is as follows:
1. The expected amount of increase in pollution due
to La in the time interval h is Lah. Letting p = Pr
[Pollution increases by amount A due to La in time h],
10
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one obtains the expected increase due to La in time h
to be Ap + o(h) + O(l-p-o(h)).
Therefore, p = Lah/A + o(h). By similar arguments:
2. Pr[Pollution decreased by an amount A due to
K3 in time h] = K3Lmh/A + o(h).
3. Pr[pollution decreases and OD increases by an
amount A due to Kx in time h]
jqLah/A + o(h) .
4. Pr[OD increases by an amount A due to DB in time
h] = DBh/A + o(h).
5. Pr[OD decreases by an amount A due to K3 in time
h] = K3Dnh/A + o(h) .
The Joint probability of finding the system with
pollution in state m and the oxygen deficit in state n
at time t is denoted by p*)n(t). Combining the factors
1 through 5 one obtains the difference equation
P. .(t+h) = p.,B(t) ri-Lah - K3Lah
A A
- K,L.h - DBh - KaDnh1 + P.-^ftJLJi + Pl+1 (t)Ka(m+l)h
A A A A
+ P.+i .^(tjK^m+lJh + P.,.-!^) E^h + p. ,n+1(t)Ka(n+l)
A
+ o(h). (18)
Let P(s,r,t) be the probability generating function of
P. ,n (t) , i.e. ,
P(s,r,t) = E E Pnjn(t)s"rn (19)
m=O n=O
Taking limits as h approaches O the following differential
equation in P(s,r,t) is derived:
BMP + Ka(r-l)d an P ^ K3 (1-s)
11
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+ iqfr-s) d Sn P = La/A(l-s) + DB/A(l-r). (20)
5s
Thayer and Krutchkoff obtained analytic solutions for
P(x,r,t) for several sets of initial conditions. The
solutions corresponding to the initial condition that
the BOD concentration is L0 and the OD is D0 at t = O
will be useful in our applications. For these initial
conditions the solution to equation (2O) is
P(s,r,t) = expf -LaK,
AK2(KS-(K1+K3))
)(l-s) + DB
A(Ka+K3) AK3
K,
A(K1+K3)(K3-(K1+K3))
, (l-e~K3t) (1-r
K3 - (K,. +K3 )
)t(l-s) ]L0/A. (21)
Equation (21) can be put in some what more manageable
form if several reocurring groups of symbols are redefined.
Oj. (t) = e~(K
K3-(K1+K3)
p,(t) = 1-cta
ag(t) = e~Kat
Pa(t) = 1-ota
Y = _ LaK
(Ka-(K1+K3)
Rewriting equation (21) gives
P(s,r,t) = expf(l-r)ir YPi + Yga+ DB 33 1 - U Bi (1-s) }
A Ka+K3 K8 Kg A(Ki+K3)
12
-------
Ll-(l-r)a3]D°/A [l-(l-r)a2-(l-s)a1]L°/A. (22)
Thayer and Krutchkoff obtained the marginal
generating functions for BOD and OD from (21) by set-
ting r = 1 and s = 1, respectively. They were able
to pick out the coefficient of s° and rn . The coef-
ficients are functions of t . These coefficients give
the complete pollution and oxygen deficit distributions
The means of the distributions were identical to
Dobbins' equations; (14) and (15) . The variances
were linear functions of A given by:
VAR(L) = Af L, +. UcUtJJMt) (23)
Ka+K3
VAR(D) = A-_₯_p3(t) + Y Pi(t)
K K
+ DeJ33(t) + D0 p3 (t) 09 (t)
K3
+ Y(a1(t) - a3(t))(l-jL(
L*
- Oa(t))]. (24)
THE MODEL OF MOUSHEGIAN AND KRUTCHKOFF
Moushegain and Krutchkoff [55J extended the Thayer
and Krutchkoff model to permit segmentation of the
stream. In essence they determined that one could
treat the probability output of one segment as the
probability input to the next segment. This was only
a crude approximation which neglected the dependence
in the probability distributions of BOD and DO. A
study of the effect of this approximation was made.
The approximation was found to be remarkably good.
It was the success of this procedure for streams
(not estuaries) which took the present project into
a blind ally.
13
-------
THE MODEL OF CUSTER AND KRUTCHKOFF
The model of Custer and Krutchkoff [13,14] is an
extention of the model of Thayer and Krutchkoff to
estuaries. A random walk mechanism is postulated as
opposed to the birth-death process used by Thayer and
Krutchkoff. The random walk mechanism permits the
representation of the true diffusion effect; not the
effect confounded with tidal motion. For this reason
the term diffusion is used in lieu of dispersion.
The diffusion model considers all factors considered
by Dobbins in his deterministic work, and consequently
by Thayer and Krutchkoff,"except
a) La the uniform increase of BOD by land runoff,
b) DB the decrease in DO due to the benthal demand
These factors are handled separately, and their effect
added by the principle of superposition.
As in the work of Thayer and Krutchkoff, the pollution
and dissolved oxygen are discretized into units of size A.
A A unit is such that it cannot be further decomposed
into smaller units. Pollution must be degraded by the
bacteria and other mechanisms in units of size A or
multiples of A.
First, the motion of a single BOD unit is considered.
This motion is treated as a random walk with decay
on the real axis. In each time interval 6t, the unit
has probability p(t) of taking a positive step of length
6x, probability q(t) of taking a negative step of length
6x, and probability r of being absorbed. A difference
equation is obtained which gives the Joint probability
of the unit being at any location x after any time t,
given that the unit was at the origin at time t0(if x
is not a multiple of 6x this probability is zero). p(t),
q(t), r, 6x, and 6t can be determined from the physical
parameters of the estuaries.
The diffusing process of a unit of oxygen deficit,(OD)
is handled in a similar manner, with the initial conditions
slightly modified. Unlike the BOD units which originate
at a uniform rate, a unit of OD is formed simultaneously
with the absorption of a unit of BOD.
14
-------
The parameter 6t used in the random walk procedure
is the length of time needed for one unit of size A to
enter the estuary. Thus, 6t is a function of the rate
at which pollution enters from the source, and the
cross-sectional area of the estuary. In order to obtain
the effect of a continuous source, units of size A are
released at each time interval 6t. The units act
independently and their behavior can be studied individually
by the random walk mechanism. Thus, the probability
of a given concentration at location x after time t is
the convolution of the probabilities associated with the
individual units
The resulting model is a transient state model;
the time parameter being defined as the time lapse since
the source of pollution originated.
Due to the fact that the velocity of the estuary is
a function of time, the distribution will be continually
changing in time and no steady state is possible. However,
after a sufficient time lapse the distribution for a given
point in the tidal cycle remains constant from cycle to
cycle. This will be defined as a pseudo-steady state
condition. The pseudo-steady can be described by taking
the time lapse to be sufficiently large. In most cases
15 to 25 days will be 99% of pseudo-steady state.
The motion of a single particle placed in a medium
where it is exposed to a great number of random forces
is described by what is commonly called "diffusion."
The diffusion process considered in the analysis was first
developed by Einstein in relation to the Brownian motion
problem. Literature concerning the Brownian motion
problem is extensive. Heuristic development of the limiting
process leading to the renowned Fokker-Planck Equation
are given by Feller [23], Rosenblatt [65], Bharucha-Reid [9]
and others [6,42,62], More advanced treatments are
rendered by Feller [24,25,26], Doob [2O] and Kac [41]
Geneticists have been particularly active in investigating
the stochastic nature of the diffusion phenomenon [23,46]
Although this is not the only mathematical description
of the diffusion process it is the most widely used and
verified. The general treatment concerns the motion of
a non-conservative process.
15
-------
The general assumption for this process is that it
is certain that the particle will move in any interval
of time 6t; however, if 6t is small the movement will
be small. The forces acting on the particle can be
summarized by two components: The symmetric random
forces described as diffusion and the non-symmetric
drift, or in this case, velocity. In the estuary velocity
is a function of time. In addition, when working with
non-conservative substances, such as BOD or DO, the
possibility of absorption must be included.
The motion of a BOD unit is characterized as follows:
in each time lapse of length 6t the unit moves forward
on the positive axis a distance 6x with probability
p(t), or backswards the distance 6x with probability
q(t),. This is the only motion possible. However,
at each time lapse of length 6t the unit may be absorbed
and lost to the system. The probability of absorption
is constant at r. Of course
p(t) + q(t) + r = 1 for all t. (25)
Let u(m,n) be the probability that after n steps
the unit of BOD is at location m6x. The total time
lapse t will be n6t.
The unit may be at location m6x after n steps in
either of two ways:
1. the unit is at (m-1)6x at (n-l)6t and takes a
positive step, or
2. the unit is at (m+1)6x at (n-l)6t and takes a
negative step.
Thus
u(m,n+l) = u(m-l,n)p(n6t) + u(m+l,n)q(n6t) (26)
for
m,n e I, - » < m < o> and O £ n < <» .
Remaining consistent with Hie physical interpretation
of the Brownian motion process, the following values for
the terms in equation (26) are adopted:
(6x)3 = 2E, (27)
5t
16
-------
p(t) =
q(t) = (l-Kd6t)/2 - U(t) 6t, (29)
2 6x
r = K< 6t (30)
where
E is the diffusion coefficient,
Kx is the coefficient of deoxygenation,
K3 is the coefficient corresponding to all non-oxygen
consuming processes ,
K^ is Kj +KS ,
and
U(t) is the velocity function.
6t is defined as the length of time required for
one unit of size A to enter the estuary, and may be
calculated from physical parameters. With the value
of 6t and the relations given above, all components
in the difference equation may be evaluated.
In order to solve equation (26) a set of initial
conditions is required. Given that the unit entered
the system at time t0 (t0 must be divisible by 6t) ,
the initial conditions are
u ( 0 , n0 ) = 1 .
u(m,n0) = 0 for m ^ 0,
u(m,n) = O for n < n0 ,
where
n0 = t0/6t. (31)
Under these initial conditions u(m,n) will be written
u(m,n|n0) .
To derive the difference equation for oxygen deficit,
it must be recalled that the absorption of a unit of BOD
generates a unit of OD of equal size. The OD is then
absorbed from the system by reaeration in the same manner
that BOD is absorbed by the bacteria.
17
-------
One can think of a unit being released at t0 as
BOD. The BOD travels in accordance with the random
walk mechanism until it is absorbed; however, the
absorption is only a metamorphosis which changes the
identity of the BOD and OD. The renamed unit then
resumed the random walk at the point where it was
absorbed, now governed by the probabilities associated
with OD.
Let v(m,n) be the probability that a unit of OD
is at location m6x after time n6t, where 6x and 6t
are as before. The probability of a forward step
will be represented by £(t), a negative step by q(t),
and absorption by ^r. An OD unit can be at m6x a?ter
time n6t in any of three ways;
1. the unit is at (m-l)6x at (n-l)6t and takes a
step forward,
2. the unit is at (m+1)6x at (n-1)&t and takes a
step backwards,
3. the unit is BOD located at m&x at (n-l)6t, and
is transformed in OD.
Thus,
v(m,n+l) = v(m-l,n)jg(n6t) + v(m+l,n)cj(n6t) + u(m,n)K16t
(32)
or m,n el, - °° < m < <», and O £ n < °°.
The transition probabilities are defined as follows:
pjf) = (l-K36t)/2 + U(t) 6t, (33)
2 6t
q(t) = (l-K36t)/2 - U(t) ^t, (34)
~ 2 6x
r = Ka6t, (35)
**w
where K2 is the coefficient of reaeration, and the
other parameters were "defined following equation (3O)
The initial condition is
v(m,n) = 0 for all m if n < n0. (36)
18
-------
v(m,n|n0) will represent v(m,n) under condition (36).
In the above work practical difficulties arose
due to the small size of 6t. Fortunately this could
be used to advantage. As 6t approaches zero, limiting
results which approximate u(m,n|n0) and v(m,n|n0)
could be obtained.
As 6.t approaches zero the probabilities u(m,n|n0)
and v(m,n|n0) approach continuous densities. These
densities will be denoted by f(x,t|t0) and g(x,t|t0),
respectively. Recalling that the location on the
real axis corresponding to m is m6x, and the time
corresponding to the nth step is n5t, equations (26)
and (32) can be rewritten as follows:
f(x,t+6t|t0) = f(x-6x,t|t0)p(t) + f(x+6x,t|t0)q(t),
(37)
g(x,t+6t|t0) = g(x-6x,t|t0)£(t) + g(x+6x,t |t0)q(t)
+ f (x,t jt0)Ka fit. (38)
Expanding the terms in (37) in a truncated Taylor
series about fx,t) it can be shown that (37) becomes
Bf(x,t 110) = E 33f - U(t) 3f - Kdf(x,t|t0). (39)
dt Bx2 dx
Similarly, equation (38) becomes
Bg(x,t|t0) = E 3sg - U(t) Bo, - Kag(x,t|t0)
Bt Bx3 Bx
+ K1f(x,t|t0). (40)
Notice that none of the parameters are functions
of position and only velocity is a function of tidal
phase.
These equations are solved analytically for f and
g holding all parameters constant with position with
the following results.
19
-------
f(x,t|t0) =
and
g(x,t|t0) =
where:
2VTT(t-t0)E
K1
exp[-(x-v(t))2
4E(t-t0)
(41)
exp[-(x-v(t))2]
2(K3-K4)7nE(t-t0) 4E(t-t0)
K^t-to)} - exp{-K3(t-t0)}] (42)
U(T)dT.
The resulting f(x,t|t0) and g(x,t|t0) are the
conditional probability density functions that a single
BOD or OD particle will be at position x at time t
given that it was released at time t0 . To find the
probabilities for the total concentrations due to
all BOD or OD particles present it would be necessary
to convolute over all the individual BOD or OD
particles present.
Custer does this by temporily reverting to the
discrete process . The event of a particular BOD or
OD being at x at time t was considered to be a
bernoulli probability generating functions were derived.
P(m,n,s) = TT [(l
i=0
for BOD probabilities
and
P(m,n,s) = TT [(l
~ i=0
u(m,n|i)s]
v(m,nji)s]
(43)
(44)
Where u(m,n|i) and v(m,n|i) were defined
previously. Utilizing the properties of probability
generating functions the following means and variances
were defined.
MEAN (BOD state) =Su(m,n|j)
j=o
(45)
VAR(BOD state) = Su(m,n|j - § (u(m,n|j))2 (46)
3=0 j=0
2O
-------
MEAN(OD state) - Sv(m,n|j) (47)
j=0
VAR(OD state) =£v(m,n|j) - § (v(m,n | j)) S (48)
j=O ji=O
By letting the time interval between successive
BOD particles approach zero, the input becomes a
continuous source and the probability mass functions
become probability density functions. That is u(m,n|j)
and v(m,n|jj) approach f(x,t|t0) and g(x,t|t0). Then
the probability of an individual successes can be
restated as
u(m,n|i) » f(x,tlt!)6x (49)
for BOD and
v(m,n|i) « g(x,t|ta)6x (50)
for OD.
Still retaining the discrete notation it can be
shown that this sum of bernoulli trials approaches
a poisson distribution as 6t (and hence 6x) approaches
zero. The state mean and variance are the same.
The significance of this result is that once
the mean concentration of BOD and OD is determined,
the poisson variance is known and the entire distri-
bution can be found.
PURPOSE OF THIS PROJECT
The purpose of this project is to expand
and further verify the model of Custer and Krutchkoff.
Specifically the project can be divided into four
tasks.
INCLUDE A VARIABLE SOURCE
Both the Thayer and Krutchkoff and the Custer
21
-------
and Krutchkoff models consider constant sources.
Examples of variable or random inputs have been given
[71,72] for the Thayer and Krutchkoff model but
these situations were not considered by Custer and
Krutchkoff. The first task for this project is to
adapt the model to accept variable or random input
loadings.
SEGMENTED ESTUARY MODEL
In the Custer and Krutchkoff report [13] it
was noted that the problem of segmenting an estuary
is not a simple problem in a stochastic model. The
second task in this project is to obtain a segmented
estuary model. This can be done either by adjusting
the Custer and Krutchkoff model or by obtaining a
new model.
VERIFY THE MODEL
The third task is to use data supplied by WQO
obtained from the Potomac Sstuar/, the Ohio River
and the Delawara Estuary to verify the models ob-
tained in tasks one and two. This means that the
model will have to predict not only the mean con-
centration of both BOD and DO for both a stream
and an astuary but it must also predict the distri-
butions about these means.
OBTAIN A METHOD FOR PREDICTING A
The stochastic parameter A enters as a scale
factor in the variation about the mean concentration
of both BOD and DO. Bosley, Cibulka and Krutchkoff [lO]
demonstrated that this stochastic parameter was a
function of the parameters and properties of the stream.
The fourth task in this project is to obtain a method
for estimating the appropriate value of A from actual
data and obtain a regression equation which could
then be used in predicting future values of A.
22
-------
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
VARIABLE OR RANDOM INPUTS
SIMULATED CASE STUDIES
Before attempting to solve this problem analytically
a stochastic simulation was made (see [8]). In this
simulation study the random walk situation was simulated.
n pollution particles entered the estuary at a point
and preformed a random walk up and down the estuary
with probabilities given by equations (28) and (29) and
with probability of being absorbed given by equation (30).
When a particle is absorbed it was turned into an
Oxygen Deficit (OD) particle and preformed a random walk
up and down the estuary with probabilities given by
equation (33) and (34). The OD particle could also be
eliminated by reaeration with probability given by
equation (35).
The computer program was so written that the motions
simulated estuaries with the usual parameters. Variable
and random inputs of several types were used. The
results are presented in 24 graphs given in \_B~]. Figures
1 and 2 are the first two graphs from that report and
are typical results The four curves shown are the
mean concentrations obtained by simulation for four
different inputs. The curve marked "Mean 5" is the
constant input result while the other three represent
a binomal distribution, a uniform (random) distribution,
and a two point distribution (ten and zero) all with
mean value equal to five. As can be seen from the
figures there is no significant difference in the mean
values for any of these inputs. All 24 graphs indicated
similar results. Conclusion: Short term random variations
of the input has little if any effect on the mean -concen-
tration down estuary.
23
-------
to
.1-.
UNIFORM
MILAN 5
TWO POINT
100 150 200 250 300 350 400 450
SECT I OFT OF ESTUARIAL REACH
FIGURE 1 BIOCHEMICAL OXYGEN DEMAND -SITUATION
500 550 600 650
-------
to
Ui
U
r:
i
55
50
45
40
35
30
25
20
15
10
BINOMIAL
UNIFORM
MEAN 5
TWO POINT
0 50 100 150 200 250 300 350 400 450 500 550 600 650
SECTION OF ESTUARIAL REACH
FIGURE 2 OXYGEN DEFICIT SITUATION 1
-------
ANALYTICAL RESULTS
The results of the simulation study encouraged
a full scale analytical approach. The approach is
reported in detail in another section of this report.
The results were as the simulations indicated. The
mean concentrations of both BOD and DO are independ-
ent of the random variability of the input source and
depend only on the mean \<*lue of the input source.
The distribution about the mean, however, does depend
on this variability.
As will become apparent later, this variablity can
be ignored in that it can be absorbed by the Poisson
Approximation used for the distribution about the
mean. This means that for all practical purposes one
need only obtain the time dependent average of the
input loading and not its distribution to adequately
emptoy The Stochastic Model. For example,the load
might have an overall sinusoidal shape with short-term
random variations about this shape. One can completely
ignore the variation about the sinusoidal function
if only the mean effect is desired. If the fluctuation
is not too large it can also be ignored when obtaining
the distribution about the mean, provided the Poisson
Approximation is used to obtain this distribution.
This Poisson Approximation is an integral part of this
report and will be discussed in detail later.
SEGMENTING AN ESTUARY
It is not possible to treat the probability output
of one segment of an estuary as the random input of
the next segment. The mathematical proof of this is
given in another section of this report. It was found
that in order to solve for the output of one segment,
equations involving the entire estuary had to be solved.
For this reason it was necessary to obtain a method
for solving all the equations necessary for a segmented
estuary at the same time. Although the task seemed
impossible at first? it became apparent that the problem
could be solved. Not only could the estuary be segmented
26
-------
but the parameters could be continuous functions of
both time and space. The derivations are given in
a later section and will only be summarized here.
The problem is divided into two parts . Finding
the mean concentration and finding the distribution
about the mean using the Poisson Approximation. In
order to solve for the mean concentration the following
equations are solved numerically on a computer xhe
equations are:
df(x,t) = Ef(x,t)a3f - U(x,t)j3f - Ki(x,t)f + LR(x,t)
at ax3 dx
+ FF(x,t) (51)
and
- U(x,t)£c; - K3(x,t)g + ^(x.tjf
at ax3 ax
+ D9(x,t) (52)
where:
f(x,t) is the BOD concentration
g(x,t) is the OD concentration
K^Xjt) is the coefficient for the decrease of BOD
by all processes, including biological
utilization and all non-oxygen consuming
processes, i.e.-Kd(x,t) = Kj_(x,t) + K3(x,t)
K1(x,t) is the coefficient for biological utilization
K3(x,t) is the coefficient of all non-oxygen
consuming processes
U(x,t) is the velocity of the water in the estuary
Kd(x,t)f is the rate of decrease in BOD due to oxygen
and non-oxygen consuming processes
LR(x,t) is the rate of increase in BOD due to land
runoff
FF(x,t) is the rate of increase in BOD due to STP
outputs
Ks(x,t)g is the rate of decrease in OD due to reaeration
27
-------
Kt(x,t)f is the rate of increase in OD due to
oxidation of BOD
D8(x,t) is the rate of increase in OD due to
benthal demand. Normally photosynthesis
will be included in this term.
The program used to solve these equations is
given in the appendix.
The analytical results indicate that the
distribution of concentration state (not concentration)
has a poisson distribution. From this it can be shown
that the distribution of the concentration itself
has a poisson shaped distribtuion, centered at the
concentration mean, but with variance equal to A times
the mean concentration. Therefore, since the solution
to the above equations provide the mean, and A is
available (see the section labled PREDICTING A), we
can obtain the appropriate variance. Knowing the
variance and the center of the poisson-like distribution
the probability distribution can easily be obtained.
If the mean concentration is near zero? then the discrete
poisson distribution must be smoothed out to provide
a more realistic distribution. It is this distribution
about the mean which indicates the proportion
of the time that the concentration will be above or
below any level. Details of these results are provided
later.
VERIFICATION OF THE MODEL
VERIFICATION ON AN IMPOUNDED STREAM
Between 1957 and 1963 a three phase program was
conducted on the Markland pool near Cincinnati, Ohio.
The objective to this work was to evaluate the effect
of the high rise Markland dam on the waste assimilative
capacity of the Ohio River. Data taken in the third
stage of this study (post-impoundment conditions)
was used here for model verification. Individual BOD
and OD samples were taken every 3 hours at 8 stations.
The results of that analysis are given in another
section of this report. The result for the mean
28
-------
concentration is summarized in Figure 3. Note how
well the theoretically predicted values for both BOD
and OD compare with the average values actually
observed
The Poisson Approximation method was then used
to obtain the distributions about these means. A
very stringent test was then given the obtained
distributions. Two sided confidence intervals were
obtained from the distribution for confidences 0.1O,
0.15, O.2O, 0.3O, O.40, and O.5O. Two sided intervals
were used to detect any departure from the predicted
degree of skewness. The observed results for the last
six stations are presented in Table 1. The observed
results are remarkably close to the predicted values
at every station. Thus the general stochastic model
obtained in this project can be said to work well for
streams, even impounded streams.
VERIFICATION ON A SEGMENTED ESTUARY
In the summer of 1967 an intensive DO and water
temperature survey was conducted for the Potomac
estuary. Sampling was done at four stations which
cover the upper 3O miles of the estuary. This stretch
provided a good test for the ability of the model to
treat a segmented estuary. The details of the analysis
are reported elsewhere in this report. Since there was
no BOD study made in that survey the only comparison
which could be made was that of Dissolved Oxygen.
Unfortunately no time dependent study was made of the
photosynthesis. In order to minimize this effect only
data taken between 5 am and 9 am could be used. This
did not prove to be much of a limitation since the
data was taken every 30 minutes for at least two weeks
at each station. The mean concentrations fit well
at the first three stations but the lack of nitrogen and
carbon recycle information made the analysis invalid for
station number 4. The model can be extended to include
the nitrogen cycle including algae but this has not yet
been done.Figures 4, 5, and 6 are comparisons of the
predicted mean OD and the observed average OD at each
29
-------
CO
o
OMEAN MEASURED OD
DMEAN MEASURED BOD
MUD
CREEK
MILL 'BROMLEY
CREEK
470
475
490
480 485
RIVER MILE
FIGURE 3 A COMPARISON OF PREDICTED AND OBSERVED
BOD AND OD MEAN CONCENTRATIONS IN THE
MARKLAND POOL OF THE OHIO RIVER
495
-------
Table 1: Observed vs. predicted fraction of values outside specified
concentration confidence intervals for the Ohio River.
Fraction Predicted Fraction Observed Outside of C. I. by Station
Outside ofC.I. 3 4 5 6 7 8
BOD
0.10
O.15
0.2O
0.3O
0.40
0.5O
0.148
0.185
0 236
O.333
0.429
0.563
O.045
0.141
0.274
0.318
0.485
O.510
O.O82
O.156
O.163
O.245
0.362
0.532
0.148
0 . 170
O.23O
O.304
0.429
0.541
0.126
O.141
0.245
0.311
O.415
0.445
0.133
O.200
0.252
0.296
O.429
O.490
10
H OD
0.10
0.15
O.20
0.3O
0.40
O.50
0.140
0.163
O.208
0.341
0.378
0.452
0.096
0.126
0.222
O.318
0.400
O.482
O.104
,0.148
0.17O
O.296
0.415
O.482
O.lll
0.126
0.17O
0.267
0.4O7
O.490
0.111
O.119
O.14O
0.215
0.349
0.467
0.14O
0.156
0.192
O.267
O.341
0.437
Station 1 and 2 were not used since their values had been used as upstream
boundary conditions. There were 135 observations/station.
-------
g
H
H
U)
to
Q
o
0
O
O OBSERVED OD MEAN CONC.
PREDICTED MEAN CONC..
1
1
1
1
0
Q2
Q8
Q4 Q6
PHASE
FIGURE 4 COMPARISON OF PREDICTED AND
OBSERVED OD CONCENTRATION AS
FUNCTIONS OF TIDAL CYCLE FOR
STATION 1, POTOMAC ESTUARY
1.0
-------
U)
8 3
§a
D
O ,
0
0
O OBSERVED MEAN OD CONC.
PREDICTED MEAN CONC.
I
I
I
02
0.8
Q4 O6
PHASE
FIGURE 5 COMPARISON OF PREDICTED AND
OBSERVED OD CONCENTRATION AS
FUNCTIONS OF TIDAL CYCLE FOR
STATION 2, POTOMAC ESTUARY
LO
-------
OJ
6
CL
0-
r\
H
H
$
H
2
8
CJ
2
O
u
Q
O
2
W
H
7
6
q
J
2
1
| IQ^P 1 D \
~->2.
_
O OBSERVED MEAN OD CONC.
PREDICTED MEAN CONC.
^
_
1 1 1 1
0 O2 O4 O6 O8 1
PHASE
FIGURE 6 COMPARISON OF PREDICTED AND
OBSERVED OD CONCENTRATION AS
FUNCTIONS OF TIDAL CYCLE FOR
STATION 3, POTOMAC ESTUARY
-------
of the first three stations The predictions can be
seen to be quite close to the observed values at all
three stations. The results of the confidence interval
comparisons at the first three stations is given in
Table 2. Once again the observed frequencies are re-
markably close to the predicted frequencies. Station
3 has concentrations of DO near zero. This means that
the poisson distribution was extremely skewed and
also required smoothing. In spite of this the results
are reasonably good.
Table 2: Observed vs. predicted fraction of values
outside specified concentration confidence
interval for the Potomac Estuary
Fraction Predicted
Outside of C. I.
Fraction Observed
Outside of C. I.
Station 1 Station 2 Station 3
O.O5
O.10
9.15
O.2O
O.25
O.30
O.35
O.4O
O.5O
0.10O
0.1O
0.141
0.193
0.242
O.285
O.335
O.38O
O.47O
O.O55
O.O87
O.127
167
199
O 246
O.310
O.365
0.5OO
O.
0,
O.O87
O.lll
0.111
0.135
0.151
0.175
0.184
0.230
O.477
Station 1 - 27O observations
Station 2 - 126 observations
Station 3 - 126 observations
PREDICTING A
Although there has been a good deal of discussion
concerning A (see [17,50,10]) its properties and, more
importantly, its true meaning were still unsettled.
The papers [5O] and [10] demonstrated that A is indeed a
physical parameter but the interpretation given to it
in the Thayer and Krutchkoff and the Custer and Krutchkoff
35
-------
models was still unappealing. In these models pollution
or DO could change in concentration only in units of
size A. This is unappealing for several reasons. Firstly,
the fact that it pertains to concentration units rather
than absolute quantities. This means that it could
possibly represent tons of BOD. Secondly, it does not
allow for smaller changes in conditions where the
concentrations are very low. Thirdly, it required the
same A for both BOD and DO. Before finding a method
to predict A it was necessary to further investigate
the meaning and properties of this A.
Our first analytical investigation which is reported
in a later section demonstrated that it was not at all
necessary to consider a discrete process with A the size
of the possible concentration jumps. The process can
be considered as a continuous stochastic process with
A entering as a scale parameter in the variance of the
distribution of the continuous process. This produces
a much more appealing result. One can now consider
the discrete process and take things to the limit with-
out changing the size of the parameter A. With this result
the new interpretation says that the change in concentra^-
tion has variance proportional to the stochastic
parameter A but makes no restrictions on the minimum size
of the degrading process. A is thus an inherent parameter
for the process. It could conceivably be different for
BOD and DO but large differences would not be likely.
The next step was to investigate by means of
Stochastic Simulation the effects on A caused by random
fluctuation in several of the input and hydraulic
parameters. This study is presented in [?]. In essence
that work ignored the stochastic models and assumed that
the variability in concentration readings was due to
random fluctuations in either the K rates or the loadings
including the benthal demand These rates and loads
were given the variability normally encountered in their
measurements and the effects were traced by simulated
case studies. The result was that the effective A
not only differed for BOD and DO but that they differed
by a factor of 1O. The data which has already been
36
-------
analyzed indicates only a few percent discrepancy
between the A values for BOD and DO. The obvious
conclusion here is that A is not caused by random
variations in the parameter but by the stochastic process
itself as the Stochastic Model predicts.
Next it became important to determine what effect
the various stream, estuary, hydraulic, loading, etc.
parameters and constants had on the value of A. The
study [lo] demonstrated the effect of temperature and
turbulence. An investigation was then made (see [ll])
which ascertained the effect of the initial concentration
level on the value of A. In laboratory experiments,
it was found that the effect was significant. Therefore,
it is clear that A should be made a function of as many
parameters, constants, loads, etc. as can be incor-
porated into a realistic program.
The programs are given in the appendix with their
documentation given in another section of this report.
To find a predicting equation for A one must do two
things. First, find the appropriate terms to use, and
second,determine the optimal predicting equation. It
is important to find the appropriate terms since data
is usually only partially taken. That is, several
possibly important parameters are not recorded or only
an insufficient number of them are reported. It would
be simple to write a program with all the important
terms included if the program was never to be used
with live data. The first stage suggested here
surveys the type of data which is or will be taken
and suggests a form for the predicting equation which
is possible with that type of data. The data is analyzed
as to how many values are available for including
certain terms in the prediction equation. If there are
not enough values, terms can be eliminated and a new
analysis made This is continued until the analysis
says that there are sufficient data available for the
prediction equation.
For the second stage the data is fit?by means of
a standard least squares program, to a linear function
37
-------
of the included terms. The included terms might be,
for example, which station, temperature, flow velocity,
concentration range, and BOD loading range. The
resulting equation could then be used to predict A for
future use at that station by putting in values for
temperature, flow, concentration range and BOD loading
range. This is done for the Ohio and the Potomac
and included elsewhere in this report.
Thus this procedure uses present data from a
stream or estuary and uses it to obtain an equation to
predict future values of A for this same stream or
estuary.
CONCLUSIONS
The present form of the Stochastic Model can handle
load inputs, rate constants, velocity, temperature,
benthal demands, land runoff, hydraulic parameters,
geometry, and random pollution inputs, all of which may
be time-and position-dependent. It can accurately
predict tte time-dependent mean concentration at any
point in a stream or estuary. It can do this in a
transient state condition as well as for the pseudo-steady
state condition. It can also accurately predict the
proportion of time that the concentrations will be
above or below any given level. It can do all this for
BOD and DO and even for nitrogen wastes provided no
algae blooms develop. For that situation the model will
have to be extended. The extension is not trival but
it can be done.
RECOMMENDATIONS
The success of the verifications of the model leads
to four recommendations.
1. The model should be used whenever algae blooms
are not prominent. The model can be used to determine
the transient effect of a change in input load simply
by putting that change in the program and watching it
proceed in time. This can be used either to determine
what effect a proposed change in input load will have
38
-------
on the stream or estuary in both the transient and the
steady state conditions. It can also be used to determine
if a suspected violation has occured by noting the
effect on the waterway and ascertaining what changes
might have caused it. This latter use was illustrated
twice during the verification phase of this project.
The model did not fit in the vicinity of Mill Creek-in
Cincinnatti, Ohio. We ascertained that the large change
in DO without a corresponding change in BOD could not
have been simply the result of an increased BOD load.
Most probably it was the effect of readily soluble
pollutents, possibly caused by anaerobic decomposition
and dumped at or near Mill Creek. This would have
caused a DO drop before the next station could pick
up any increase in BOD. In another instance three days
of data had to be eliminated from the Potomac analysis.
The DO values could not have resulted from the residual
BOD loads upstream as reported. Evidently a major
upstream source was shut down for three days and no
record was made on the data presented us. The Stochastic
Model detected these situations since it predicts values
continuously. Values outside the usual ranges can be
interpreted as a break in steady state conditions.
2. Although we like to think of the present Stochastic
Model as being all useful it has one severe limitation.
It cannot predict the effect of algae. This restriction
can be eliminated with further effort. The basic model
need not be changed--only extended Several more terms
could be put into the equations and the equations
resolved.
3. It would be a worthwhile project to verify the
prediction methods for A by considering data taken on
the same estuary at different times. This might involve
revising the prediction system and then verifying the
revision on still more data. In any event this task
would have to be accompanied by an efficient data
collecting system.
4. This last recommendation pertains to water
quality standards themselves As we have seen? concen-
trations have natural fluctuations. It is unrealistic
39
-------
to require a stream or estuary to have at least 5 ppm
dissolved oxygen all the time. The standard should
contain restrictions on the proportions of the time
that concentrations can be outside preset limits.
Although this can possibly be done even now using the
Stochastic Model as a base, one must proceed
cautiously. A standard is unrealistic if violations
cannot be detected. The standard must be written in
terms of sampling schemes. The sampling scheme must
say how often, where and how many samples should be
taken. The standard should say that if there are more
then a specified number of samples outside specified
limits then there is a standard violation. This type
of standard is more realistic and enforcible.
40
-------
RANDOM OR VARIABLE INPUTS
BACKGROUND
As pointed out earlier, the model developed by
Custer and Krutchkoff for BOD and DO in estuaries
simulates a continuous release of pollution A in each
time interval 6t. The first release is at t0=0 and
the last release is at t0=t, where t is the time of
interest. The probability of one of these releases
being at location x after time t was obtained by using
a random walk mechanism to generate difference equations
which are then approximated in continuous time. Since
the individual particles are independent it follows
that the probability of a given concentration at
location x after time t is the convolution of the
probabilities for the individual particles.
To obtain a convolution, Custer and Krutchkoff
assume that each unit of pollution behaves as an
independent bernoulli random variable. If a given
unit is at x after time t, a success is recorded; other-
wise a failure is recorded. The probability of success,
given that the pollution was released at step ni? is
u(m,n |nt ), where u(m,n|n1) is defined after equation (31).
Let
pk(m,n) = Pr[k BOD units at location m&x after time n6t]
(53)
and
pk(m,n) = Pr[OD concentration is kA" at location m&x after
~ time n6t]. ' (54)
The above probability, pk(m,n) is a convolution of the
individual bernoulli trials. The probability generating
function (pgf) for pk(m,n) is given by
09
P(m,n,s) = £* pk(m,n)sk
k=0
= TT Gi (m,n,s) (55)
i=0
41
-------
where
G! (m,n,s) is the pgf for u(m,n|n1).
Thus,
P(m,n,s) = TT [l-u(m,n|i) + u(m,n|i)s]. (56)
i=0
Similarly, for OD
P(m,n,s) = £ pk(m,n)sk
~ k=0
= n [l-v(m,n|i) + v(m,n|i)s]. (57)
i=0
Where v(m,n|i) is the probability that a unit of OD is
at location m6x after time n&t given that the unit of
BOD entered the estuary at n .
The probability of the system being in any particular
state can be found by picking out the desired coefficients
in P(m,n,s) and P(m,n,s).
The means and variances of the distribution given
above can be obtained using the pgf and are given by
MEAN (BOD state) = &u(m,nlj) (58)
j=0
VAR (BOD state) = £u(m,n|J) - £ (u(m,n | j)) *
j=0 j=0 (59)
n
MEAN (OD state) = E v(m,n |jj) (60)
j=0
n a n 8
VAR (OD state) = 2Jv(m,n|j) - S (v(m,n |j))
j=0 j-0 (61)
Custer and Krutchkoff obtain continuous approximations
for u(m,n|j) and v(m,n|j) which allow the moments to be
calculated more rapidly. These will be explained shortly.
42
-------
DERIVATION
Suppose the input BOD into the estuary is not a
constant uniform input as assumed by Custer and
Krutchkoff, but enters in some random fashion. Let
us assume, however, that the number of BOD units
entering the estuary can be discretized into multiples
of A units.
Since the input is random, it must enter the estuary
at each point in time according to some discrete
probability distribution. Let Y represent the random
input and let P[Y = yt ] = ft have pgf F(s) where i
denotes the time of input .
Now define
pki(m,n) = Pr[K1 of the yi BOD units are at location
m8x after time n6t |yt units enter at time
n, ] (62)
Since each of the individual units released at the
same time are independently and identically distributed,
the probability pkj (m,n) is a compound probability.
Thus,
Pki(m,n) = E P[Yi =y1]P[X0+X1 + ....+ Xy =ki](63)
71=0 l
where
Xj is the jth unit entering the estuary at time nj and
is a bernoulli random variable.
Therefore, the pgf for pk (m,n) is given by
P^m.n.s) = F(G1(s)) (64)
where
G! (s) is the pgf for Xj . The expected value of Xt is
utnijnlni) which Custei *nd Krutchkoff define as the
probability that after n steps the unit of BOD is at
43
-------
location m6x given that the unit entered the estuary at
step r\i .
To find the final probability of k BOD units being
at location m6x after n6t one must convolute the
Pfc (m,n) for i=o,...,n. Using the convolution property
of generating functions,
P(m,n,s) = TT PI (m,n,s)
i=o
= " FCG^S))
i=o
= % Sf^G^s))3. (65)
i=o j=o
P(m,n,s) is the pgf for pk(m,n) as defined previously
with kg + kx + ... + kn = k. Since Gt (s) is the pgf
for bernoulli random variable,
P(m,n,s) = n £ fj[1 - u
-------
MOMENTS OF THE RESULTING DISTRIBUTION
To find the moments for distribution of BOD and OD
for any point in time and space it is possible to use
the pgf . This immediately yields
MEAN (BOD state) = PXm,n,l) (68)
VAR (BOD state) = F"(m,n,l) + F^n^n,!)
- (F"(m,n,l))3 (69)
MEAN (OD state) = Pf(m,n,3,) (7O)
i-*j
and
VAR (OD state) = Pf(m,n,I) + ?(m,-n,l)
r*t *^*
- (P^n,!))3 (71)
Now let
E(Yt) = \t
E(Xi) = Uj i=o, 1, . . . , n (72)
where E represents the expected value and where the
pgfs corresponding to Yt and Xj are F1(s) and Gj (s)
respectively .
Using equation (65) and setting n=o, the moments for
the BOD state are
MEAN (BOD state) = ^(m^,!)
= uo*o (73)
VAR (BOD state) = F'(G0 ( 1) )<#!) - G^ GoQ) GkQ
+ F'(G0(l))G'0(l)-(F'(G0(l)))a(G'o(3))8
45
-------
= \0 VAR X0 + UQ VAR Y0 (74)
For n=l
P(m,n,s) = F(G0)F(G1) (75)
and
MEAN (BOD state) = F(Go ( 1) )F/(G1 (1) JG^ ( 1)
= XlUl + X0u0 (76)
For notational convenience let Fj = F(G^ (1)) and
= G! (1) . Then
VAR (BOD state) = F0F/1G1"+F0G?F/1'
F1GgF/0'+F/0G0'F'1G'1
-2F/1G'1F/0G '
'-H^ -Gg ]+F; [Gi'+c;
Gg [F'o'+F'o -F- ]+Gj [FY+Fi -Ff
= X0VARX0+X1VARX1+xa|VARY0+u^VARY1,
(77)
In general it can be shown that for any n
MEAN (BOD state) = S Xji^iUjnU) (78)
i=o
46
-------
and n n
VAR (BOD state) = D A^VAlQq +S (u(m,n | i) ) 3VARYt .
i=o i=o
(.79)
Since Xl is a bernoulli random variable with mean
u(m,n]i) the variance becomes
n n s
VAR (BOD state) = E \1u(m,n|i)+E (u(m,n|i)) VARYt
i=o i=o
n a
- E X1(u(m,n|i)). (80)
i=o
A similar derivation for oxygen deficit yields
n
MEAN (OD state) = E ^vfm.nli) . (81)
i=o
v(m,n|i) is the probability of an OD particle being at
location m&t after time n6t given that the BOD particle
entered the estuary at time i&t. Also
VAR (OD state) = E X1v(m,n|i)+£ (v(m,n|i)) VARY^
i=o i=o
- E\v(m,n|i))8. (82)
i=o
CONTINUOUS APPROXIMATIONS
Numerical solutions for u(m,n|i) and v(m,n|i) can
be obtained, but for small values of &t steady state solutions
require an enormous amount of computer time. Custer and
Krutchkoff, however, are able to obtain continuous
approximations for u(m,n|i) and v(m,n|i) as &t-*o. Let
u(m,n|i) »f(x,t|ti)6x (83)
v(m,n|i) » g(x,t|ti)6x
Solutions for functions f and were given previously.
47
-------
Let the average increase in the BOD concentration at
the source in time 6t be A.A where X is less than one.
Thus
\A = W6t (84)
A6x
where W is the rate at which pollution enters the estuary
and A is the cross sectional area. 6x and 6t are both
small but consistent with
E = (5*)8 (85)
26t
E is the diffusion coefficient. X is the average number
of BOD units of size A entering the estuary in a time
interval 6t and need not be preassigned since it
depends on 6t.
At time i6t Yt units enter the estuary. Where
Yt =1 with probability p and Yt=O with probability
1-p. As 6t-»o, p-*o. Making appropriate substitutions
yields
n
MEAN (BOD state) = W S B(Yj)f(x,11tt ) 6t.
AA\ i=o (86)
Letting 6t-»o yields
MEAN (BOD state) = _W_ J* p( T) f (x, 11 T) dr (87)
AA °
where
p(r) = E(Y<) at time T.
\
If for example E(Yt) = \ for all i then
MEAN (BOD state) = _W_ J f(x,t|r)dT (88)
AA °
which is the result obtained by Custer and Krutchkoff.
Also
n
VAR (BOD state) = W E E(Yj)f(x,tjtt)6t
AAX i=o
48
-------
n
Ws S VARYtfg(x,t |ti )(6lf
A3 Aa Xs i=o
W8 . §E(Y1)f3(xJt|t1)(6f.
A.8 A3 Xs i=o (89)
Since Yt is defined as a bernoulli random variable
n
W S
AAX i=o
n
VAR (BOD state) = W S E(Yt )f (x, t | tj ) 6t
(E Yi)Sf3(x,t|tl)(61)s
A3 A3 Xs i=o ( 90)
Since EYt is the same order of magintude as X when
6t-»o the second term vanishes and the variance becomes
VAR (BOD state) = _W_ ftp( T) f (x, 1 1 T) dr . (91)
AA °
If for example E(Yt ) = X for all i then
VAR (BOJJ state) = JW^JQf (x,t|r)dT (92)
AA
which is the result previously derived by Custer
and Krutchkoff.
Similar derivations hold for OD states such that
t
MEAN (OD state) = _W_ J p ( T) g(x, 1 1 T) dr (93)
AA °
and
VAR (OD state) = _W_ J%( T) g(x, t J T) dr . (94)
AA °
Once again Custer and Krutchkoff 's results are obtained
when E(Yj) = X for all i.
Letting |a(x,t) and as(x,t) represent the BOD mean and
variance, respectively and noting that the level of
pollution is XA times the state one obtains,
49
-------
M(x,t) = wJta(T)f(x,t|T)dT (95)
A °
where
a(T) = E(Yi) at time T (96)
and
o«(x,t) = XAn(x,t) . (97)
Similarly, if |a(x,t) and£3(x,t) denote the mean
and variance for OD, one obtains
t
ja(x,t) = Wj a(T)g(x,t|T)dT (98)
~ A o
and
£s(x,t) = XAu(x.t) . (99)
If once again E(Yj ) = X for all l
|a(x,t) = XwJtf(x,t|T)dT (100)
A
as(x,t) = XA|j(x,t) = X8WAj f(x,tJT)dr
A ° (101)
|a(x,t) = XwJ>tg(x,t|T)dT (102)
~ A °
and t
a3(x,t) = XAu(x,t) = X8WAf g(x,t|r)dT
* ~A~~ ° (103)
which are the results previously obtained by Custer
and Krutchkoff except for the extra parameter. When
E(Yj ) is not constant but allowed to vary in time,
then the appropriate final equations are (95) , (97) ,
(98), and (99). The important things to notice are that
1. The distribution about the mean effect E(Yj ) does
not enter into these equations. This variability
disappeared when the continuous approximation was made.
2. The variance is X.A times the mean However, XA
can be considered the A for the process. This result
is called the Poisson Approximation.
5O
-------
THE SEGMENTED ESTUARY MODEL OUTPUT-INPUT MODEL
In Moushegian and Krutchkoff [55] it wag found
that a segmented stream solution could be obtained
by using the probability output of one segment as
the probability input of the next segment . Although
an estuary is far more complicated than a stream, this
simple approach might produce approximate solutions
which could be used for a segmented estuary. This output -
input approach is described here.
Let us say that the pollution loading function is
given by W(t) . Thus W(t)6t is the amount of pollution
entering the estuary in time 6t. If the fluid in the
estuary moves a distance 6x in time 6t then the con-
centration entering the estuary in time 6t is given by
Concentration = W(t) 6t (1O4)
A6x
where A is the cross sectional area of the estuary.
In order to put this into the framework of the Custer
and Krutchkoff model we assume that this concentration
is measured in multiples of A and therefore,
\A = W(t)6t (105)
A6x
where X is the average number of concentration units
of size A entering the estuary in time 6t. Of course
6t and 6x are related by the relation
E = l&*l. (106)
26t
where E is the diffusion constant.
If in equations (87) and (93) we use W(t) for Wp(t)/\
then we obtain
t
MEAN (BOD state) = _Lj W( t) f (x, t | T) dr (107)
AA °
51
-------
and t
MEAN (OD state) = _^JQW( t) g(x, 11 T) dr (108)
AA
where f(x,t|r) and g(x,t|r) are given in equations
(41) and (42) .
Let us say that at x0 there was a source with input
function Wt(t) . Let us assume further that the first
segment extended from x0 to xx . Then the mean state
output for BOD at xx is given by
t
M(x1,t) = X f.W, (t)f, (x, ,tJT)dT
A! A (109)
where the subscript 1 on f indicates that all the
parameters and constants in f are for the first segment
A similar result holds for OD. Now the mean concen-
tration is given by
m(Xl,t) = AM(x15t). (110)
For the second segment, which we can assume extends
from xx to x3, we know that the concentration is given
by
m(x1?t) = W9( t) 6t (HI)
A3 6x
with 6t and 6x now related by
E3 = (6x)a (112)
26t
where E3 is the diffusion constant of the second segment
which could conceivably differ from the constant for the
first segment. It should also be clear that for any
instant of time
U3(t) = 5x/6t (113)
where U3(t) is the velocity function for the fluid in
the second segment. Therefore ,
52
-------
W,(t) =m(x1,t)A3U3(t). (114)
Using this we obtain the mean BOD state a c xg to be
given by
t
m(*S,t) = Aj m(x1,t)U3(t)f3(x8,t|T)dT
A ° (115}
with a similar result for OD.
At this point it will pay to write out equation
(115) in detail This provides
m(xs,t) = \3 J Ua(r) T
exP{-(x1-tf^U1(s)ds)8-Kd(T-§)}d§]exp{-(xs-J*U3(s)ds)3
4E1(r-|) 4E3(t-T)
-Kd(t-T)}dT. (116)
The corresponding equation for OD is given by
m(x3,t) = Xs J K,Ua(T) _
~ AAX °2(K8-Kd)7ETT(t-T)
2(K3-Kd)VETT(T-§)
exp{-(xT-|^U1(s)ds)3[exP{-Kd(T-5)}
4E(T-5)
-exp{-.K8(T-§)}]d5]exp{-(xs-J'TlMs)ds} [exp{ -Kd (t-r) }
4E3(t-r)
-exp{-K3(t-T)}]dT. (117)
These equations are not simple equations, but they
can be solved numerically by computer. They are double
integrations and their solution requires a good deal
of computing time. Therefore, before using the solutions
as obtained from the computer programs, it was important
to check to see if they gave the correct answers. This
53
-------
could be done by a means used in the work of Moushegian
and Krutchkoff f55]- Tne technique is to assume a
constant input at XQ and solve for the mean values at
xs in two ways: first, by using the unsegmented
formulas already developed and secondly by using
equations (116) and (117) assuming some arbitrary
segmenting point XL.
Unfortunately, the two solutions obtained at
point x were significantly different. Unlike the
situation for a stream, the fact that probabili-
ties are used for both output and input functions
could not compensate for the feedback necessary
from the succeeding sections in an estuary. The
magnitude of the discrepancy, even in this simple
test, made it clear that the output-input approach
could not be used as an approximate solution to
the segmented estuary problem
The fact that this procedure is not theoretically
sound is easily seen with this following example.
Assume that there is a constant input W at XQ . After
a time the concentration at XQ is made up of two
parts W and the residual effect of the previous
inputs. This result is obtained by the Custer and
Krutchkoff model. That is, the concentration at XQ
is significantly larger than would be obtained by
using W alone. On the other hand the output at
point xx is the total concentration at that point
at any time. If this is used as the input of the
next segment at xx ami the equations resolved then
the net concentration at X-L would be the sum of the
output from the first segment plus the residual
concentration However, the output of segment one
is the total concentration at xx. Thus the procedure
cannot even provide the proper answer at the point xx.
Since the Output-Input extension to the Custer and
Krutchkoff model could not provide even an approximate
solution to the segmented estuary problem a new model
had to be derived.
54
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DEVELOPMENT OF THE NEW STOCHASTIC MODEL
The model developed by Custer and Krutchkoff, [14],
describes the stochastic nature of BOD and OD in an
estuary but with the limitation that in order to get
an analytic solution the process coefficients were
held constant. Here a stochastic model for BOD and
OD is developed in which the process coefficients
(Kj, , Kg, E, Vt , etc.) are functions of position in
the estuary and, if necessary, functions of tidal phase.
The model which is developed here is more than a
segmented model in that the assumption of constant
coefficients within a segment has been bypassed and
a model is developed which describes the system para-
meters as they actually occur.
The development will, in general, follow that of
the previously discussed Custer and Krutchkoff model.
Units of pollution and dissolved oxygen are visualized
as taking a nonconservative walk in the estuary. In
each time interval it a unit of BOD can either move one
unit £x to the left (upstream) with probability q(x,t),
one unit Jx to the right (downstream) with probability
p(x,t), or be biologically utilized with probability
r(x,t), such that p(x,t) + q(x,t) + r(x,t) = l.O. These
probabilities include the mean velocity of the tidal
excursion. On decomposition a unit of BOD becomes a
unit of OD and this OD unit continues the random walk
until it is eliminated by reaeration from the atmos-
phere above the estuary or until its walk carries it
permanently outside of the part of the estuary which
is of interest. An important property of this random
walk is that one unit of BOD or OD is not affected by
any other unit. Thus the units are statistically
independent.
With this foundation, difference equations are
formulated which give the joint probability that a unit
of BOD (or OD) will be at a point x in the estuary
after any time t, given that the unit was introduced
at the origin such as at a Sewage Treatment Plant, (STP)
at time t0. Recall that the walk takes place in steps
of size 4x, so that the probabilities for any x which
is not a multiple of 4x will be zero. The quantities
p(x,t), q(x,t), and r(x,t) can be determined from the
55
-------
physical properties of the estuary. For example, see
equations (28), (29), and (30).
The unit of BOD used in the above discussion is the
amount of BOD material needed to increase the concen-
tration of a cross sectional sheet in the estuary with
width 6x by an amount A. A is a measured stochastic
coefficient which is set by the physical, chemical, and
biological properties of the estuary by methods given
later. This discretizing of concentration is done to
make the mechanism a stochastic process but is not a
limitation as was pointed out in the INTRODUCTION.
The total concentration due to many units of BOD occurs
in states, which correspond to integer multiples of
A. The states are determined by dividing the concen-
tration by A, or if the state is known, concentration
is determined by multipling the state number by A.
THE DIFFERENCE EQUATIONS
Difference equations are used to determine the
probabilities of a given BOD (or OD) unit being at
a given location at a given time. Let u(m,n) be the
probability that after n steps the unit of BOD is at
location m6x. The total time lapse t is n6t. The unit
of BOD can be at location m&x after n steps in either
of two ways:
1. At time (n-1)5t it is at location (m-1)6x and
takes a postive step (moves down the estuary),
2. At time (n 1)5t it is at location (m+1)&x and
takes a backward step.
Thus,
u(m,n+l) = u(m-l,n)p( (m-1) 6x,n5t)
+ u(m+l,n)q((m+l) ,n6t) (118)
where
me(-°°,<=) and ne (0,°°)
56
-------
which are equivalent to
-oo < x < o> and 0 ^ t < oo .
As mentioned above the quantities p(m6x,n6t),
q(m6x,n6t), and r(m&x,n&t) can be determined from the
physical properties of the estuary. Techniques have
been developed by Einstein and others to describe the
behavior of a particle placed in a medium in which
it is exposed to a large number of random forces. The
forces acting on the particle can be summarized into
two components: the symmetric random forces described
as diffusion and an asymmetric drift which is in
this case due to velocity. This process is usually
called the trdiffusion" process. The classical problems
in the diffusion process have been concerned with
conservative particles. In our problem, however,
there is a non-zero probability that the particle will
be absorbed. These techniques provide a method by which
the p(x,t) and q(x,t) can be determined. They provide
p(x,t) = (1-Ka(x,t)6t)/2 + U(x,t) 6t
2 &x
(119)
q(x,t) = (l-Kd(x,t)6t)/2 - U(x,t) 6t
2 6x
(120)
and
r(x,t) = K*(x,t)6t (121)
where
Kd(x,t) is the coefficient for the decrease of
BOD by all processes, including biological
utilization and all non-oxygen-consuming
processes, i.e. Kd(x,t) = K-^Xjt) + K3(x,t)
Kj(x,t) is the coefficient for biological utilization,
K3(x,t) is the coefficient of all non-oxygen-con-
suming processes.
U(x,t) is the velocity of the water in the estuary.
57
-------
The values of 6x and 6t used must remain consistent
with the following relationship
(6x)3 = 2E(x,t) (122)
6t
where E(x,t) is the diffusion coefficient.
The initial conditions for the difference equation
are as follows
U(0,n0) = 1.0
U(m,n0) = O For all m^O
U(m,n) = 0 For all n(x,t), or a
backward step is c^(x,t), and of absorption is r(x,t).
The OD unit could be at location m6x at time n6t
in three possible ways
1. By being at (m-1)6x at time (n-1)6t and taking
a forward step
2. By being at (m+1)6x at (n-l)6t and taking a
backward step.
3. By a unit of BOD at m6x and (n-1)6t being
absorbed.
Thus,
v(m,n+l) = v(m-l,n)p((m-1)6x,n6t)
/~*~t
6x,n&t) + u(m,n)K1(x,t)6t (124)
58
-------
where
me (-», °°)
and
ne[O,»).
The probabilities are specified by:
p(x,t) = (l-Ka(x,t)6t)/2+U(x,t) 6t
~ 2 6x
(125)
q(x,t) = (l-Ka(x,t)6t)/2-U(x,t) 6t
~ 2 6x
(126)
and
r(x,t) = Ka(x,t)6t (127)
*-w
where Ka(x,t) is the coefficient of reaeration.
The initial condition is given by, v(m,n) = O for
all m and n < n0.
The two difference equations, (118) and (124), could
be solved iteratively, but this type solution is quite
time consuming. The two equations would have to be
solved for each unit of BOD introduced into a 2O-mile
estuary for at least twenty days in order to reach
steady state. Then all these individual particle
probabilities would have to be convoluted to obtain
the final result. Also it should be noticed that the
terms u(x,t) and v(x,t) are probabilities for one unit
of BOD being at x at time t given that the unit was
introduced at time t0. Thus u(x,t) is really'the con-
ditional probability u(x,t|t0). The t0 is important
for two reasons: first, there must be a simple way to
distinguish when more than one particle is present,
and second, the probabilities depend on t0, i.e. two
particles with the same elapsed time in the estuary
usually have different probabilities if they were
introduced at different phases in the tidal cycle.
59
-------
CONTINUOUS LIMIT FOR DIFFERENCE EQUATIONS
Since the pollution flow, absorption, etc. of BOD
in an estuary are actually continuous processes, a
Taylor's expansion will be made on the two difference
equations (118) and (124) and the limits taken as
6x-»O. As 6x-»0 the discrete probability mass function
u(x,t|t0) and v(x,t|t0) will approach continuous
probability density functions denoted by f(x,t|t0) and
g(x,t|t0), respectively. The difference equations
(118) and (124) can be rewritten with the new notation
as
f(x,t+6t) = f(x-6x,t|t0)p(x-6x,t)
+ f (x+6x,t |t0)q(x+6x,t) (128)
and
g(x,t+6t|t0) = g(x-6x,t|t0)p(x-6x,t)
t^-j
+ g(x+6x,t|t0)q(x+6x,t)+f(x,t|t0)K1(x,t)6t (129)
r*j
Expanding equation (128) in a truncated Taylor's
series about (x,t) yields
f(x,t|t0)+6t5f+(6t)gSaf+o(6taj =
at 2
5x3 dx 2 dx»
+o(5xs) 1+ff (x,t |t0)+6xdf+(6x)8
dx 2
x) (130)
2 dx3
Carrying out multiplication on the right side of
equation (13O) and neglecting terms of o(6x3) or
smaller, f(x,tjt0) will be denoted by f .
60
-------
right hand side = fp-6xpdf+(5x)gpdgf-6xf3p+(6x)8 9f
ax 2 ax3 ax 2 ax ax
+(6x)3fa8p+fq+ 5 xgaf+(6x)gqa3f+ 6xfaq+(6x)3 a_f
2 ax ax 2 dxs ax 2 ax ax
+(6x)gfa3q+o(axa) . (131)
2 ax3
Regrouping the entire equation and dividing by 6t
yields,
jrt a3f+o(6tg) = f| p+g-i+6x/ag-apj
at 2 ats I 6t 6t[ax ax
+a8f I (6x)3(p+c
ax axil
26t \axs ax3|J ax|_6t 6t
+o(6x8). (132)
There is a reason for the particular way in which these
terms were grouped. Rearranged and modified forms of
the p(x,t), q(x,t), etc. definitions can now be substituted
into the differenital equations.
Recall that
a) (6x)8 = E
26t
b) q(x,t)+p
-------
g) -U(x,t) = (q-p)6x
6t
and
h) .^Bp.+.Bci = -BU- 6t
Bx Bx Bx 6x
Substituting these expressions into equation (132)
yields
= t {-KA -BU-EB3Ka 5t]
3
Bt 2 Bt3 Bx 3x
+Bf {-U-2EdKa_6t}+^ff{E(l-Kd 6t}+o(6x) (133)
Bx 3x dx8
Taking the limit as 6t and 6x-»O yields:
Sf = -FQf-fdU-U^f+E^f (134)
&t dx Bx dx8
or
Bf(x.t|tQ) = E(x,t)daf-U(x,t)^f
dt "dx5" Bx
-fBU(x,t)-Kdf . (135)
3x
This is the Fokker-Planck Equation for the continuous
diffusion processes but with extra terms to account
for the nonconservative nature of our process.
A similar derivation of g(x,t|t0) results in the
following equation
,t|t0) = E(x,t)B8g-U(x,t)Bg
Bt Bx3 Bx
-(K8(x,t)+BU(x,t))g+K1(x,t)f. (136)
Bx
Notice that f is coupled into this equation to account
for the transformation of BOD to OD. Thus when a unit
of BOD is introducted into the estuary, its behavior
62
-------
is described by equation (135) until it is biologically
utilized. Then it becomes a unit of OD and follows
equation (136) .
Recall that the system under consideration is a
representation of a very thin cross sectional sheet
of an estuary which BOD (or OI) equation, describes the
probability of a particular particle being at any
position, x, at any time, t. A plot of f(x,t) for
several different times would look like Figure 7.
SMALL t
LARGE t
T
O
POSITION
FIGURE 7 THE PROBABILITY DENSITY OF A UNIT
OF BOD AT VARIOUS TIMES
At small time all the probability is centered near
the STP outfall, XQ- As time increases the probability
spreads out due to diffusion, migrates down stream due
to fresh water flow, and the area under the curve
decreases due to biological utilization. At large
time the processes of spreading out, migration , and
biological utilization continue. The effect of
each of the terms can be seen in the figure. A more
detailed description is given below.
The expression E(x,t)dsf/dx3 is the net difference
between the rate of diffusion of probability into the
differential sheet and the rate of diffusion out of
the sheet. That is the term Edsf/dx^ is the rate of
increase of f due to diffusion.
63
-------
The term U(x,t)df/dx accounts for the effect of
bulk flow, both fresh water and tidal flow. The
amount of probability being swept into the sheet by
bulk flow is different by -df/dx from the amount
being swept out. Then -Udf/dx is the rate of increase
in f due to bulk flow.
The term fBu/dx is a correction for compressibility
of the fluid in question. Since water is incompressible
this tp^Tii has been neglected.
The term K^ f accounts for the disappearance o±
BOD units due to both oxygen and non-oxygen consuming
process
The corresponding terms for OD have equivalent
meanings .
Although these equations were derived from a
probabilistic point of view and have a probabilistic
interpretation, they also have a concentration inter-
pretation. The terms f and g can be considered to be
continuous probability density functions or they can
be considered to be concentrations of OD and BOD. That
is, where probability is high average concentrations
must be high. This is an extremely important property
and will be discussed in detail at the end of the
following section. In addition, a derivation of a
general diffusion equation from a concentration point
of view will be made in a later section of this work.
CONTINUOUS SOURCE
Equations (135) and (136) are in the probabilistic
point of view differential equations for the continuous
probability density functions for a unit of BOD and OD,
respectively, given that the unit of BOD was released
into the estuary at time, t0 . If 6t, the time between
the introduction of successive BOD units, is made small
the pollution input will approach a continuous source.
Then the probability of concentration being at a
specified level at a certain time and position can be
determined by convoluting the probabilities of the
64
-------
individual units. The convolution can be derived by
considering the process as a series of individual
bernoulli trials. A. given unit being at x at time t
will be considered a success, where x and t are the
position and time of interest. Reverting temporarily
to the discrete notation of equations (53) and (59),
denote the probability of success for the release at
step nt by u(m,njnt), where n = x/6x and n = t/6t.
Let pk(m,n) = Pr[k BOD units are at location m6x
after time n6t] and j>k(m,n) = Pr[k OD units at m6x
after time n&t]. Recall that k OD units correspond
to a concentration of
Let
P(m,n,s) = Z) pk (m,n) s* (137)
k=0
and oo
P(m,n,s) = E pk(m,n)sk, (138)
~ k=O~
Then n
P(m,n,s) = TT [(l-u(m,n| i) )s°+u(m,n (i)s1 ]
i=0
= TT [CL-u(m,n|i))+u(m,n|i)s]
i=0 (139)
and n
P(m,n,s) = n [(l-v(m,n |i)) +v(m,n|i) s]
~ i=0 (140)
P(m,n,s) and P(m,n,s) are respectively probability
generating functions for the probabilities of BOD and
OD concentrations being in their various states. The
probability of the system being in any particular state
can be found by picking off the desired coefficients of
P(m,n,s) and P(m,n,s). The complete set of probabilities
can be determined by multiplying out equations (139)
and (140). However, the values for the mean and variance
can be evaluated without resorting to this time consuming
procedure. The mean and variance of a distribution with
generating functions F(s) are given by
E(k) = F/(s) I , (141)
o ~~ J-
65
-------
and
Var(k) = F"(s)
For this case
S=l S = l 5=1
(142)
?(m,n,s) =£u(m,n|j) ft [(l-u(m,n| i) )
j=0 i=0
i^J
+u(m,n|i)s] (143)
and
F"(m,n,s) = S u(m,n|j) £u(m,n|k)
j=O k=0
TT [l-u(m,n| i) )+uvm,n| i)s] .
i=0
Therefore ,
MEAN (BOD state) = Z)u(m,n|j) (145)
j=0
and n n 8
VAR (BOD state) = ^ u(m,n |j) - S (u(m,n|j)) .
j=O j=O (146)
Similarly for OD
n
MEAN (OD state) = Bv(m,n|j) (147)
j=0
and n n _
VAR (OD state) = S v(m,n | j) - S ( v(m,n J j) ) .
j=0 J=0 ( 148)
Once again allow 6t and hence 6x to become small,
consistent with (6x)3/6t = 2E(x,t), such that the process
66
-------
approaches being continuous. Thus there will be a
very large number of both BOD (or OD) units and of
possible positions. Since there will be a very large
number of possible positions, the probability, u(m,n|j)
(or v(m,n|j)) of any individual BOD (or OD) unit
being in a given position will be very small. Hence
as 6t becomes small u(m,n|ji)3 (or v(m,n|_i)3) become
very small and
n
VAR (BOD state) - Eu(m,n|J) (149)
JNO
and n
VAR (OD state) - £v(m,n|j) (150)
3=0
which equal the mean BOD and OD states. Thus, the
mean and variance of the BOD and OD state distribution
are equal, after the convolution operation has been
carried out. Not only do the state distributions
have equal mean and variance but these distributions
can be shown to be poisson.
B. O. Koopman [48] gives necessary and sufficient
conditions for a set of bernoulli trials (with probabil-
ities of success not necessarily equal ) to converge to'
a poisson distribution. Let P(k) = Pr|"X=k] where X is
a poisson random variable with mean m. That is P(k) is
the probability of BOD being in the kth state assuming
that the pollution is poisson distributed. Let
n -,
Pn (k) = Pr[Y = k, Y = £ yt I (151)
where yt is the outcome of the i-th bernoulli trial,
Pn (k) is the probability that k of the n units of BOD
are at x at time t. The mean of Pn (k) is p(n) .
Koopman 's theorem states that
lira Pn(k) = P(k) (152)
n-*<=°
or the bernoulli becomes a poisson distribution if
and only if
67
-------
a) lim m(n) = m (153)
n-»oo
and
b) lim max Pn }i = O (154)
where Pn l is the probability of success on the ith
trial of 'the nth set.
For condition (b) as n, the number of BOD units,
approaches inf inity?; 5t and the distance between
adjacent positions both approach zero. Then
lim max Pn t = lim max u(m,n|i)
= lim max f(x,t|i)6x=O
6x->o l^i^n (155)
Thus satisfying condition b)
for all finite f(x,t|i). Condition a) is satisfied
by defining
lim m(n) = m . (156)
n-»oo
Thus the sum of these independent bernoulli trials
converges to a poisson distribution with equal mean.
It is very important to note two very broad general-
izations on the interpretation of the result. First,
this result holds for pollution entering at any point
in the estuary (various STP outfalls, a line source of
land runoff, etc.). That this is true can be easily
seen by recalling that individual units of BOD (or OD)
are assumed to be independent of every other unit of
BOD (or OD) This assumption would obviously extend
to units of BOD discharged from different pollution
sources. The probabilities of the total concentrations
would be the convolutions of the concentrations due to
the various sources. Since the distributions due to
individual sources are poisson and the convolution of
poissons is poisson with parameter equal to the sum of
the individual parameters, the total concentration
must be poisson distributed with parameter equal to the
68
-------
total of the individual parameters or equivalently it
is equal to the mean total concentration times A.
Secondly, this result holds for any type of pollution
which obeys the above assumptions of independence.
This includes carbon and nitrogen forms of BOD, land
runoff, ben thai demand and any other components as
long as their probability density functions are
finite. Due to the relatively stable behavior of
this natural proo-sss, it is unlikely that a proba-
bility density function would not be finite. A
possible exception is the distribution of pollution
at the instant of introduction to the estuary. The
unit of BOD has not had time to be diffused. This
should involve no difficulty for two reasons. First,
the effect of the overall concentration by an individual
BOD particle is negligible and the concentrations near
3TP outfalls ara of less interest than tha concen-
trations downstream at the dissolved oxygen sag point.
This result we call the Poisson Approximation.
Recall that the pollution states wer-,5 defined
previously as the pollution concentration divided by
A, the stochastic coefficient. Thus the mean concen-
tration is equal to the product of the mean state and
A. Similarly the concentration variance is the state
variance times A3 or the mean concentration times A.
So, if the mean concentration is known, then the
concentration variance can be calculated and since the
distribution about the mean concentration is poisson,
the entire concentration distribution is known
Recall that at the end of the previous sec.tion,
it was pointed out that the differential equations
(135) and (136) which were derived for probability
density functions also have concentration interpre-
tations. This fact together with the result just
mentioned yields a great simplification to the con
volution over the many pollution units involved and
thus to the ultimate solution of the problem If
the equations (135) and (136) are allowed to take on
69
-------
their concentration interpretation, they can be
rewritten with the added term
M = Eflfjf-Udf+Rf (157)
dt ax3 3x
and
ac; = Ega^g-Uag,+Rf (158)
at as? 3x
where
Rf(Rg) is the net rate of increase in BOD (OD)
at (x,t) due to all sources and sinks, this
includes K^f, LR , FF, etc. for BOD and Kgg,
Kjf, DB, photosynthesis, etc. for OD
K^f is the rate of decrease in BOD due to oxygen
and non-oxygen consuming processes
LR is the rate of increase in BOD due to land
runoff
FF is the rate of increase in BOD due to STP
outputs
K2g is the rate of decrease in OD due to
reaeration
Ktf is the rate of increase in OD due to oxidation
PS is the rate of decrease in OD due to photo-
synthesis
DB is the rate of increase in OD due to benthal
demand. Normally PS will be included in
this term.
Thus, the solution of equations (157) and (158) for
concentration, carried out so that the source and sink
terms are incorporated into the solution, automatically
convolutes the individual BOD and OD units» This one
solution together with 1he stochastic coefficient A yields
the complete probability density function for all points
in the tidal cycle for every position in the estuary.
Once the concentration is determined, it is multiplied
by A to get the poisson variance about the mean and the
complete distribution is then known.
7O
-------
SOLUTION OF THE DIFFERENTIAL EQUATIONS FOR THE MEAN
Equations (157) and (158) rewritten in a computa-
tional form are given by
af (x,t) = Ef (x,t)a3f-U(x,-$af
at ax3 ax
-K< (x, t) f +LR (x, t) +FF(x, t) ( 159)
and
= E
e(x,t)agg-U(x,t)ag
^
at ax ax
-K8(x,t)g+K1(x,t)f+DB(x,t) . (160)
These equations can not be solved analytically, there-
fore, a computer program was written to solve them
numerically. All the terms on the right hand side of
(159) and (160) can be evaluated so that af/at and
ag/at can de determined. The differentials are evalu-
ated with sixth order difference equations and the
coefficients, sources and sinks are determined for the
estuary in question and fed into the program as input
data. With values of af/dt and 3g/at the solutions are
integrated through time using the Runge-Kutta-Mersen
method. A program listing (simulation program) is
given in the appendix.
The section of the estuary which is of interest is
divided into "finite thickness" cross sectional sheets.
The sheet thickness used in the OD solution may be some
integer multiple of the BOD solution sheet thickness.
The BOD concentration profile would be expected
to be more sharply peaked than the OD profile since
vast quantities of pollution are being introducted
into the BOD process by "point sources" while OD is
being created due to line sources which are spread over
the entire estuary section. The center of each sheet
is called a grid point. Point values for each of the
parameters, feeds, etc. are assigned for each grid point
71
-------
That is, the continuous process is discretized. Then
the sheet thicknesses are reduced in repeated computer
runs until further reduction in grid spacings (sheet
thickness) has no effect on the predicted concentration
profiles. Thus, a continuous limit is taken of the
discretized process. Due to the way the pollution
input must be handled, it may not be practicaj. to
require a complete convergence near the major pollution
source. This will be discussed further at the end of
this section.
DATA REQUIREMENTS.
Listed below are those parameters, etc. for which
information is required.
1. NG and NF The smallest number of sheets which
can be used in the OD and BOD solutions and still get
convergent solutions. NF can be any integer multiple
of NG provided both solutions converge. The numbers
are increased until further increases have no effect
on predicted profiles.
2. XI and XO. The upper and lower boundaries in
miles from some convenient upstream landmark. The fresh
water flow is from XI toward XO. XO must be greater than
XI. XI is usually set at or above the upper limit of
tidal action.. XO is set beyond our field of interest
and in an area in which concentrations are not chang-
ing wildly through the tidal cycle.
3. TI and TM. Beginning and ending values in "real
time" hours of the solution. TI must correspond to
the initial values given for the G and F profiles. TM
is set at a value greater then the value needed to
reach pseudo-steady state. TM is determines by making
several computer runs at different values of TM.
4. PRI. Number of real time hours between printing
of predicted profiles.
5. OMEGA. Tidal frequency. 2rr/(JU, (O.507 for the
Potomac Estuary and O.O for the Ohio River).
6. OMEGAF, Frequency of sinusoidal variation in
feed rate 2rr/24 = 0.262 -*f variation is over a 24 hour
72
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period. The program can be easily modified to handle
any reasonable functional form to describe the feed
input from STP as a function of time.
7. NS and XS(i), i=l, 2,.... ,NS. The number of
places and their corresponding positions in miles at
which output is required. Thus, after every print
interval is completed, predicted concentrations are
given at each position XS(i), i=l,2,...,NS. The concen-
tration profiles are determine from these values.
The XS values (positions) should be selected to give
maximum information. That is, more should be placed
in area in which concentrations vary considerably and
fewer in areas of stable concentrations.
8. G and F. Initial values of the G and F profiles
corresponding to the initial time, TI. Generally
both G and F are initially set equal to zero through
out the estuary.
9. UF and UT. Fresh water and tidal components of
velocity. The following functional form was used for
U(x,t) in equations (159) and (160)
U(x,t) = UF(x)+UT(x)'SIN(u)t) (161)
where
U(x,t) is the average cross sectional fluid velocity
UF(x) is the average cross sectional fresh water
velocity as a function of position
UT(x) is the average cross sectional value of
maximum tidal velocity as a function of
position or
is the average cross sectional tidal velocity
at rush tide
ou is OMEGA, in 5. above.
UF is calculated from the fresh water flow rate and channel
geometry.
UT can be measured or can be approximated from the lower
boundary tidal elevation function, channel geometry, and
hydrodynamic relationships
10. EG and EF. Diffusion coefficients for OD and
BOD respectively. Both can be functions of position.
11. Kj . Reaction rate constant for biological
utilization of BOD as a function of position.
12. K
-------
and non-oxygen consuming process as a function
of position.
13. Kg. Reaeration rate constant as function of
position.
14. DB and LR. Rate of increase in OD and BOD
concentrations due to benthal demand and land runoff,
respectively. Both can be functions of position. PS
must be included in DB.
15. FF. Rate of increase of BOD concentration due
to STP outputs. The amounts of first and second stage
UOD for each STP with the STP positions must be
available.
16. Upstream boundary conditions. Measured concen-
trations if possible arbitrary but reasonable values
if necessary for both F and G.
Note that K3 is a function of turbulence, among other
factors. Thus, if an estuary is being simulated, K3
must be adjusted for tidal velocity. The function used
in this work for the adjustment is
K3(x,t) = OKa(x)- |SIN(cut) | (162)
where
C is a proportionality factor so that the average
value of Ka(x,t) over a full tidal period will
equal Ks(x).
C is evaluated by setting
_C_J12'4K8(x) | SIN (cut) | dt = Ka(x)
12.4 o (163)
which yields
If simulating a river, no correction to K3(x) is needed.
Of the parameters given above, different parameters
are estimated with vastly different degrees of accuracy.
For example KL, UF, and FF can probably be estimated
with ±1O% without much difficulty. While estimates
for DB, LR , E6, and Ef are often considered good if
74
-------
they are within 5O% of their true values. Thus, it
was recognized that attempting to find LR, for example,
as a function of position would be completely point-
less and that an average value for the entire estuary
section should be used. But at the same time, some
parameters could be measured or estimated with a degree
of accuracy that would reasonably permit them to be
considered as functions of position, That is, estimates may
be available for some but not all the parameters as functions
of position. For these reasons several different
parameter catagories will be given here, the use of
these will be discussed in the PROGRAM DOCUMENTATION
section. This is done to reflect the degree of in-
formation available on the individual parameters. Also,
the different catagories are handled differently as
input data. The catagories are the following:
A. The parameter is constant throughout the estuary
section of interest.
B. The parameter is constant within a segment, having
different values in different segments.
C. The parameter is a smooth function of position,
several pairs of values for position and parameter
value at the position are available for curve fitting.
D. Values are used only at certain grid points.
This is primarily for FF input.
Items 1 through 15 in the above list are supplied to
the program in the form of data. Item 16 and the
correction to K3(x) must be included inside the program.
How this is done is explained in the documentation
section along with several actual examples.
The process parameters, Eg, Ef Kx, K2, Kd, etc.
are used in the simulation as point values at the grid
points. Benthal demand, land runoff, and STP outputs
are not incorporated so easily. Each of these terms in
equations (159) and (16O) have the units Ibs/hr/vol,
but are usually available only in units of Ibs/hr
in the case of STP output or Ibs/hr/segment in the cases
of land runoff and benthal demand.
75
-------
Land runoff and benthal demand are handled in the
following way:
1. Divide Ibs/hr/segment values by the corresponding
vol/segment values.
2. Use the resulting Ibs/hr/vol as input to the
program as the units are now correct. Since land
runoff and benthal demand are introduced all along
the estuary (line source) , a value for each should
be defined at each grid point.
STP outputs are handled in the following way:
1. Divide the Ibs/hr values by the cross sectional
area at the STP outfall . Car«= should be used to get
an accurate value for cross sectional area, as the
solution is quite sensitive to it.
2. Use these Ibs/hr/a^ea values as input to the program,
Since the STP outputs are point sources, they will
have non-zero values only at specific grid points.
3. The program divides the Ibs/hr area by the
"differential sheet" thickness converting to units
of Ibs/hr/vol.
Thus land runoff and benthal demand would be classified
in either catagory A, B, or C, while STP output would
be classified in catagory D.
Notice that as the grid spacing approaches zero
the STP output approaches the function
lim FF(XO)(U(XO)-U(XO+AX))/AX =
Ax-»O (164)
where
u(x) is the unit step function
FF is the STP output rate
&(x) is the dirac delta function or unit inpulse.
The dirac delta can be defined in either of the
following ways :
76
-------
6(x0) = lim Z (165)
Ax-*O
where Z is a constant function with value I/Ax and
width Ax centered around x0 or alternatively
6(x) = 0 for all x^x0 = location of
STP plant
and co
J 6(x)dx = 1.0. (166)
oo
Thus FF6(x0) approaches infinity as the grid spacing
approaches zero. This is the reason that complete
convergence near the STP outfall may not be practical.
DISCUSSION OF MODEL
At this point a model has been developed and the
information needed to use it has been itemized. In
this section a discussion will be given of what this
model will and will not do.
Basically the model describes an irreversible series
chemical (biochemical) reaction of the type.
A -» B -* C
or
BOD -» OD - C (167,
where C is of no interest. The reaction takes place
in a one dimensional flow process in which mass trans-
fer by bulk flow and diffusion is permitted. Also in
this flow process are several point sources of BOD (STP)
and line sources for BOD and OD (land runoff and
ben thai demand) .
From basic chemical reaction kinetics it is seen
that concentration profiles similar to those in Figure
8 would be expected.
77
-------
g
H
1
POSITION
FIGURE 8 BOD AND OD PROFILES IN AN ESTUARY
The arrow indicates the location of the BOD input.
The BOD concentration decreases moving away from the
STP location in both directions, due to both biological
utilization and bulk flow above the plant and utiliza-
tion below the plant. Below the plant, the concentration
decreases to a value a little greater than zero.
This non-zero value, far from the source, is the result
of the BOD line source, land runoff. The OD profile
is smoother than the BOD profile and displaced down-
stream from it. The concentration increases with
position until a point is reached at which the rate
of creation of OD from benthal demand and biological
utilization of BOD just equals the rate of absorption
of OD by reaeration. Beyond this point OD decreases
until it reaches a small non-zero value, which results
from the creation of OD from the small amount of BOD
remaining and from benthal demand.
An interesting special case of this occures if the
diffusion coefficients are set equal to zero. The model
then simplifies to a variable coefficient and variable
feed version of Dobbin's model. In such a case concen-
tration profiles similar to those in Figure 9 would
78
-------
H
§
§
U
POSITION
FIGURE 9 BOD AND OD PROFILES IN A RIVER
be expected.
Several recent studies, Jaworski [4O], Thomann,
O'Connor, and Di Toro [76], have indicated that pollu-
tion in estuaries follows a more complex reaction path-
way than the simple series reaction discussed above.
A brief outline of the pathways is given here
BODcarbon -* CO3+OD
BOD - NO3+OD
nitrogen *
NO8 -». NO3+OD
OD - C
CO3+NO3 -» Cell Mass
Cell Mass ^ -OD Photosynthesis
Cell Mass -» BOD , + BOD . ^ On Death
carbon nitrogen
where C is a component which is not of interest and
X signifies sunlight. See Figure 10 for a schematic
79
-------
WASTE SOURCES
1
03
o
ORGANIC
CARBON
BIOLOGICAL
UTILIZATION
OXYGEN
CARBONATE
CARBON
SWEPT OUT OF ESTUARY
NUTRENT TO ORGANISMS
CONSUMPTION
OXYGEN
DEFICIT
t
REDUCED BY,
FEED BACK
ON DEATH
CELL
CARBON 8
NITROGEN
ORGANIC
NITROGEN
HYDROLYSIS
OR SWEPT
^PHOTOSYNTHESIS
OUT OF ESTUARY
/ \
AND REAERATION
NUTRIENTS
NUTRIENTS
OXYGEN CONSUMPTION
AMMONIA
NITROGEN
NITROSOMONAS
NITRITE
NITROGEN
I
NITROGEN REDUCTION
NITROBACTER
NITRATE
NITROGEN
I
WASTE SOURCES
WASTE SOURCES
SWEPT OUT OF ESTUARY
f WASTE'SOURCES
N2 RELEASE
FIG. 10 SCHEMATIC DIAGRAM OF PARALLEL- SERIES REACTION
WITH NITROGEN AND CARBON RECYCLE
-------
diagram of parallel-series reaction with nitrogen
and carbon recycle.
In this reaction pathway nitrogen and carbon pollu-
tants and the creation of dissolved oxygen by photosyn-
thesis must be considered separately, and an accounting
for the recycling of carbon and nitrogen through
organic forms must be performed. Obviously, the simple
model obtained in this project can not accurately
describe the behavior of BOD in an estuary in which the
above three (and other) processes are important. See
the RECOMMENDATIONS for further discussion.
The concentration profiles expected with a parallel
series reaction of this type as compared with the
simple series reaction would be similar to those in
Figure 11.
8
§
POSITION
FIGURE 11 COMPARISON OF BOD AND OD PROFILES
WHICH WOULD BE EXPECTED WITH THE
SIMPLE-SERIES AND PARALLEL-SERIES
BOD, which is the sum of the carbon and nitrogen
pollutants, would stay at a higher level downstream
due to recycling of these components through organic
forms. OD would be less peaked due to the effect of
81
-------
photosynthesis, but would have a high concentration
further downstream due to the contribution of the
recycled nitrogen and carbon components.
Another limitation on this and- any other reaction
rate model of its type is that the BOD processes
have been assumed to be independent of the OD level.
This is probably a good assumption for relatively high
DO levels. Field work seems to indicate that the
assumption fails for DO concentrations below 1 ppm.
Thus, this model must be restricted to estuaries in
which the DO level does not frequently fall below 1 ppm.
STOCHASTIC COMPONENT OF THE MODEL
It has been shown previously that once the mean
concentration of pollutant has been found, the proba-
bility distribution about this mean can be found by
superimposing the stochastic component, a scaled and
translated poisson distribution, over the mean. This
scaled and translated poisson distribution and how it
is found will now be discussed.
SCALE FACTOR, STOCHASTIC COEFFICIENT, OR A
First to be considered is the scale factor. Recall
that it has been shown that the poisson variance of
the concentration values around their mean is equal to
the stochastic coefficient, A, times the mean. The
coefficient, A, can be calculated by rearranging the
expression variance = A-mean into the form
A = Variance (168)
Mean
Then by using observed data from the estuary in questio
to get means and variances, A can be found. Care must
be used in calculating these values, however, to avoid-
distortion. The data used in calculating a mean and
the corresponding variance must have the same true mea
Thus if a large amount of data were taken over some
time interval at a certain point in an estuary, car
82
-------
must be used to remove any deterministic diurnal
variations due to photosynthesis and tidal excursion.
From this point on, the discussion of A will carry
through, as an example, data which was taken by WQO
in the summer of 1967.
DO and water temperature measurements were taken
every half hour for 3O days at one sampling station
and for 14 days in three others. The four stations
covered the upper 30 miles of the Potomac estuary.
To check for time of day variation, twenty-four
hourly OD averages were calculated for each of the
four sampling stations. Inspection of the means
indicated a large variation with days due to photo-
synthesis, see Figure 12. Only the data which was
taken between 5 and 9 am were used because during
this time the data appeared uniform and the effect
of photosynthesis would be minimized. Data which
was taken within this time interval was then sub-
divided into 12 groups according to tidal phase to
remove tidal effects. Means, variances, and A values,
were calculated for each tidal phase subgroup and
an overall average A was calculated for each station.
These calculations were done by a computer program
(A program) which is given in the appendix. Different
programs were needed for estuaries and rivers. A A
program was written for each case and listed in the
appendix.
The
estuary A program works in the following way.
1. A. header card is read which indicates the
sampling station number, number of samples taken at
this station and the time of high tide on a specified
day.
2. Data cards are read one at a time, one DO value
for each card. The number of cards read corresponds
to the number of samples given in the header card.
3. For each DO value the following operations are
carried out.
83
-------
00
a
a
H
1
§
8
7
6
J O O O
4
H
Q
3P
3
a
^
0
O STA 1
O STA 4
D STA 2
A STA 3
O O o O
O O O O °
OOO
6
}-° 0
0 0
0 0
D D
A A
A
0
8
12
16
006
o o o
D D D D D
A
A 9
0
20
24
HOUR OF DAY
FIGURE 12 HOURLY AVERAGE OF DO CONCENTRATIONS AS FUNCTIONS OF
TIME OF DAY FOR THE POTOMAC ESTUARY
-------
A. Check for time of day. If outside of
5 to 9 am interval the data value is not considered.
(This program can easily be changed to any approprate
time interval.)
B. If the DO sample was taken between 5 and
9 am, the DO value is converted to OD
C. The tide phase corresponding to the time
and day the value was taken is calculated. Then
the or value is placed in one of the twelve sub-
groups according to phase value.
D. Within each subgroup sums of OD and sums
of OD values squared are accumulated.
Steps A. through D are repeated for each card read in
step 2. Step 2 is repeated for all the data specified
in Step 1.
4. Means and variance are calculated for each sub-
group using the sums and sums of squares. Then A values
for each subgroup and an overall average A is calculated
for the station.
Steps 1 through 4 are repeated for each additional station.
The A values calculated for each of the four stations
are given in Table 3.
Table 3. A values for the Potomac by station
Station 1 Station 2 Station 3 Station 4
O.226 O.26O O.O254 0.2O22
The values for stations 1,2 and 4 are in reasonable
agreement. The station 3 value is certainly out of range.
This is an important result and will be discussed later.
Inspection of the individual DO values for station 3
reveals that many are near O ppm and that the average is
approximately l.O ppm. You will recall that 1.0 ppm DO
has previously been set as the lower limit on the range
over which this model can be used.
The relatively close agreement of A values from
station 1, 2, and 4 does not imply that A is a constant
85
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through out the estuary. It is entirely possible
that A could be a function of several estuary char-
acteristics, conditions, etc The functional form and
estimation procedures for A will be discussed in
another section of this report.
THE COMPLETE STOCHASTIC MODEL
A method is now available to calculate the scaling
factor for the poisson probability distribution around
the mean. Next to be discussed is the addition of the
stochastic component to the deterministic mean. This
stochastic component could be added by repeatly taking
random values from the poisson distribution and adding
them to the deterministic mean. This would be a
stochastic model in the Monte-Carlo or Stochastic
Simulation sense. However, this is usually done when
the type of probability distribution and the value of
its parameters are not known and the simulation is
done to help determine them. This is not the case
here. Thus, the generation of thousands and thousands
of random stochastic components using the known dis-
tirbution is not necessary and will not be done.
Another method of adding the stochastic component is
to take the mean, determine the poisson variance and
using a poisson distribution calculate confidence limits
about the mean.
This complete stochastic model, deterministic plus
stochastic components, could be verified by making repeated
comparisons between observed and predicted values and
counting the number of times the observed values fall out-
side of the predicted confidence limits. If the 5% con-
fidence limits are being considered, approximately 5% of
the observed data would be expected to fall outside of
the confidence limits. Since the model variance does not
include the variance component due to lack of fit of the
true mean concentration, nor the component due to random
variation of the observed average about the true mean (samp-
ling errors), a percentage of data outside confidence limits
somewhat greater than 5% would not be unexpected. To account
for these variance components, the A value may be adjusted.
86
-------
To carry out this comparison, computer programs
vanalysis program, see appendix) were written which
will carry out the following operations:
I. Read: 1. card output of simulation program, 2.
the time at which high tide occured on a specified day
at each sample station, and 3. the positions in miles
for the 16 points at which predicted means are given
by the simulation program.
II. Subroutines are called which calculate concen-
tration profiles through position in the estuary for
fixed tidal phases of O.O, O.25, O.50, and O.75.
Then profiles are calculated through the tidal cycle
at each station of interest.
III. Now the verification portion of the program
begins. A header card is read for each sampling
station giving the number of data cards to follow for
this station (1 BOD or DO value/card), the position in
miles of the station, and the station number.
IV. Next data cards are read one at a time on which
the month, day, and time of day at which the sample
was taken and the observed BOD or DO sample value.
V. A check is made on sampling time. If the sample
was not taken between 5 and 9 am the sample is dis-
regarded and a new data card is read.
VI. If the sample was taken between 5 and 9 am, and
DO is being considered, the DO value is converted to
OD.
VII. A subroutine is called which calculated the tid-
al phase when the sample was taken using month, day,
and time of part IV above. This subroutine is geared
to the day for which the time of high tide was 'given
in part I above.
VIII. Then, using the position in the estuary and the
tidal phase when the sample was taken, a predicted mean
concentration is determined by interpolating, if
necessary, between the tidal phase and positions given
by the simulation program.
IX. The poisson variance and cc.% confidence limits
about the predicted mean are calculated. Different
values for a can be used.
X. The observed value is compared to the confidence
87
-------
interval limits. The number of values which do not
fall inside the limits is tabulated and printed out
after all the data for this station is read. Then steps
III through X are repeated for each station of in-
terest. In step VIII confidence intervals are
calculated considering concentration as a continuous
variable. Since the poisson is a discrete distribution,
it was necessary to convert from a discrete to a
continuous distribution. The method which was found
most practical required that the poisson probabilities
massed at the discrete values be spread uniformly
over the interval from 3§ unit below to % a unit above
the respective integer values. Figures 13 and 14
illustrate how this is done. Once the conversion
is made, the point which has a/2 of the area under the
curve to the left of it and the point with a/2 area
to the right of it are found. These two points
represent the a level confidence limits. If a - O.1O
the points A. and B in Figure 14 would be those limits.
This method is quite accurate for moderate values
of the poisson parameter, X. But the method fails
for very small X values. This can easily be seen by
considering the extreme case of X = O.O. In this case
all the probability occurs at the zero value. Since
in the poisson parameter X is both the mean and the
variance, the true confidence units must fall on zero.
In the converted poisson this does not happen. The
converted poisson minimum confidence interval length
is 1-a. See Figures 15 and 16 for this comparison.
Thus, for very small values of X some correction of the
converted poisson limits may be necessary.
The above program is primarily meant for use in the
verification of the simulation program results. Another,
possibly more useful, approach would require a program
which would yield a summary of the probabilities of
exceeding a given level of OD. Such a program has been
written (see Limits Program in the appendix) and is
used in the folowing way:
I. Feed output of simulation program.
II. Read card giving the position number where output
88
-------
CD
^ *
s
e
M
M
PQ
O
ft!
rt
0
0
n
.4
.2
n
_
1"
1 , .
e
M
U)
H
O12345678
FIGURE 13 POISSON PROBABILITY MASS FUNCTION
WITH DISTRIBUTION PARAMETER EQUAL
TO 2.0
0.4
M
CQ 0.2
(X 0-. 0
8
FIGURE 14 CORRESPONDING CONVERTED POISSON
PROBABILITY DENSITY FUNCTION
-------
1.0
0.8
c/) 0 6
(/)
^j
s
K 0.4
M
M
M 0.2
O
K
Oi n n
1 1
_
.
.
l.U
0.8
s
H
gO. 6
W
Q
£0.4
M
gO. 2
CQ
§
°- 0.0
1
t
I,
1 1
.
-
-
-
V
012
FIGURE 15
w y \
yT\i
FIGURE TD6
COMPARISON OF POISSON AND CONVERTED POISSON WITH
DISTRIBUTION PARAMETERS EQUAL TO ZERO
-------
is required. The position number will range from
1 to 16 corresponding to the 16 position of I above.
III. For each card read in II a table of confidence
limits is generated for each O.O1 increment in the
tidal phase. The table is in the form given in
Table 4.
Table 4. Table of alpha levels generated by the computer
Alpha Level
PHASE O.O5 0.10 O.15 0.20 0.25 0.30 O.4O 0.45 etc.
O.OO
0.01
0.02
Here the alpha level signifies the fraction of obser-
vations predicted to fall above the OD concentrations
given in the table. Once familar with the layout,
the fraction of values predicted above a certain level
can be determined at a glance In addition a plot
showing the IO%, 2O%, 3O%, 50%, 70%, QO%, and 90%
limits is generated. At a glance the fraction of
values predicted above a given OD concentration can
be determined.
PROGRAM DOCUMENTATION
Given here is a detailed documentation of the
simulation program. It is thought that the A programs
»nd the analysis programs have sufficient documenta-
:ion in the respective program listings (see the
»ppendix) and in the previous discussion to permit
;heir useage without further explanation.
A detailed list of inputs to the simulation program
s given, with descriptions, in the DATA REQUIRMENT
91
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subsection of the SOLUTION OF THE DIFFERENTIAL EQUATIONS
FOR THE MEAN section. Most of the information needed
for a simulation is fed to the program on data cards.
Internal modifications are currently required to
incorporate the upstream boundary conditions, the
correction of Kg(x) for variable fluid velocity, feed
time variable functional forms, and a punched card out-
put option.
INTERNAL MODIFICATIONS
Boundary conditions: Refer to simulation program
in the appendix. Find the comment card "upstream
boundary conditions" and carry out the directions
given.
Correction factor for K2(x): Find comment card
"correction factor for K3(x)M. In the card following
the comments card, two options are available. The
term XKSIN, the corrected Ks(x) or K3(x,t), can be
left if an estuary is being simulated or it can be
replaced by K2(I) if a river is being modeled.
Variable feed: If it is necessary to use a time
varing feed, find comments card "variable feed". The
variable "SFT" at this point is the fraction deviation
of the current feed rate (STP output), FF(t), from the
long term average output, FF. The functional form used
in this example is
FF(t) = FF+O.OO1 FF-COS(OMEGAF«t)
(169)
This is the functional form used in the Potomac
verification. An essentially non-varying feed was used
due to lack of information on FF(t). Any other
reasonable functional form can be substituted here as
the need occur s.
Punched card output is possible: Find "punched
card output option" comments cards. In the cards which
follow these two comments cards, replace 40O with
92
-------
"real time" hours at which punched output is desired.
The time should be greater than the time necessary to
reach steady state.
Data input: .Since the formatting of FORTRAN IV is
more stringent than that of PL/1, and this program
is available in both languages (see the appendix),
the explanation here will be for the FORTRAN IV program,
The first data card must have the information listed
in Table 5.
Table 5: Information required for first data card
CARD Column Variable Description
1-5
6-10
11-20
21-30
31-40
41-50
51-60
61-70
71-80
NG Number of grid spacings in
estuary for OD.
NF Number of grid spacings for BOD
XI Upstream position. Upper
boundary of estuary in miles.
XO Downstream boundary.
TI Time at beginning of simulation,
usually O.O.
TM Time in hours at end of
simulation.
PRI Interval in real time hours
between outputs.
OMEGA Tidal frequency, 2rr/uu for
estuaries, 0 for rivers.
OMEGAF Frequency of sinusoidal feed
rate .
AN EXAMPLE: The Potomac
60 120
0.0
20.0
0.0 500.O 1.0 0.5067 0.262
A listing of the actual data used is given in the
appendix following the FORTRAN differential equation
program.
93
-------
The next set of information to be read is the number
of points in the estuary that output is required of and
the positions. This is given in Table 6.
Table 6: Information required xor subsequent data cards.
Card Column Variable Description
1-5
11-2O
21-3O
71-80
1-1O
61-7O
1-1O
NS The number of positions
XS(1) The 1st position in miles
at which output is needed.
XS(2) The 2nd position for output.
XS(7) The 7th position for output.
XS(8) The 8th position for output.
XS(14) The 14th position for output
XS(15) The 15th position for output
etc ... as many as required
EXAMPLE: The Potomac
16 0.0 3.0
11.0 11.0 13.0
4.8 6.0 8.O 9.O 10.0
14.0 15.0 16.O 17 O 2O.0
The remaining estuary parameter variables can be
classified into one of four catagories, depending
on the variable and the degree of accuracy with which
it can be measured. The variables (and parameters)
which fall in the same catagory are read in together
as a group.
The following is a summary of the four catagories
94
-------
Catagory Description IPX
A The parameter is a constant -2
throughout the estuary
B The parameter is constant 0
within an estuary segment
but may have different values
in different segments
C The parameter is a smooth >1
function of position through-
out the estuary and several
pairs of values are available
for the parameter at different
positions. The number of pairs
is equal to the IPT number.
D The variable takes on non-zero -1
values only at certain positions.
This is used only for point
source, STP outputs.
FOR the purpose of input, the various parameters must
be given numerical identifications. The identifications
used are summarized in the following:
Variable Description Number, NV
G Initial OD concentration 1
profile
F Initial BOD concentration 2
profile
UF Fresh water velocity 3
UT Tidal velocity 4
EG OD diffusion coefficient 5
EF BOD diffusion coefficient 6
Kj BOD utilization rate constant 7
Ks Reaeration constant 8
Kd Rate constant for decrease in 9
BOD by oxygen and non-oxygen
consuming processes
DB Benthal demand 1O
LR Land runoff 11
FF STP output 12
95
-------
This data is read in the following way. The
computer must first be told the data catagory, and
the variable number about to be read. The next card
(after the NS and XS cards which were discussed above)
must have the appropriate values for IPT and NV.
The catagory index, IPT, and variable number, NV,
in card columns 1-5 and 6-1O, respectively.
Example:
-2 1
This says the initial G profile (NV=1) will be read
as a constant (IPT=-2).
Now that IPT and NV have been read, the next card
must have the constant G value and the variable number
to be read next.
Example:
O.O 2
The initial OD profile. G, is zero for the whole
estuary and the value for initial BOD profile, F
(NV=2), will be read next.
Cards like this, constant value for current
variable and identification number for next variable,
will be used until all the parameters in catagory
"A" (IPT=-2) have been read. On the last card an
NV value of zero should be used. A zero NV tells the
machine to read a new IPT card. An example of how
Catagory A might be done is given in Table 7.
96
-------
Xable 7: Information for IPX card.
cc 5 cc 1O cc 15 Explanation
-2 1 IPX = -2 (IPX card)
0.0 2 G(x,o) = 0.0
O.O 5 F(x,o) = 0.0
0.1042 6 EG(x) = 0.1042
0.1042 7 EF(x) = 0.1042
0.02O 9 iq(x) = O.020
0.020 11 Kd(x) = O.O20
2OOOO 0 LR(x) = 200OO
End of catagory A.
A new IPX card must be given for catagory B if
there are any variables in this catagory. After IPX
card, a card must be read which gives the downstream
boundary of the first segment. Xhis card is followed
by a card which gives the value of the parameter in
the first segment. Xhen a position card and a value
card follow for the second segment, etc. for each
segment. A position card with a negative position
should follow the value for the last segment as in
Xable 8.
Xable 8: Example of use of position card.
cc 5 cc 1O Explanation
0
IPT = O (parameter constant within
a segment)
5.O
O.O8
10.0
0.10
15
0.
20
0.
-1
.0
12
.O
1O
.O
EG =
=
=
0
O
0
0
.08
.10
.12
.10
A position
EG has
been
from
from
from
from
value
0 to 5 miles
5 to 1O miles
10
15
<
to
to
O i
15
2O
miles
miles
£ XI means
that
complete .
97
-------
These data cards could be followed by an NV card
with NV = 0 (return for a new IPT card) or be a
legitimate NV card and the whole process repeated
for one or more other parameters which are in catagory
B. An example with two parameters in catagory B is
given in Table 9.
Table 9: Example with two parameters in Catagory D.
cc 5 cc 10 Explanation
O 5 IPT = O
1O.O
O.1O EG = 6.1O from 0 to 1O miles
2O.O
O.12 =O.12 from 10 to 2O miles
-l.O End of EG
6
1O.O
0.10 EF = O.1O from 0 to 1O miles
20.0
0.13 =0.13 from 10 to 20 miles
-l.O End of EF
O End of Catagory B
Next a new IPT card is read for catagory C. The
IPT value gives the number of pairs of values which
will be given for variable beings considered. The
pairs of values will be in this order; position 1 and
value of parameter at position 1, position 2 and value
at position 2, position 3 and value at position 3, etc.
see Table 1O.
Table 10: Example (variable NV=8, 5 pairs of values).
cc5 cclO cc20 cc30 cc4O cc50 cc60 cc70 cc8O
5 8
O.673 O.OO2O8 2.O2 O.OO2O8 3.212 O.OO375 4.255 O.OO375
5.217 O.OO7O8
98
-------
Several variables in catagory C would be handled in
the way depicted in Table 11.
Table 11: Example with several variables in Catagory C.
5 8
0.673 0.002O8 2.02 O.00208 3.212 O.O0375 4.255 0.00375
5.217 O.OO7O8
0
6 4
0.0 O.O 12.3 0.3863 3.735 0.4421 5.655 0.4812
7.185 0.568 8.775 0.805
0
Notice that after each variable in cacagory C the
return for a new IPT card is given. This is not
absolutely necessary if two successive parameters in
catagory C have the same number of pairs. A real NV
could be used.
Catagory D, FF, would be handled in the following
way. Read an IPT card given in Table 12.
Table 12: IPT card.
cc 5 cc 1O
-1 12
Follow this by a card with the position of the upper-
most STP plant. This is followed by the rate of pol-
lution input by this plant in units of Ibs/hr/square mile
Position and input rate cards should follow for each
STP plant in the estuary under consideration. After
the last rate card insert a card with -1 in cc 4 and 5.
If the position of an STP is outside of the interval
XI to XO it is not included as data here, but must be
included elsewhere. Either in the upstream boundary
99
-------
conditions if upstream of XI or, if it is downstream ,
either neglect it or extend XO to include the STP.
See Table 13.
Table 13: Example for FF.
cc 5 cc 1O
-1 12
9.0
1.5E+06
10.0
1.12E+07
12.2
O.728E+06
19.6
etc.
-1
-1
The second -1 tells the machine that all the data has
been read.
The input for the PL/1 program is exactly the same
as this except that it is "Free Format Input". The
above example for FF would be given by Table 14 in
PL/1.
Table 14: FF in PL/1
-1 12 9.O 1.5E+06 1O.O 1.12E+07 12.2 0.728E+06 19.6 0.37E+O5
22.0 0.18E+O5 -1 1.
100
-------
A GENERAL PARTIAL DIFFERENTIAL EQUATION DESCRIBING THE
BEHAVIOR OF ANY SOLUBLE POLLUTION COMPONENT IN AN ESTUARY
Here we derive an extension to the present stochastic
model which can be used for any soluble pollution
component in an estuary. It is this extension which can
be used to solve the algae problem.
Previously it has been shown that to stochastically
model pollution concentrations in an estuary, it is
necessary only to determine the mean concentration.
Once the deterministic mean is known the probability
distribution about the mean is found by superimposing
a translated and scaled poisson distribution onto the
mean. The degree of scaling is determined by the
stochastic coefficient, A, which is determined from
the observed OD and BOD data from the estuary in
question. The scaled poisson is then translated until
its mean coincides with the deterministic mean mentioned
above. Thus the difficulty is in determining the mean
concentration as a function of position and time. This
is a difficult problem in that many, as yet not fully
understood, processes must be incorporated into the
model. Some of the more important processes include:
1. Estuary .Hydraulics
2. Photosynthesis
3. Nitrogen and Carbon Recylce Through
Organic Forms
4. NH3-NO8-NO3 series reaction.
The first step in this overall problem is the
derivation of a general partial differential equation
with which the behavior of any soluble pollutant can
be described. If this step is done properly, the
physical processes (hydraulic and diffusion processes)
will immediately be incorporated into the model and
the chemical, biochemical, and biological processes
can easily be added to the extent to which they are
understood. In this section such an equation is derived.
101
-------
Consider a cross-sectional sheet in an estuary
such as given in Figure 17.
A(x,t)
C(x,t)
U(x,t)
A(x+5x.t)
C(x,t)
U(x+6x,t)
U-««I
x+6x
FIGURE 17 DIFFERENTIAL CROSS SECTIONAL SEGMENT
OF AN ESTUARY
with all concentrations, parameters, estuary char-
acteristics, feeds, etc. being functions of time (not
just tidal phase) and position.
Using the general law of conservation of mass on
a particular but unspecified pollution component,
Input - Output = Accumulation -
Generation + Depletion. (170)
Input: The rate of mass input at x and t is
E(x,t)A(x,t)dC(x,t)/dx]
= [u(x,t)A(x,t)C(x,t)-
(171)
I(x,t) is the rate of mass input at x and t. The rate
of mass input at x and t+6t is
I(x,t+6t) = I(x,t)+(3I(x,t)/dt)6t
(172)
Using a truncated Taylor's series, the average mass
input at x over the interval t to t+6t is
102
-------
[l(x,t)+%(ai(x,t)/at)5t]6t = I(x,t)6t
(173)
Output: The rate of mass output at x+6x and t is
O(x+6x,t) = [l(x,t) + (ai(x,t)/Sx)6x].
(174)
The rate of mass output at x+6x and t+6t is
O(x+Sx,t+6t) = O(x+6x,t)+[dO(x+6x,t)9t]6t
(175)
The average mass output at x+6x over the interval t
to t+6t is
[o(x+6x,t)+%(dO(x+6x,t)&t]6t
or
[l(x,t)+(dl(x,t)/dx)6x+%{(dl(x,t)/dt)6t
+ (aSI(x,t)/5xdt) 6x6t}]6t
or
I(x,t)6t+(dl(x, t)/8x)6x+l;(dl(x,t)/at)6t2
(176)
Input-Output: The difference input-output can be expressed
as the difference in equations (173) and (176)
I(x,t) 6t+3g(dI(x,t)/dt)&tg-I(x,t) 6t
-(dl(x,t)/dx)&x&t-(91(x5t)/6t)6ts-3g(dsl(x,t)/dxdt)&x5ts
(177)
Cancelling Terms, neglecting all terms of o(6x5)
and dividing by 6x6 t yields:
Input -Output = -(ai(x,t)/9x) (178)
where
I(x,t) = [u(x,t)A(x,t)C(x,t)
103
-------
- E(x,t)A{x,t)ac(x,t)/3x]. (179)
Then
Input -Output = -ACSU-UC5A-UAJ3C+A3E dC
dx dx 3x 3x dx
+ EM dC+EASf_C (180)
dx dx dx
Accumulation: The average mass content of the section,
x to x+6x, at time t is
[c(x,t)+%(dC(x,t)/dx) 6x][A(x,t)
+ %(BA(x,t)/dx)6x]ax . (181)
For convenience let
[C(x,t)+%(ac(x,t)/3x)6x] = M(x,t)
and
[A(x,t)+%(3A(x,t)/ax)6x] = N(x,t) .
(183)
The mass content at time t+6t is then
[M(x,t)+(BM(x,t)/3t6t][N(x,t)
+ (aN(x,t)/at)6t)]6x. (184)
Then using the expression
Accumulation - Mass at time t+6t-Mass
at time t
= [M(x,t)N(x,t)+(aM(x,t)/at)
N(x,t) 6t+M(x,t) (9N(x,t)/dt) 6t+(BM(x,t)/at) (3N( ,st)/St) 6ts
-M(x,t)N(x,t)]6x . (185)
Cancelling terms, neglecting all terms of ©(Sx8), and
dividing by 6x6t uields
Accumulation = (3M(x, t) /at)N(x, t)
+ M(x,t)(aN(x,t)/at) . (186)
104
-------
Recalling the definition of M(x,t) and N(x,t) gives
Accumulations = [ dC(x, t) +%3sC(x, t) 6x A(x,t)
I at axat '*
5x I + [C(x,t)+3§SC(x, t) ftxU aA(x, t) +?§a3A(x, t) 5x) .
« \ ax M 9t xat '
6x « ax
(187)
Taking the limit as 6x and 6t approach zero
Accumulation = A(x, t) 5C(x, t)
at
+ C(x,t)aA(x,t) . (188)
at
Generation and Depletion: All generation and depletion
terms will be considered together. The net effect of
all source and sink terms will be considered as a net
source term. Let R(x,t) be the net rate of increase
in C(x,t) due to all source and sink terms.
The average rate of increase of concentration
over the section with volume (A(x, t) +3§(aA(x, t) /ax) 6x) 6x
can be expressed at time t as
P(x,t) = [R(x,t)-f-%(dR(x,t)/9x) 6x].
(189)
The average rate of increase in concentration
over the section at time t+6t can be expressed
P(x,t)+%(3P(x,t)/at)6t. (190)
Then the average rate of increase in concentration in
the section over the time interval t to t+6t is
P(x,t)+^(3P(x,t)/at)6t = R(x,t)
(191)
Multipling out, dividing by 6x6 t, and taking the limit
as 6t and 6x-O yields
105
-------
Generation - Depletion = A(x,t)R(x,t)
(192)
Grouping all the expressions derived above,
equations (173), (176), (188), and (192) according to
the general law of concervation of mass yields
Input-Output = Accumulation
- Generation + Depletion
Aac+caA-RA .
at at (193)
Rearranging and dividing by A(x,t) gives
ac = Eaac+EaAac+aEac-uac-ucaA-cau-caA+R .
at a xs axax axax ax A ax ax at
(194)
All the terms on the right hand side of this equation
can be evaluated. The differentials can be done
numerically and the coefficients are fixed by estuary
properties.
If C(x,t) is known and ac/at at time t can be
evaluated, then C(x,t+6t) can be found using numerical
integration techniques. Specifically, the Runge-Kutta-
Mersen method would be used.
Any soluble pollution component can be des-
cribed by this expression . The only difference
in equations from one component to another
would be the source and sink term R(x,t). The
solution of the overall problem (BOD, NH3 -NO3 -NO3 , OD)
would require the solution of a coupled set of about
five equations of this form. The equations would be
coupled in their respective source and sink terms, R(x,t)
That is, BOD, NH3 , and NO2 would appear in the R(x,t)
term for OD for example.
106
-------
In the solution of this problem great care should
be used in specifing the different source and sink
terms and determing the U(x,t) term.
A comparison with previous work can be made by
comparing this equation With an equation derived by O'Connor
fSE^nd others. Their equation is derived assuming a
constant fresh water flow rate and considering only
one point in the tidal phase and is given by
dC = _! _a_EA^C -USC-KC (195)
A Zx\ dx| dx
where all the terms are the same with the exceptions
that parameters are functions of position only and
that the only source or sink considered is the sink
of first order absorption of C. This can be compared
with a rearranged form of equation (193) , derived
above
C\-l _d_(UAC)+R.
A at A S:x\ ax I A dx (196)
O'Connor claims that for some purposes tidal variation
can be ignored since the net effect over a tidal cycle is
zero. This might be true in a psuedo-steady state regime but
in an estuary which is not at steady state it is not true.
Fresh water flow rate, sun light intensities, pollution
loads, temperatures, etc. are constantly changing
from day to day and especially from season to season.
Also, an approach of this type does not permit modeling
within a tidal cycle This is an important limitation
if it is necessary to predict the mean within a cycle
for some resource management decision.
It can be shown that O'Connor's equation is a special
case of the equation derived above. If fresh water
flow rate is held constant with time and position (no
tributaries) and only solutions at slack tide are
considered, then fluid velocity and cross sectional
area become functions of position only and
107
-------
U(x) = Q/A(x) (197)
where Q is the constant volumetric fresh water flow
rate. Then
U(x)A(x) = Q (198)
and
d(U(x)A(x))/dx = d(U(x)A(x))/dx = O .
(199)
If the only source or sink term to be considered
is the biological utilization of C, then R = -KC.
Now equation (196) can easily be reduced to
i 5(AC) = i _a_(EAdc)-i _3{uAc)+R
A dt A dx dx A dx
1 (AdC+CdA) = 1 JL(EA.SC)-UdC+C _d_(UA)-KC
A dt 9t A dx dx dx A dx
or
^c = i _a_(EAd_c)-uac-Kc (200)
St A 9x dx dx
which is O'Connor's equation.
108
-------
VERIFICATION OF THE STOCHASTIC MODEL
Discussed here are comparisons between predicted
values and observed BOD and OD data from the Potomac
estuary, the Ohio River and the Delaware estuary.
POTOMAC ESTUARY
In the summer of 1967 an intensive OD and water
temperature survey was conducted for the Potomac
estuary. These data were made available through the
Chesapeake Field Station, Annapolis, Maryland and can
be found in the appendix. Sampling was done at four
stations which cover the upper 3O miles of the 116
mile estuary. In order to model the estuary, information
had to be gathered on all parameters, pollution sources,
fresh water sources, etc. for this part of the estuary.
Listed in Tables 15, 16, and 17 are the values for the
respective parameters, feed rates, etc. which have been
used and/or recommended by previous workers.
Table 15: Major pollution sources for the Potomac.
Name
Arlington STP
D. C. STP
Alexandria &
Westgate STP
Little Hunting
Creek STP
Dogue Creek
Position,
Miles from
Chain Bridge
8.9
1O.O
12.25
19.6
22.0
UOD*
Ibs/day
43,4OO
318,000
3O,1OO
2,OOO
1,2OO
UOD
Ibs/hr/square mile
1.507x10
1.12X107
7.28xlOE
3.7x10*
1.8xlO4
6
*Taken from Hetling and O'Connell [36].
109
-------
Table 16: Various estuary physical parameters for the
Potomac
Segment Position, Miles Ks** Vt* DB*
Beginning End 1/hr mi/hr Ibs/hr/cubic mile
1 0.0 2.69 O.OO208 0.3863 O
2 2.69 4.78 O.OO7O8 0.4421 14,90O
3 4.78 6.53 O.0154 0.4812 150,700
4 6.53 7.84 O.O129 O.5683 301,400
5 7.84 9.71 O.O1625 0.8O5O 273,500
6 9.71 11.82 O.0122 1.042 347,300
7 11.82 14.39 O.O1333 1.120 384,5OO
8 14.39 16.58 O.O104 1.144 279,700
9 16.58 19.O2 O.O1333 1.168 256,8OO
10 19.02 21.O8 O.OO958 1.19 211,500
11 21.08 23.33 O.O1O83 1.20 159,900
12 23.33 27.33 O.1083 1.20 154,100
13 27.28 30.22 O.1O83 1.112 137,600
*Taken from Hetling and O'Connell [36]
**Taken from Custer and Krutchkoff [13]
110
-------
Table 17: Fresh water velocity component for the Potomac
Location,*
Miles from
Chain Bridge
0.0
2.69
4.78
6.53
7.84
9.71
11.82
14.39
16.58
19.0?
21. Ot
23.33
27.28
30.22
Fresh Water**
Flow Rate
ft/sec.
Cross sectional*
Area, fts
Fresh Water
Velocity,
mi/hr.
4,6O5.
30 , OOO .
24,3OO.
29,000.
34,300.
32 , 7OO .
47 , 600 .
49 , OOO .
43 , 600 .
59 , OOO .
66 , 5OO .
84,9OO.
111,OOO.
130 , OOO .
0.75
0. 1153
0 . 142
0.119
O.1O1
0.106
0.0075
0.0755
O.O847
O.O626
O.O555
0 . O435
O.O333
O.O284
Dept. of Interior
50 5O.
5O5O.
5050.
5O5O.
5O50.
5050.
540O.***
540O.
54OO.
5400.
540O.
54OO.
5400.
54OO.
*Hetling and O'Connell [36]
**Taken from unpublished U. S
Geological Survey data
***Increase due to volumetric flow of D.C. STP output
as recommended by Hetling and O'Connell [36].
Values for somo parameters could not be found as
functions of position. The following constant values
were taken for EG, EF, DO , , temperature, Kx and Kt
(corrected for temperature;, and land runoff: 1.O42 x 10~
square miles/hr, 1.042 x 1O~J square miles/hr , 8.O ppm,
27°C, 0.02/hr., O.O2/hr. anr> 9OOOO Ibs/hr/cubic mile,
respectively.
All these values but land runoff were taken from
Custer and Krutchkoff [13] An estimated value for LR
was necessary since none were available. The solution
was not found to be sensitive to the land runoff rate
in this range of values.
The upstream, XI, and downstream, XO, boundaries
were fixed at O and 3O miles from The Chain Bridge,
respectively. The minimum numbers of grid points
111
-------
necessary for a convergent solution of the BOD and OD
differential equations were found by experimenting
with the program and were set at 120 and 6O, respec-
tively. The initial concentrations for both BOD and
OD were 0.0 throughout the estuary. The initial time
corresponding to this was 0,0 hours. The minimum real
time necessary for steady state was found experimentally
to be approximately 4OO hours. The solution was run
for 5OO real time hours. The added time was necessary
in order to get output through several tidal cycles
after pseudo-steady state was reached. Predicted
concentrations were printed and punched out every
1.0 real time hour. This relatively small interval
was used so that information concerning steady state
concentrations within the tidal cycle could be observed.
Notice that an option exists for output in punched
card form. This option was utilized in the Potomac
verification. The card output of the differential
equations program is input to the analysis and limits
programs.
Data was printed out at 16 positions. The upstream
boundary condition for BOD was fixed at 3.6 ppm using
information from Jaworski [40]. The boundary value for
OD was arbitrarily selected to be l.O ppm from a
reasonable range of values The reaeration rate was
made a function of fluid velocity. The option of a
variable feed rate was not used as it would have made
the model verification more complicated and no data
was available over this time period for feed rate as
a function of time.
The only adjustment made on this data was to the
tidal component of velocity. The values for Vt 3.isted
in Table 16 were all multiplied by 1.5 to compensate
for using an average cross sectional tidal velocity.
This was necessary to account for the fact that the cross
sectional velocity gradient is not flat but actually is a
somewhat flattened parabolic shape during most of the tidal
cycle. The value of 1.5 was selected for two reasons:
First, it is the midpoint between no correction, 1.0, and
the maximum possible correction, 2.0, (for sampling at the
water surface, in the middle of the estuary under conditions
of pure laminar flow); and secondly, this value was selected
to bring the station results into agreement with observed
data. With this done it was found that the other stations
were in essential agreement also.
112
-------
The difficulties of using cross sectional average velo-
cities was recognized by Feigner and Harris [20a, page 20].
Using this data the estuary was modeled. It was
found that from the Chain Bridge down through the
15th or 20th mile that there was relatively good
agreement with the observed data but from the 2Oth
through the 3Oth mile, there was little agreement.
In the lower section (2O-3O miles) the predicted
concentrations both dropped to near zero values, as
all the BOD was oxidized and OD eliminated, while
the observed values remained at levels of 3.0, to
5.0 ppm OD. It was pointed out in the model discussion
that this is what would be expected if the parallel
series reaction were taking place instead of the
simple series reaction. Processes which are taking
place in the estuary are not being accounted for in
the model. This led to some disagreement in the upper
section (O-20 miles) because photosynthesis is not
being considered, but carbon and nitrogen recycling is
not yet important. However, in the lower section a
great deal of disagreement between the predicted and
observed values occurs because the interacting pro-
cesses of photosynthesis, algal growth and death
(or carbon and nitrogen recycling through organic
form), NH3-NO3-NO3 series reaction etc. have become
important.
For these reasons it was decided to make no attempt
to verify the model beyond the 2Oth mile and to adjust
the predicted values above 2O miles for photosynthesis
when necessary so that the average predicted concentration
over a full tidal cycle was the same as the mean
observed concentration over a tidal cycle. The ad-
justment necessary for OD were -0.10 ppm for station 1,
-0.55 ppm for station 2, +O.48 ppm for station 3 and
station 4 was omitted because it was below the 2Oth
mile. Although these adjustments are not large, ad-
justments of this type should not be necessary in an
estuary model. This is strong evidence that the nitrogen
and algae processes should be included in the estuary
model. Inspection of the adjustment for station 3
indicates that the lack of the recycling processes
has had some effect as far up as the station 3 (17.8
miles). Plots comparing the observed average concentrations
113
-------
to the adjusted predicted values for stations 1, 2,
and 3 are shown in Figures 18, 19, and 20. Inspection
of the figures indicates an excellent fit to the
stations 1 and 2 data and a good fit for station 3.
The concentrations for station 3 are very near the
maximum oxygen deficit level. This indicates that for at
least short periods of time, there were anaerobic condi-
tions. For this reason some lack of fit is expected.
The A program was used to calculate A values for
the four stations. As mentioned in the stochastic
component section the resulting average station values.
were as given in Table 18.
Table 18: Average values of A by station.
Station 1 Station 2 Station 3 Station 4
0.2260
O.26O3
0.0254
0.2O22
Table 19 is a summary of the A values as broken
into tidal phase subclasses.
Table 19: A values by tidal subclass.
Tidal
Class
1
2
3
4
5
6
7
8
9
1O
11
12
Station
1
0.167
0.191
O.185
O.131
O.253
O.270
O.226
0.453
O.239
O.133
O.131
0.334
Station
2
0.372
0.175
0.194
O.O97
0.137
0.104
0.329
0.666
O.188
0.263
0.232
0 367
Station
3
O.O41
O.O46
O.O43
O.O22
O.O01
O.O01
O.O64
O.O53
O.OO8
O.O18
O.O03
O.OO4
Station
4
O,
0,
,382
532
O.648
O.040
O.015
O.OO2
182
194
O.OO9
O.027
O.O79
O.315
0.
O.
114
-------
I 3
Ui
i
U
a
o
o
O
OOBSERVED OD MEAN
PREDICTED MEAN
1
1
0 02 Q4 Q6 Q8
PHASE
FIGURE 18 COMPARISON OF PREDICTED AND
OBSERVED OD CONCENTRATION AS
FUNCTIONS OF TIDAL CYCLE. FOR
STATION 1, POTOMAC ESTUARY
l.O
-------
H
H
OOBSERVED MEAN OD
PREDICTED MEAN CONCENTRATION
O Q2 Q4 Q6
PHASE
FIGURE 19 COMPARISON OF PREDICTED AND
OBSERVED OD CONCENTRATION AS
FUNCTIONS OF TIDAL CYCLE FOR
STATION 2, POTOMAC ESTUARY
-------
8
a
a
a
§
H
H
§
u
Q
O
OOBSERVED MEAN OD
^PREDICTED MEAN
1
1
1
1
Q2
Q8
Q4 06
PHASE
FIGURE 2O COMPARISON OF PREDICTED AND
OBSERVED OD CONCENTRATION AS
FUNCTIONS OF TIDAL CYCLE FOR
STATION 3, POTOMAC ESTUARY
LO
-------
The card output of the differential equations
program along with individual observed OD values pro-
vided by WQO were used as input to the analysis
program. The adjustment to the predicted means
were included internally in the program. The analysis
program gave the following output:
1, Adjustment concentration profiles through a
tidal cycle for stations 1, 2, and 3. See Figure 21.
2. Unadjusted concentration profiles through
the upper section for tidal phases of 0.0, 0.25, 0.50,
and O.75. Adjustment factors were available only at
the three sampling stations. See Figure 22.
3. Individual observed OD values, the corresponding
predicted mean OD value, and the number of observed
values which fell outside of the confidence limits.
More detailed representation of the BOD and OD mean
concentration profiles through the estuary for various
phases are shown in Figures 23-26.
These runs were initially made using a A value of
0.243 (the average of O.226 and O.260 which were not
significantly different from each other) for stations
1 and 2 and O.O25 for station 3. See Table 18. The
result was that the fraction of observed data outside
the predicted confidence interval was always slightly
higher than predicted. This can be explained by the
amount of variation in the true mean due to all other
sources not simulated. The A value for stations 1 and
2 was increased to 0.275 and the A value for station 3
was increased to 0.0475. The final value used is ob-
viously arbitrary since it is not possible to estimate
the variance component due to lack of fit. The results
then yielded slightly lower fractions predicted than
observed indicating that this was an over-correction.
However, no further adjustment was made. The results
are shown in Table 2O.
A pictorial comparison of the predicted mean and
confidence limits and the individual observations are
shown in Figures 27, 28 and 29.
118
-------
8
6 6
a
a
§
0
^^.^, ^\ STATION 2 _
11.8 MILES
STATION 1, 4.8 MILES _^.
0
Q2
Q4
Q6
Q8
LO
FIGURE 21 OD PROFILES THROUGH TIDAL PHASE FOR 3
STATIONS IN THE POTOMAC ESTUARY
-------
to
O
LOW TIDE
POSITIVE RUSH TIDE
NEGATIVE RUSH TIDE
HIGH TIDE
0
16
20
4 8 12
POSITION IN MILES
FIGURE 22 OD PROFILES THROUGH THE POTOMAC ESTUARY FOR
4 TIDAL PHASES
-------
'
9
8
6 7
CU '
§ 6
:
8
§
U
o
S
0
T
I
0.010
0_. 172 0.253
f ^'\*/ 0.333
/ / f-^
/ \ A V"\
7 X vx \ \
\/ \/\ \
-0.495
)
I
0 4 8 .12 16 20
RIVER MILE FROM CHAIN BRIDGE
FIGURE 23 BOD PROFILES FOR THE POTOMAC ESTUARY
AS FUNCTIONS OF TIDAL PHASE (O.O1 TO
0.495)
-------
8
0
H
H
( ]
: '
:
Q
O
0
0.253
0. 172
0.010
/W/0495
I
I
I
o
20
4 8 12 16
RIVER MILE FROM CHAIN BRIDGE
FIGURE 24 OD PROFILES FOR THE POTOMAC ESTUARY
AS FUNCTIONS OF TIDAL PHASE (O.O10 TO
0.495)
-------
e
a
'
: -,
;
Q
9
8
6
5
I
1
0.495
0.979
i
0 4 8 12 16 20
RIVER MILE FROM CHAIN BRIDGE
FIGURE 25 BOD PROFILES FOR THE POTOMAC ESTUARY
AS FUNCTIONS OF TIDAL PHASE (0.495 TO
0. 979)
-------
M
4-
e
a
px
7
6
H
H 4
Is
D 2
O
O
O 979
I
0.737
I
I
I
0 4 8 12 16 20
RIVER MILE FROM CHAIN BRIDGE
FIGURE 26 OD PROFILES FOR THE POTOMAC ESTUARY AS
FUNCTIONS OF TIDAL PHASE (O.495 TO 0.979)
-------
to
Ul
§
H
H
1
0
.INDIVIDUAL OBSERVATIONS
_PREDICTED MEAN AND CONFIDENCE
LIMTS
I
I
I
I
I
0
0.2
0.4
0.8
1.0
0.6
PHASE
FIGURE 27 COMPARISON OF PREDICTED MEAN OD CONCENTRATION AND
CONFIDENCE LIMITS WITH OBSERVED OD DATA AS FUNCTIONS
OF TIDAL CYCLE FOR STATION NO 1, POTOMAC ESTUARY
-------
ro
INDIVIDUAL OBSERVATIONS
PREDICTED MEAN AND CONFIDENCE LIMITS
0.1
0.4
0.8
1.0
0.6
TIDAL PHASE
FIGURE 28 COMPARISON OF PREDICTED MEAN OD CONCENTRATION AND
CONFIDENCE LIMITS WITH OBSERVED OD DATA AS FUNCTIONS
OF TIDAL CYCLE FOR STATION NO.2, POTOMAC ESTUARY
-------
to
9
8
6.
§
U 3
. INDIVIDUAL OBSERVATIONS
PREDICTED MEAN AND CONFIDENCE
LIMITS
0
0.2
0.4
0.8
1.0
0.6
PHASE
FIGURE 29 COMPARISON OF PREDICTED MEAN OD
CONCENTRATION AND CONFIDENCE LIMITS WITH
OBSERVED OD DATA AS FUNCTIONS OF TIDAL
CYCLE
-------
Table 20: Observed vs. predicted fraction of values
outside specified concentration confidence
interval for the Potomac Estuary
Fraction Predicted
Outside of C. I.
O.05
O.1O
O.15
O.20
O.25
0.30
O.35
0.40
O.50
Fraction Observed
Outside of C. I.
Station 1 Station 2
0.100
O 10
O.141
O.193
0.242
0.285
O.335
0.380
O.47O
Station 1
Station 2
Station 3
270 observations
126 observations
126 observations
0.055
O.087
0.127
0.167
O.199
0.246
0.31O
O.365
0.5OO
Station 3
O.087
0.111
0.111
O.135
0.151
O.175
0.184
0.230
0.477
OHIO RIVER
Between 1957 and 1963 a three phase program was
conducted on the Markland pool near Cincinnati, Ohio
(see [12]). The objective of this work was to
evaluate the effect of the Markland dam on
the waste assimilation capacity of the Ohio River.
Data taken in the third stage of this study (post-
impoundment conditions) was used for model veri-
fication. Individual BOD and DO samples were taken
every 3 hours at 8 stations in the Markland pool at two
depths. To help insure the validity of the uniform
cross sectional concentration assumptions, the average
sample value over the two depths was always used.
The section of the river between the Southern Rail-
road Bridge at Cincinnati (river mile 472.3) and a point
just below the great Miami River confluence (river
mile 492.3) was modeled.
128
-------
The information used in che study is given in
Tables 21, 22, and 23.
Table 21: STP outputs for the Ohio River.
STP
Location Cross Sectional Area Pollution Load*
Mill Creek 472.55
Bromley 474 OO
Muddy Creek 481.45
41,290 ft!
44,56O ft"
45,OOO ft:
135,450 Ibs/day
27,O20 Ibs/day
5,500 Ibs/day
*These values reflect first stage BOD loadings only. This
creates no difficulty since the nitrification process is
not important in the section of the river being modeled.
Table 22: Physical and biological information for the
Ohio River.
Variable or Parameter
Value
average temperature
saturated O? cone.
upstream boundary condition
BOD
OD
average volumetric flow rate
diffusion coefficient
adjustment to Kg(x)
tidal velocity
BOD and OD grid spacing
steady state time
time variation of feed rate
24°
8.25 ppm
1.78j xaken from observed
1.72 data stations 1 and 2
O.16 day (adjusted to 24°C)
0.05/day
14,8OO ft3/sec
O.24mileVhr
O.O Ibs/mile3/hr
3O,OOO Ibs/mile3/hr
none
none
\ mile
14O-20O hours
none
129
-------
Table 23: Fluid velocity as a function of position
for the Ohio River.
Position, Velocity
river mile miles/hour
472.35 0.269
472.55 0.244
472.60 0.226
477.55 0.236
481.45 0.224
482.65 0.196
486.80 0.217
489.6O 0.194
491.20 0.262
492.30 0.226
The only change necessary in these values for
modeling was in the iq (x) rate. The observed BOD data
indicated a very fast utilization of BOD in the river
Just below the Mill Creek outfall To reflect this in
the model, a Kx rate 5 times the suggested value was
used for the first 4 miles below Mill Creek and a
value twice the suggested value was used for the next
8 miles. The suggested value was found adequate for
the remaining 8 miles. This somewhat empirical changing
of the K! was done to make the predicted profile for
the mean BOD concentrations agree with the observed
values. A test of this procedure can be made now by
seeing how closely the predicted OD profile fits the
observed OD concentration. If a close fit is obtained
it is probable that the method used above is correct.
The fit obtained was good as can be seen in Figure 30.
Thus it can be seen that this model can accurately
predict mean concentrations when the nitrogen processes
are not important.
Now that the mean concentration has been predicted?
the predicted distribution around the mean must be
130
-------
H
U)
OMEAN MEASURED OD
DMEAN MEASURED BOD
470
475
490
480 485
RIVER MILE
FIGURE 30 A COMPARISON OF PREDICTED AND OBSERVED
BOD AND OD MEAN CONCENTRATIONS IN THE
MARKLAND POOL OF THE OHIO RIVER
495
-------
verified. Since the more elaborate A predicting program
had not yet been completed, the river A program was
used. The individual BOD and OD values were fed to
the program for stations 2 through 8. The program averaged
the two individual values at the two water depths and
then subdivided the data according to station (7 classes)
and time of day (8 classes) and determined A values in
each subclass. Tables 24 and 25 are summaries of these
results for BOD and OD.
Inspection of these results indicate that the OD
A values are greater then the corresponding BOD A
values. This was verified by statistical analysis.
There is less then 1 chance in 100O that the observed
A values would be this different if they were really
equal.
Next the river analysis program was used for the
distribution verification. The average station A
values, row averages, were incorporated into the LIMRIV
subroutine. Because there was excellent agreement
between the predicted and observed means, the A values
did not have to be adjusted for lack of fit to the means.
Also an empirical correction was made to the way the
poisson limits were determined. A reasonable correction
was made for one confidence level for BOD so that the
observed number of values outside of the confidence
interval should agree with the predicted. Then with
the correction method remaining constant, all other
confidence levels for BOD and then OD were run. The
correction method used was the following. The length
of confidence interval was multiplied by 0.6(0.5-A.)
if \ < O.5, \ is the poisson parameter. No correction
was made if \ '^ O.5. Thus, the smaller the X value
the more correction was made. The results obtained
this way were quite good and are given in Table 26.
These results are very good. Both the mean
concentrations and the distributions about these
means have been very closely fit.
132
-------
Table 24: A summary of A values for BOD for the Ohio River
U)
Station
NO.
2
3
4
5
6
7
8
1
O.O49
0.140
0.200
O.O64
0.090
0.031
O.035
Time of Day
2
O.085
O.107
0.172
0.181
0.237
0.041
0.049
3
O.124
0.097
0.171
0.345
O.236
0.089
0.056
Classification
4
O.124
0.143
0 . 152
O.255
0.3O7
0.069
0.062
5
0.076
O.138
O.147
0.143
0.133
O.062
0.039
0
0
O
0
0
O
0
6
.045
.135
.213
.157
.131
.087
.073
0
0
O
0
0
0
0
7
.067
.176
.159
.095
.087
.067
.055
8
O.O30
0.145
0.111
O.079
0.077
0.089
0.063
Row
Average
O.O74
0.135
0.166
O.165
0.162
0.067
0.054
co 1m
aver. 0.087 0.125 0.160 0.159 0.105 0.120 0 100 0.085 0.118*
*The overall average BOD A value.
-------
H
10
Table 25: A summary of A values for OD for the Ohio River.
Station Row
No __ 1 2 3 4 5 6 7 8 Average
2 0.1O7 0.140 0.102 O.206 O.099 0.1O2 0.1O4 O.142 0.125
3 0.112 O.152 0.267 0.309 0.242 0.268 0.156 0.102 0.201
4 0.206 0.183 0.284 0.247 0.269 0.223 0.182 0.104 0.212
5 0.258 0.204 O.217 0.181 O.118 0.200 0.254 0.270 0.214
6 0.242 0.185 0.202 O.195 0.192 0.225 0.192 0.223 0.207
7 0.130 0.095 0.115 0.098 0.124 O.198 0.177 0.102 0.130
8 0.087 0.084 0.097 0.100 0.102 0.134 0.140 0.097 0.105
colm
aver. 0.163 0.149 0.183 0.191 0.164 0.193 O.172 0.150 0.171*
*The overall average OD A
-------
Table 26: Observed vs. predicted fraction of values outside specified
concentration confidence intervals for the Ohio River.
Fraction Predicted Fraction Observed Outside of C. I. by Station
Outside of C. I. 3 4 5 6 7 8_
BOD
0.10
0.15
0.20
0.30
0.40
0.50
0.148
0.185
0 236
0.333
0.429
0.563
O.O45
0.141
0.274
0.318
0.485
0.510
0.082
0 156
0.163
0.245
0.362
0.532
0.148
0.170
0.230
0.304
0.429
0.541
0.126
0.141
0.245
0.311
0.415
0.445
0.133
0.200
0.252
0.296
0.429
O.490
U)
ui OP
0.10
0.15
0 20
0.30
0.40
0.50
0.140
0.163
0.208
0.341
0.378
0.452
0.096
0.126
0.222
0.318
0.400
0 . 482
0.104
0.148
0 170
0.296
0.415
0.482
0.111
0 126
0.170
0.267
0.407
0.490
0.111
0.119
0.140
0.215
0.349
0.467
0.140
0.156
0.192
0.267
0.341
0.437
Station 1 and 2 were not used since their values had been used as upstream
boundary conditions. There were 135 observations/station.
-------
DELAWARE ESTUARY
Initially it was planned to model the Delaware
Estuary as was done for the Potomac Estuary and Ohio
River. However, a lack of sufficient DO and BOD
sample values taken over a short period of time was
not available for verification of the stochastic
model.
Listed in Tables 27, 28, and 29 is that information
which was found and which would be good starting
information for modeling the Delaware.
Table 27: Physical and biological data for the Delaware
Variable Value
Upstream boundary conditions
BOD 2.0 ppm
OD 1.0 ppm
Correction for K.s(x) yes
K! and Kd O O17 hr
LR rate O.O Ibs/mile3/hr
DB rate O.O Ibs/mile3/hr
It would be useful to make a comment here concerning
the amount of work necessary in doing this modeling.
The first time that a particular stream or estuary is
modeled a great deal of time is required to find
information which is pertinent to this model. This is
true for several reasons including the fact that this
model is quite different from the presently used model
and that this is a stochastic model which requires
many OD and/or BOD observations for verification. The
important point is that once a stream or estuary has
been modeled, additional work can be done quite quickly.
136
-------
Table 28: Fresh water flow rate for the Delaware
Position Flow Rate
Miles from arbitrary miles/hr
Point 1O miles above
Trenton, N. J.
10. OO
13.79
17.57
21.36
25.15
28.93
32.72
34.62
36.51
38. 4O
40.29
42.19
44.08
46.00
0.479
0.205
O.156
0.136
0.118
0.10
0.0805
O.0676
O.O66
O.O613
O.O593
O.0561
O.0554
0 O50
Table 29: Reaeration rate for the Delaware
Position Reaeration rate
Miles from point 1/hrs
10 miles above
Trenton, N. J.
11. 9O
15.69
19.47
23.26
27. 04
33.67
35.56
37.46
39.35
41.24
43.14
45.03
0.027
0.015
O.OO96
O.O096
O.O067
O.OO92
0.0092
O.0067
O.0067
O.0067
O.O05O
O.O05O
137
-------
USING THE MODEL: CASE STUDIES
Frequently when a physical system is being
analyzed the question is raised, "What if...".
In our case, what would happen to the pollution and
oxygen deficit levels in a particular estuary if
some specific change were made in it. In this
section several of these questions are answered for
the Potomac estuary and the method of answering
others will be demonstrated using the model developed
in this work.
The first set of variations to be considered is
the method of introducing the pollution into the estuary.
Several variations in the method of introducing the
pollution are considered here:
I Introduce pollution at the current STP
positions but at a rate proportional to the fluid
velocity at the STP outfalls. This will permit
maximum dilution given that the outfalls are fixed.
II. Introduce it at a constant rate into the river
just above the tidal portion. This may permit more
uniform dispersion.
III. Introduce it as a line source over the upper
3O miles of the estuary. This method would permit
uniform loading and prevent one section being over
loaded
IV. Introducing it at a constant rate at the
present STP outfalls.
For lack of better information, Case IV is
considered the method of present operation. The
simulation of Case I is accompolished by multiplying
the feed rates of the standard, Case IV, by 1.57O8|siN(uut)
This is the same factor used to make the reaeration
rate constant proportional to tidal velocity.
Case II is simulated by calculating the pollution
concentration if all the pollution were introduced
into the river beyond any tidal effect. The concen-
tration of pollution from upstream is added to this
138
-------
and the sum in ppm is used as the upstream BOD
boundary condition.
Case III is simulated by dividing the pollution
rate, in Ib-BOD/hr by the estuary volume in cubic
miles and incorporating the result in to the model
as land runoff.
The BOD and OD profiles at high tide resulting
from this simulation are shown in Figures 31 and
32 respectively. A brief inspection of these figures
indicates that Case I has little effect. Case II
has a strong detrimental effect. Introducing the
pollution above the tidal section would not be a good
idea. Case III, uniform loading, seems to yield a
large inprovement in the maximum oxygen deficit.
Next a series of three run groups are shown and
discussed. In each group a process parameter or
condition will be set at its standard level, one
half its standard level and twice its standard level.
First to be considered is reaeration rate K8.
The results, at high tide, obtained for this group of
runs are shown in Figures 33 and 34 Inspection of
the BOD curve indicates that anaerobic conditions would
be reached if K3 were reduced by 5O%. Where the OD
profile would drop below 8 ppm (0 dissolved oxygen)
is not known. The small differences in the BOD
curves are due more to the fact the different data
plotted was not all taken at exactly the same phase
value but ranged from 0.99 to 1.01. The BOD curve
which would actually result for the %K3 case is not
known since this is not an anaerobic model.
Next to be considered is the biological utilization
rate Kx, see Figures 35 and 36. The expected result
of quicker utilization of BOD with a greater Kx
value is seen in the BOD curve. The OD curve indicates
a quicker and higher OD peak with greater fq rates, as
would be expected.
139
-------
e
8-
(X
g
H
H
-------
-I 1 1
-II INTRODUCE ABOVE TIDAL
8
6
-
2:
o
H
H
H
O
§
a
o
1
0
T
T
/ X PORTION OF RIVER
/ \
/I SET FEED RATE V
PROPORTIONAL
/ TO FLUID
/ VELOCITY s
/ // 'v. \v
IV STANDARD
CURRENT METHOD
III INTRODUCE
UNIFORMLY IN UPPER
3O MILES
1
1
0 4 8 12 16 20
MILES FROM CHAIN BRIDGE
FIGURE 32 OD PROFILES RESULTING FROM FOUR DIFFERENT
METHODS OF POLLUTION INPUT TO THE POTOMAC
ESTUARY
-------
10
9
8
e
a 7
H
H
§ 3
D
§ 2
O
1 I I I I
n *
18
20 22
0 2 4 6 8 10 12 14 16
MILES FROM CHAIN BRIDGE
FIGURE 33 BOD PROFILES RESULTING FROM THREE LEVELS OF
REAERATION RATE FOR THE POTOMAC ESTUARY
-------
8 -
0.20 LEVEL CONFIDENCE
LIMITS F.OR THE STANDARD
02 4 6 8 10 12 14 16
MILES FROM CHAIN BRIDGE
FIGURE 34 OD PROFILES RESULTING FROM THREE LEVELS OF
REAERATION RATE CONSTANT FOR THE POTOMAC ESTUARY
-------
£
td
L>
§
0
§
o
4 8 12 16
MILES FROM CHAIN BRIDGE
FIGURE 35 BOD PROFILES RESULTING FROM THREE LEVELS OF THE
RATE CONSTANTS FOR OXYGEN AND NON-OXYGEN CONSUMING
PROCESSES FOR THE POTOMAC ESTUARY
24
-------
0.20 LEVEL CONFIDENCE
LIMITS FOR THE STANDARD
8 12 16
MILES FROM CHAIN BRIDGE
FIGURE 36 OD PROFILES RESULTING FROM THREE LEVELS OF THE
RATE CONSTANT FOR BIOLOGICAL UTILIZATION OF BOD
FOR THE POTOMAC ESTUARY
-------
The effect of various STP output rates can be seen
by inspecting Figures 37 and 38. The OD curve indicates
that anaerobic conditions would be reached with feed
rates at twice their normal level. Once again the exact
BOD curve corresponding to this cannot be predicted.
The last group studied was of various levels of
the diffusion coefficient, E. Increasing the E value
seems to have more effect on the BOD and OD curves
than reducing it. The greater the diffusion rate,
the better the OD conditions. See Figures 39 and 40.
146
-------
o
16
14
6
S1 12
ex
O 10
M
H
H
§
(J
g
U
8
CQ
8
0
0
I
20
4 8 12 16
RIVER MILE FROM CHAIN BRIDGE
FIGURE 37 BOD PROFILES RESULTING FROM THREE POLLUTION
INPUT RATES FOR THE POTOMAC ESTUARY
-------
00
0.2O LEVEL CONFIDENCE
LIMITS FOT? THE STANDARP
8 12 16
RIVER MILE FROM CHAIN BRIDGE
FIGURE 38 OD PROFILES RESULTING FROM THREE POLLUTION
INPUT RATES FOR THE POTOMAC ESTUARY
-------
vO
0 2 4 6 8 10 12 14 16
MILES FROM CHAIN BRIDGE
FIGURE 39 BOD PROFILES RESULTING FROM THREE LEVELS OF
DIFFUSION RATE CONSTANT FOR THE POTOMAC ESTUARY
-------
Ul
o
8
* "
a
§
§ 2
O
I I I I I --I
N
N
-O.20 LEVEL CONFIDENCE
LIMITS FOR THE STANDARD
I
I
I
I
I
I
I
I
02 46 8 1O 12 14 16 18 20 22
MILES FROM CHAIN BRIDGE
FIGURE 4O OD PROFILES RESULTING FROM THREE LEVELS OF
DIFFUSION RATE CONSTANT FOR THE POTOMAC ESTUARY
-------
A METHOD FOR PREDICTING A
As was mentioned in the INTRODUCTION, this task
had many subprojects which were necessary in order to
determine the nature of A. Several of these sub-
projects are discussed in the INTRODUCTION. Here
we will give the details of two of these subprojects .
CONTINUOUS STATE SPACE
The stochastic models for streams and estuaries
considered by Thayer and Krutchkoff, and Custer and
Krutchkoff , and the model considered in this report
were derived by considering discrete processes and
then letting 6t -* O in order to obtain continuous
time solutions. Thayer and Krutchkoff obtained a
set of differential-difference equations and then
used the probability generating function technique
to obtain a solution to these equations. Custer and
Krutchkoff and the model derived in this report
obtain solutions to a set of difference equations and
then use continuous approximations to estimate the
BOD and OD concentrations for the estuary. These
approaches are correct, although the models could
have been derived by initially considering the pro-
cess as continuous. Here we present a continuous
space derivation and then use the simple model of
Thayer and Krutchkoff to illustrate the similarities
and differences in the two approaches.
Let X(t) represent the pollution concentration
at time t. Also let X(t) and X(r) take on values x
and y at times t and r, respectively. We will treat
the pollution model as a continuous Markov process.
More specifically, we assume that there exists a
density f(x,t|y,r) such that
a
t time = t|x = y at time = r]
x
J f(z,t|y,r) dz. (r
-------
This is the probability that the pollution is x or
less at time t given that it was exactly equal to y
at some previous time r
The assumption of the Markov property means that
given the present state of the system the future
behavior of the system is independent of any past
behavior. It can also be shown that f must satisfy
00
f(x,t|y,r) = Jjf (x,t|z,s)f (z,s|y,r)dz
r
-------
and the forward equation"
3f(x,t|y,r) = Ji[a(x,t)f(x,t|y,r)]
dt dx
+%£[b(x,t)f(x,t|y,r)] (206)
Either equation may be used to find the density f .
A solution to the forward equation will provide f
for fixed initial conditions; namely y fixed and r
fixed. Since, by assumption the process is homo-
geneous over time, i.e. the transition probabilities
depend only on the tn".me difference t-r, we can write
a(y,r) = a(y) b(y,r) = b(y)
a(x,t) = a(x) b(x,t) = a(x) (2O7)
Appropriate substitutions can be made in equations
(205) and (2O6) .
THE MEAN AND VARIANCE FOR THE CONTINUOUS MARKOV PROCESS
Now assume that a(xj and b(x) are functions such
that the forward equation can be written
df = anf+(a, +aax) df+(a3+a4x) daf .
at * dx 3xs
(208)
Such a form will arise whenever a(x) and b(x) are
linear. Rather than going immediately into the
assumptions about Kx , Kg , K3 , L^ , D0 , and A df the
pollution problem, let us first solve the more
general equation above. Thayer's assumptions, as
we shall see, simply assign specific values (depending
on the K's) to the constants in the general equation
above .
Finding f from the equation above is an exception-
ally difficult task. The first two moments, however,
are not too difficult to obtain. Let us then find the
153
-------
mean and variance of X(t). Let f be a density
function of the random variable X' which also involves
another mathematical variable t. Suppose X is described
by the partial differential equation
df = a0f+(a1+aax)df+(a3+a4x)d*f.
dt dx dx8
(209)
We wish to find the first two moments of X, namely
u (t) and a*
Let us multiply the whole equation (209) by x and
integrate over the range (o, «) .
00 00 CO
J xdfdx = a0J xfdx+J" (at +aax)xdfdx
dt °
+ J (a3+a4x)xBafdx. (21O)
0 "ix3"
Equation (210) can be written
CO
= a0|ax(t)+(a1+a3x)xf |
00 00
-J0(a1+2aax)fdx+(a3+a4x)xafl -J (a3+2a4x)9fdx.
~5x o o dx (211)
by using the integration by parts. Therefore
dt
- ( a3 +2a4 x) f | + j Q ( 2a4 ) f dx
= (ao-2a3)u (t)+2a4i-al .
(212)
154
-------
This is an ordinary differential equation for
\JL (t) . From the theory of ordinary differential
equations any linear first order equation of the form
dz+P(s)z = Q(s) (213)
ds
has solution
-J P(y)dy
+ ce . (214)
Application of formula (214) to equation (212) provides
/*x +(a0-2a8)t _t -(a0-2a3)t
[ix(t) = e J (2a4-a1)e dt
+(a0-2a,)t X °
+ ce
+(a0-2ag)t -(a0-2a3)t
= e (2aA-a, )[e -l]
-(a0-2a?)
+ (a0--2aa)t
+ ce
... (aq-2ag)t
(2a,-a0)
(a0-2a3)t
+ ce . (215)
Now letting nx(t) = E{x8|t], multipling equation
(209) by x and integrating over the range (o, <=°)
one obtains
= ao
j x f<*x+j' (ai+a3x)x39fdx
+ J (a3+a4rx)xS£vfdx (216)
0 - Sx8
155
-------
or a,
XX 0
QQ 1"^^ ^^
-f (2a1x+3a3x3)fdx+(a3+a4x)x39f-J (2a3x+3a4x?)9fdx
*^ rt -x. ^* ^ _ .
= a0rix(t)-2a1|ix(t)-3aBTix(t)
rt
-(2a3x+3a4x )f| +J (2a3 +6a4x)fdx
= (a0-3a8)ri:x.(t)-2a1|ax(t)
(217)
Applying formula (214) to (217) above,
CO
9
rix(t) = e
t
(a0-3a3)t (a0-3aa)t
+2a3]e dt + ke . (218)
If the constants are specified, Moc^) can easily
be determined. After finding |dx(t)> cr3x(t) can
easily be evaluated by putting Hx(t) in (218) and
then setting
a«x(t) =
COMPARING WITH THAYER AND KRUTCHKOFF
Thayer and Krutchkoff assumed that pollution
entered the streams in discrete increments of size
A and the factors which cause the concentration of
pollution x to change are as given in the INTRODUCTION.
Directly from these factors one can obtain that
E(Jump) = E(iA) = [La-(K1+K3)x]h+o(h)
and (22O)
VAR(Jump) = VAR(iA) = ^[l^ +(Kj +K3 )x]h
+o(h8) (221)
156
-------
where i is the number of unit jumps in time period h.From
the general results on continuous stochastic processes
[6], it is reasonable to assume that the infinitesimal
mean a(x) and variance b(x) given previously are
proportional to the pollution concentration. Thus, if
the mean and variance of the Jump are given appropriately
by (22O) and (221) then a(x) and b(x) become
a(x) = La-(K1+K3)x (222)
b(x) = [La+(K1+K3)x]A. (223)
The parameter A considered in this way is not a
mechanism for discretizing pollution concentrations,
but is merely a scale factor in the basic variance of
the problem. If A were large, x could undergo wide
swings in a time increment h; if small, x would remain
fairly stable. We do not need to consider pollution
as coming in A-size increments. A is a characteristic
of the stream or estuary and of the biological
process .
Let us now write the forward Kolomogorov equation
with a(x) and b(x) given by equations (222) and
(223) . This becomes
b±_ = J3[a(x)f]+%a£_[b(x)f]. (224)
St 9v~
Thus, as a continuous analog to the Thayer and Krutchkoff
assumption
at ax
(K1+K3)x)f]
= -LaSf+(K1+K3)xaf+(K1+K3)f
ax ax
+K3 ) Bf+(K1 +K3 ) af+(Ka +K3 ) x3af3
2 ax ax ax
157
-------
ax
Thus,
-(Kj+Kg) t
+ce
and
J
t x
J e
1 +K3 ) A+(KX +K3 ) x) M+A
9x 2
(225)
= -La
(226)
-2(K1+K3)t
= e
-2(K1+K3)trr ..
= e {[(K1+K3)A+2La]
J* e2 <*! +K3 )
-2(K1+K3)trr
= e s; {[(K1+K3)A+2La]
.+o,
x 3; }dt
_ 2(K1+K3)t
L. A fe l -1 3/ -1]+K]
2(K1+K3)
= e
-2(K1+K3)t
[(K1+K3)A+2La]
K1+Ka
158
-------
2(K1+K3)t
_A [e -1
2(K1+K3)
= e
-2(K1+K3)t
2(K1+Ka) (K1+K3) Kx+K
2(K. +K3) t
V l 3l -1
2(iq
.fe
2
2 (Kx
= e
t (Ki+Kg
-e
[(K1+K3)A+2LB ]
'-!]
2(K.-*-K3)t
V x 3/ -l
= e
-2(K1+K3)1
[e
-2(K1+K3)t -e(K1+K3)t
[1-e J+Ke
+K3 t
2(K1+K3)
2(KX+K3)
159
-------
(227)
and
a
-c e
= H (t)- L,
2(K1+K3)
*T
2(K1+K3)
a -2(k1+K3)t
+(k-c )e X
-(K1+K3)t
-(K1+K3)t (K1+K3)t
+ce [l-e 1+ U
-2(Kl+K3)
2(K1+K3)
(228)
where
M°) = c g
and g (o) = K-c .
.X.
3
Now suppose that c=L^ and CT x(°) = °> then
and
(229)
a (t) = A
2(K1+K3) (K1+K3)
160
-------
-2(K1+K3)t -(iq+KgJt -2(Kz+K3)t
e +La e -L» e
2(K1+K3)
-2(iq+K3)t
+ Lft
2(K1+K3) 2(K1+K3)
= A
1-e
-(K1+K3)t
(230)
The mean (229) ana variance (230) are identical
to the mean and variance for the amount of pollution
given by the corresponding equations in the Thayer
and Krutchkoff model. Thus, we have shown that one
obtains identical means and variance for the amount
of pollution using either a continuous approach or
a discrete approach and then letting h -> 0. The
fundamental difference between the approaches is the
interpretation of A. Using the "continuous derivation,
A is given a much more meaningful interpretation
with respect to the actual physical situation.
THE TWO STAGE METHOD FOR PREDICTING A
The first stage of tn« TWO STAGE METHOD
takes all the available data and checks to see how
to factor the variables to obtain a reasonable with-
in factor estimate of A. These factors and the
estimates of A are then put into a standard regression
program to obtain the best least squares fit. This
is the second stage.
If used with a good deal of insight, as to which
factors are important, the first stage will make op-
tional use of the data available. If used without
this, the first stage program will still do a reasonable
job in deciding which factors and how many levels
are required for a reasonable regression equation.
Since the second stage program is any standard
161
-------
regression program we will only discuss the FIRST
STAGE PROGRAM here.
THE FIRST STAGE PROGRAM
The FIRST STAGE PROGRAM FOR PREDICTING DELTA
was written so that more efficient sets of deltas can
be obtained in order to form an accurate regression
type prediction model. This program will handle up
to 6 variables, one of which will be used to calculate
the deltas. The variable will be referred to as the
dependent variable. The other variables will be
referred to either as independent variables or as
factors. These variables may be punched anywhere on
the data card because no standard data input format
is used. The program sorts the data into cells
according to the number of levels pla.ced on each
factor and to the range values or cut-off points for
each of these levels.
As an example of this, suppose that there are
3 variables, the first being the dependent variable
(e.g. OD), the second variable factor 1 (e.g. tempera-
ture) ; and the third variable, factor 2 (e.g. BOD
concentration). One may, for example, first decide
to try 3 levels on factor 1 and 4 levels on factor 2.
The range values or cut-off points for the levels of
factor 1 might be 65.0 and 80.O, and for factor 2
8.O, 12.0, and 16.0. Thus, if an observation on
factor 1 is less than or equal to 65.0, it will be
classified as level 1 of factor 1. If it is greater
than 80.0, it then falls in level 3. Thus, if factor
1 was 55.6 and factor 2 was 16.5, then this observation
would be level 1 of factor 1 and level 3 of factor 2
and would thus fall in cell (1,3).
The programmer can decide on the number of levels
he would like to start with for each factor and also
the range points. The program will sort the data
according to these levels and will store these facts
in the cell corresponding to these factor levels.
The program then prints out a histogram showing the
number of cells that had 0 observations in it, 1
162
-------
observation in it and on up to the number of cells with
19 observations in each. This histogram is truncated
at 20 and thus if a cell has 20 or more observations
in it, these cells are all considered as having 20
observations by the histogram. This histogram is
made first over all levels of all factors. It is then
broken down for each factor at each of its levels.
For an example of one of these histograms see the
sample output in the appendix. From runs like this
the programmer can change his range values and number
of levels in an attempt to have enough observations
in most cells to compute accurate delta values. If
desired, the program will just sort and print the
histograms.
It is advisable to run the program several times
to decide on the number of levels and the Cut-off points
for these levels, and then make one final run and have
the deltas computed and punched. The programmer may
also set the minimum number of observations that must
be in a cell before a delta for that cell is calculated.
This minimum must be at least 2 since delta is a
function of the variation within the cell. Therefore,
to obtain an estimate of this variance, we need at
least 2 observations. Obviously, we can get a much
better estimate of the mean and the variance with
more observations. The estimators used to calculate
the sample average and sample variance are:
Xn = L, X, (231)
i=l
and
n _
s8 = _1_ E (X.-X,)3 (232)
n-1 i=l
where n is the number of observations in the particular
cell in which we are calculating the delta and Xt
refers to the value of the dependent variables for
i=l, 2, ..., n. Delta is then calculated as
s
A = s/Xn . (233)
163
-------
This is done for each cell for which the number of
observations equals or exceeds the minimum number
specified.
The level averages are computed for each factor
at each level. This means that for all values of
factor 1 that fall in level 1, the average value was
computed. The average was computed for each level
of each factor. Thus, if factor 1 has 4 levels then
4 level averages will be computed. When the A is
computed, it is printed in the output and is punched
on a data card in the following way:
1. The number of observations in the cell from
which A was computed.
2. The value of A.
3. The level average for factor 1 for the level
associated with cell for this A.
4. The level average for factor 2 for the level
associated with cell for this A.
5. The level average for factor 3 .
This continues for all factors.
If one requires the level numbers printed and
punched instead of the level averages, the program can
be easily modified. In the program listing at format
number 59, appears eight lines with AVE on the right
side of the printout (columns 75-77). Directly
below these lines are comment cards which explain how
to replace these cards with AVE, in order to have level
numbers punched instead of level averages.
If the number of observations of the cell associated
with levels L2, L3, L4, L5, L6 of factors 1 through 5
respectively, is less than the specified minimum, then
the A is not computed and a card is not punched for
this cell. The cell identification and number of
elements in the cell is printed in the output along
with the deltas and level numbers. It is printed in
a different format and is easily distinguished from
the cells that had deltas computed. The following
format is used:
164
-------
ICOUNT (1, L2, L3, L4, L5, L6) = n
where L2 is the level number for variable 2 or factor
1. If you had only 4 varaibles, when L5 and L6 would
be 1's. The level of the first variable, the dependent
variable, will always be 1. The number of observations
in the cell is n. See the sample output in the appendix.
When we have the deltas calculated, we know from
which cells no deltas were computed; and from the deltas
that were computed, we know how many observations were
used to compute this value. Ideally, we would like
to have 5 or more observations in each cell and also
approximately the same number of observations in each
cell. This would give us approximately the same
precision for each delta. Obviously this is not always
possible. This program is an attempt to help to the
investigator obtain this result.
There are several restrictions to this program,
the first being that the dependent variable is considered
in the program as variable number 1. It is not necessary
to have A punched with the dependent variable as the
first on the card, however, because the program re-
orders the A variables as they are read. This way
one can make one run with OD as the dependent variable
and later with BOD as the dependent variable. Another
restriction is in the number of levels the factors can
have. One factor which must be renumbered as factor
number 1 can have up to 10 levels. All other factors
can have no more than 5 levels. Also, as previously
stated, one can have only 5 factors and 1 dependent
variable In the order that the variables are read
in, they are considered as variables 1, 2, ..., NVAR
where NVAR is the number of variables (NVAR £6).
.You next tell the program how to rearrange the variables
so that the dependent variable will be variable 1;
variable 2 will be factor 1 (if a factor has more than
5 levels it must be this one); and the other factors
will be variables 3 through NVAR.
When working with esturial data it will pay to
165
-------
use the tidal phase as a factor. Subroutine TIDAL may
be used to have a tidal phase returned between 0.0 and
1.0. One might also need a program to change DO
to OD, for the deltas should be computed from the variable
OD.
Data control cards, which are read by the program,
explain the incoming data to the program. The data
control cards should be punched as indicated below.
Card
Number Columns Description
10
11-20
30
40
44-45
the number of variables (including
dependent variable) (NVAR ^6)
the number of data cards (put in
the rightmost columns; i.e. if 100
data cards put the 1 in col. 18)
the number of format cards (^2)
put a 1 in this column if you desire
the deltas computed and punched, if
not leave blank
the minimum number you desire in a
cell before computing A
Card
Number Columns Description
5
10
This card is used to rearrange the
variables. As the variables are read
in from the data cards, they will initally
be called variables 1, 2, ..., NVAR in
the order they are read in. The dependent
variable must be rearranged to become
the first variable. If any factor has
more than 5 levels, it must be rearranged
as variable number 2. No other factor
may have more than 5 levels
Put a K in this column if the kth variable
is to be the dependent variable.
Put an m in this column to make the mth
variable read in as the 2nd variable
166
-------
(i.e. the first factor).
15 Put an n in this column to make the
nth variable the 2nd factor.
continue for as many factors as
were read in.
(When we now refer to variable number i, we are
referring to the ith rearranged variable.)
3 5 the number of levels of factor 1
1O the number of levels of factor 2
15 the number of levels of factor 3
continue for as many factors as
you have (NVAR-1)
(If a factor is to be sorted into all values >x and
all £x, then it will have 2 levels, and its one range
value will be x.)
4 consider for example that factor 1
has n levels (n^lO)
1-1O Put the upper range for level 1 of
factor 1 such that if the value is
less than or equal to this number,
it will be classified as level 1.
Note: This number must be a real
number not an integer, Example: 3.O,
not 3.
11-20 The upper range of level 2 of factor
1 such that if the value is less than
or equal to this number but greater
than the number in columns 1-1O, it
will be classified as level 2.
21-3O
167
-------
Card
Number Column Description
Continue to the (n-l)th level. This
number gives the upper range on the
(n-l)th level. All values greater
than this (n-l)th range number will
be classified as the nth level.
Do the same thing for factor 2, on
a new card.
Continue this until you have given
the range of all levels for all factors.
This card or cards indicates the format
that will be used to read the variables
from the data cards. The variables
must be read in as real numbers , not
as integers. Start in Column 1 with a
left parenthesis, then use standard
Fortran formating, ending with a right
parenthesis. Example: Suppose we have
4 variables with the decimal points
punched in the cards with numbers in
columns 6-1O, 20-21, 30-41, and 76-77.
With the ( in col. 1 the card would
look like
(5x,F5.0,9x,F2.0,8x,F12.0,34x,F2.0).
If you have integers on your data cards,
such as sampling stations 1, 2, and 3,
just read this integers as a real number
with an Fl.O format.
Following these cards are the data cards.
168
-------
PREDICTION EQUATION FOR THE OHIO
The first ;tage program for predicting A was
first used on data from the Ohio River. The original
variables were station number, time, temperature, DO,
and BOD. A simple program was first written to change
the DO variable to OD. CD was then used as the dependent
variable and the others were used as factors 1, 2, 3,
and 4. In our final run to compute the deltas, we used
7 levels for station number, 4 levels for time (2:15 pm
was read in as 14O0015), 2 levels for temperature, and
3 levels for BOD. We thus had a total of 168 cells to
compute the deltas from. After sorting, there were 68
cells with less than two observations in them, so we
had 100 deltas computed . The same thing was done again
using BOD as the dependent variable and OD as a
factor.
With the output of this program, we used the deltas
as the dependent variable and the factor level averages
as independent variables in a standard regression
program. We used a multiple regression program from
the Biomedical Computer Programs, BMD03R. Any standard
regression program would work The best regression fit
was obtained using the model:
y = -0.1998+0.0823X1+O.002Xg+0.0078X3
-0.0081X4 -0 .0088X-L a +O . 00004X3 8 ( 234)
where
y is A (OD)
Xx is the sampling station number
X3 is the time of day
X3 is the temperature
X4 is the BOD.
g
Only the regression coefficients for Xx and Xa were
significantly different from zero when using a t test.
These coefficients were significant at the 97%
significance level. This indicates that the average
value at each station is as good a representation of A
169
-------
as can be expected from the type of data available.
That is, A does not vary significantly (except from
station to station) with any of the variables for
which data was available.
PREDICTING A FOR THE POTOMAC
THE FIRST STAGE PROGRAM FOR PREDICTING A was also
used on Potomac estuary data and the deltas were
computed. The original variables were DO, time, station
number, and temperature. The DO variable was changed
to OD to be used as the dependent variable and using
the subroutine TIDAL the tidal phase was computed using
the date and the time of day. We used 1O levels on
tidal phase, 4 levels on station number, 4 levels on
time, and 2 levels on temperature. There were thus
32O cells of which 32 had fewer than 2 observations.
The multiple linear regression program was then run
using the deltas as the dependent variable and the
factor level averages as the independent varaibles.
The best regression fit was obtained using the following
model:
y = 2.73054-O.07955XJ-0.51446X8
+O.O2114X3-0.02569X4+0.11264X8S-O.00078X38 (235)
where
y is A (OD)
Xx is the tidal phase
X3 is the station number
Xs is the time of day
X4 is the temperature.
All regression coefficients were significantly different
from 0 at the 7O% significance level, with the regression
coefficients for X3 and X3 significant at the 8O% level,
X4 at the 90% level, and Xg and X88 significant at the
99.9% level.
This indicates that in an estuary A is a function
17O
-------
of all the variables for which data was available.
Equation (235) can now be used to determine the A
value for any station at any point in the tidal phase
at any time of day and any temperature. We would,
however, suggest further verification of this procedure
before using equation (235) for another estuary.
171
-------
ACKNOWLEDGEMENTS
This project is the collective effort of many
people. Names and affiliations of those directly
related to the proj'ect are given below in alphabetical
order by catagory.
PRINCIPAL INVESTIGATOR:
Richard G. Krutchkoff
Virginia Polytechnic Institute and State University
RESEARCH ASSISTANTS:
Sandra G. Bratley
Virginia Polytechnic Institute and State University
Samuel V. Givens
Virginia Polytechnic Institute and State University
Barry S. Griffen
U. S. Air Force
James T. Massey
Virginia Polytechnic Institute and State University
Andy Meddleton
Virginia Polytechnic Institute and State University
William R. Schofield
Virginia Polytechnic Institute and State University
John T. Sennetti
Virginia Polytechnic Institute and State University
CONSULTANTS:
John J. Cibulka
Clemson University
Pinshaw N. Contractor
Virginia Polytechnic Institute and State University
173
-------
Paul H. King
Virginia Polytechnic Institute and State University
T. A. McCracken
Clemson University
Clifford W. Randall
Virginia Polytechnic Institute and State University
COMPUTER PROGRAMMERS:
Charlie Flagg
Radford College
John Hall
Virginia Polytechnic Institute and State University
Tom W. Jones
Virginia Polytechnic Institute and State University
Janet S. Marshall
Virginia Polytechnic Institute and State University
Harvey Rosenberg
Radford College
TYPISTS:
Sandra A. Bixton
Virginia Polytechnic Institute and State University
Joan S. Dunton
Stochastics.Incorporated
Melody W. Fields
Virginia Polytechnic Institute and State University
Jeannette D. Morse
Stochastics Incorporated
174
-------
The following is a list of officers in the
Water Quality Office whose assistance was of signifi-
cant value and is greatly appreciated.
Leo J. Clark
Chesapeake Technical Support Laboratory
Norbert Jaworski
Chesapeake Technical Support Laboratory
Victor F. Jelen
Office of Operations, Cincinnati, Ohio
Bernard R. Sacks
Ohio Basin Region
Roger D. Shull
Division of Applied Science and Technology
Ethan T. Smith
Hudson-Delaware Basins Office
The following two officers are in Interstate
Agencies and their assistance is also greatly
appreciated.
Robert Boes
Ohio River Valley Water Sanitation Commission
Ralph Forges
Delaware River Basin Commission
175
-------
176
-------
REFERENCES
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177
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,
25. Feller, W., Some Recent Trends in the Mathematical
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26. Feller, W., Two Singular Diffusion Problems,
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27. Feller, W., Zur Theorie der Stochastischen
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28. Haight, Frank A., Handbook of the Poisson
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29. Harleman, D. R. F., The Significance of
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30. Harleman, D. R. F., The Significance of
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31a. Harleman, D. R. F., C. Lee, and L. C. Hall,
Numerical Solution of the Unsteady, Estuary
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32. Hetling, L. J., A Mathematical Model for the
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33. Hetling, L. J., and N. A. Jaworski, The
Role of Mathematical Models in the Potomac
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Dec. 1967.
34. Hetling, L. J. and R. L. O'Connell, A Study
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CB-SRBP Technical Paper No. 7, FWPCA.
35. Hetling, L. J. , and R. L. O'Connell, A Study
of Tidal Dispersion in the Potomac River,
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36. Hetling, L. J., and R. L. O'Connell, An Of
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37. Hetling, L. J., and R. L. O'Connell, Estimating
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39. Hildebrand, F. B., Introfuction to Numerical
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1956.
40. Jaworski, N. A., Water Quality and Waste
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41. Kac, M., Random Walk and Theory of Brownian
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Sewage and Industrial Waste, Vol. 23, No. 2,
February 1951, p. 198.
44. Kells, Lyman M., Elementary Differential Equations,
McGraw-Hill Book Co., New York, 1965.
45. Kent, R., Diffusion in Sectionally Homogeneous
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No. SA2 March I960, Paper 24O8, pp. 15-47.
46. Kimura, Motoo, Stochastic Processes and
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of Wastewater Treatment and Disposal Systems,
Dept of Civil Engineering, University of Illinois,
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181
-------
SO. Krutchkoff, R. G., Closure of Stochastic
Model for BOD and DO in Streams, ASCE J.
Sanitary Eng. Div., October 1968, pp. 1025-1027
51. Lauff, George H., (ed) Estuaries, Publication
No. 83, American Association for the Advancement
of Science, Washington, D. C., 1967.
52. Leeds, J. V., and H. H. Bybee, Solution of
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pp. 29-36.
53.. Loucks, Daniel P., A Probabilistic Analysis
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1965.
54. Lynch, William O., Discussion of "BOD and DO
Relationships in Streams" (Dobbins), ASCE J
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1965, pp. 82-83.
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Generalized Initial Conditions For the
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Center of Virginia, Bulletin 28, August 1969.
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182
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184
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GLOSSARY AND ABBREVIATIONS
A matrix of equation coefficients
A or A(x,t) cross sectional area
a(x,t) or a(x) infinitesimal mean
BOD biochemical oxygen demand
b(x,t) or b(x) infinitesimal variance
c concentration variable
c vector of average segment concentrations
C. I. confidence intervals
D oxygen variable
DB or DB(x,t) benthal demand
D0 initial oxygen concentration
DO dissolved oxygen
E or E(x,t) diffusion coefficient
EF BOD diffusion coefficient
EG OD diffusion coefficient
E(Y) mean value of Y
F initial BOD concentration profile
F vector of BOD or OD sources
FF(x,t) rate of increase of BOD at STP
f(x,t) distribution of BOD
G initial OD concentration profile
G(m,n,s) probability generating function
g(x,t) distribution of DO or OD
IPX catagory index
Kx or K^Xjt) coefficient defining rate of deoxgenation
Kg or Kg(x,t) coefficient defining rate of reaeration
K3 or K3(x,t) coefficient defining rate of deoxgenation
due to benthal demand and algea
Kj or Kd (x,t) Ki+Kg
L pollution variable
La initial BOD concentration
Lm concentration of state m
L0 initial pollution concentration
LR or LR(x,t) rate of increase in BOD due to
land runoff
M(x,t) mean state concentration
m position state value
mean concentration
m(x,t)
185
-------
NF
NG
NS
NV
n
OD
OMEGA
OMEGAF
o(h)
PRI
P(s,r,t)
ppm
p(t) or £(t)
q(t) or
R(x,t)
r(t) or
S
STP
TI
TM
t
U or U(x,t)
UP
UT
u(m,n)
VAR
V(m,n)
W
XI
xo
XS(n)
x
a
number of grid spacings for BOD
number of grid spacing in estuary
for OD
number of outputs
variable number
time state value
oxygen deficit
tidal frequency 2TT/12.4 for
estuaries, 0 for river
frequency of sinusoidal feed rate
small with respect to h
interval in real time hours
between outputs
probability generating function
for BOD and DO states
parts per million
probability of a forward step
in BOD or DO
probability of a backward step
in BOD or DO
sources, sinks, coupling terms
probability of absorption of
BOD or DO
sources or sinks
sewage treatment plant
time at beginning of simulation
time in hours at end of simulation
real time
velocity function
fresh water velocity
tidal velocity
probability of finding a BOD
particle in state m,n
variance
probability of finding an OD or DO
particle in state m,n
rate of pollution loading
upstream position, upper boundary
of estuary in miles
downstream boundary
the nth position for output
position along.stream or estuary
confidence of confidence interval
186
-------
A stochastic parameter
6t time increment
6x space increment
X mean concentration input
|a(x,t) mean BOD concentration
ja(x,t) mean OD concentration
as(x,t) variance BOD concentration
28(x,t) variance OD concentration
187
-------
APPENDICES
PROGRAM LISTINGS
SAMPLE INPUT
SAMPLE OUTPUT
189
-------
/# DIFFERENTIAL EQUATIONS PROGRAM #/
/##*^##*#*#***-*:S*#**#**#*##*#**#^
/* */
/* PROGRAM TO DETERMINE BOD AND 00 PROFILES IN AN £STUAR> WITH */
/* BOTH FRESH WATER AND TIDAL VELOCITIES. */
/* */
/* THIS PROGRAM USES RUNGE-KUTTA-MERSEN INTEGRATION IN TIME. #/
/* #/
/4#* ****£#**** *##:4.:fc:^£*#;.K#^
POLUO: PROC GPTIONS(MAIN);
ON ERROR GO TO DATA;
UN ENDFILE(SYSIN) GO TO ENC2;
DCL XZ(2t">0);
DCL LC-l:12) LABEL;
£ DCL XS(50),XM(151),NS;
O OCL (UF(151),US(151),EG(151),EFC151)tKl(151),K2(151),KD(151)*OB
(151},LR(151) ,FF(151),GF(2t302),DGF{2,3n2)f
DZ(302)» 02(302),DX TDX6Ut DX2ISO,DXI2,U,DUtXI,
0X212,TIfTMr P«I» Tf DT) FLOAT;
DCL IONT112) CHAR(20);
GF=0;
IDNT(1)='G PROFILE ;
IDNT(2)=«F PROFILE «;
IDNT.<3) = «FRESH WATER VELOCITY/;
IDNT(4)=»TIOAL VFLQCITY
IONT(5)=«G DIFFUSIVITY*;
IONT(6)=«F OIFFUSIVITY*;
IDNT(7)=«Ki PROFILE ;
ICNT(8)=«K2 PROFILE «;
IDNT(9)=«KD PROFILE f;
IDMT(10)=«DB PROFILE «;
IONTni) = 'LR PROFILE «;
IDNTM2)='F FEED RATES';
-------
OATAs GET LlST(NG,NFtXI,XO,TI,TM,PRI, OMEGA,OMEGAF);
PUT PAGE EDITC'INPUT DATA','NO. G INCREMFNTS*,NG,
'NO. F INCREMENTS',NF,'UPSTREAM X»,XI,'DOWNSTREAM X'fXO,
'INITIAL TIME«,TI,»F1NISH TIMS',TM,
PRINT INTERVAL1 ,PRI ,
TIDAL FREQUENCYS'OMEGAt"POLUTION FREQUENCY*tOMEGAF)
{SKIP(5),X(5i?) >A92(SK,IPI2)fX(20)»AI20}f F(10) )fi5 ( SK IP (2) ,X( 2L ) ,
NGF=NF/NG;
TPR=TI;
T=T I;
DT=PRI/4 ;
Jj=l;
KK=NG-«-l;
J=NG-»-2;
OXF=(XO-XI)/NF;
DXG=(XC-XI)/NG;
KL=NF+l;
XM(1)=XI;
DO 1=2 TO KK;
XM(i)=XM(i-i)+nxti;
END;
xzd)=xi; DO 1=2 TO KL; xz( i)=xz( I-II+DXF; END;
GET LISY(NSf
-------
END;
**##***###*^.-;!#«:*#^
/* */
/* UPSTREAM BOUNDARY CONDITIONS */
/# */
/* REPLACE 3.6 IN THE FOLLOWING TWO STATEMENTS WITH THE APPROPRIATE*/
/* UPSTREAM HOD CGNCFNTRAT I CNS IN PPM. */
/* */
GF( It J)=(9.
/* */
/* REPLACE l.C IN THE FOLLOHIN'G TWO STATEMENTS KITH THE APFRGPFIATE*/
/* UPSTREAM OC CONCENTRATIONS £N PPM. */
/* */
*^K.^s':;;--<):«.t.**^***:t-** ********
GF dtl )=(c'. 19e+06)*l,ifOO ;
GO TO L(NV) ;
L(3): CALL 5TORF { J J,KL,UF, D.
GO TO L(NV) ;
L<4): CALL STOPPC J J,KL, US, DXF } ;
DO 1 = 1 TO KL ; US(I)=US(I)*1.5f- ; END
GO TO L(NV) ;
L<5): CALL STORE (JJtKKfEGfOX-G);
GO TO UNV);
LC6): CALL STDKHJJ,KL,EF,DXF) ;
GO TO LCNVJ;
L(7): CALL STORF ( J J,KK,K1 , DXG) ;
GO TO L(NV) ;
L(8Js CALL STC«e(,UtKK,K2f OXG);
GO TO L
-------
vO
U)
L(10»: CALL STORE(JJ, KK,D8,DXG);
GO TO L(NV);
L(ll): CALL STOR£(JJfKL,LRi.DXF);
GO TO L(NV);
L<12): CALL STOUfc ( J J,KL ,FF,OXFJ ;
DO 1 = 1 TO KL; FF( I) = FF(I)/DXF; END;
GO TO L(NV);
L(-l): PUT PAGfc;
ILC=150;
SCCK: IA=l;
IB=2;
CALL FUNCT(GF(1.*),OGFC1,*) );
GO TO PCAL;
RSTR: D02=DT/2;
DGB=DT/3;
D015=DT/.15;
RCAL: IF T + OOTM THEN GO TO FINIS
CALL RKMI(GF< IB,*), GF{ IA,*),DGFt IB,*)»DGF( IA,*), IER) ;
IF I£R=3 THtiN DO; DT=DT/2«'J; GC TC RSTK;
FND; IC=IA; IA=IB;
IB=:IC; T=H-DT; IF i£R=i THEN GO TO PCAL;
PCAL
FINI
/*
/*
/*
/*
IF DT>PRI THEN OT=PRI;
DZS=DT;
TIOE=T/12.4;
CALL POUT;
DT=OZS;
GO TO RSTP ;
PUT SKIP(3) LISTC 'SOLUTION IS COMPLETE*);
GO TO DATA;
4 #####;# ^
SU8KCUTINE TC CARRY CUT CNE STEP OF THE RUNGE-KUTTA-KEPSF.N
INTEGRATION. CALLS SUBROUTINE NAMED "FUNCT".
*/
*/
-------
ri!i)i:$:4t **#.«:*#****####* ******* ***^:*^**:4:S:*4** ****** *
RKMI : PROC(X,Y,e,A,J);
OCL (X (*)tY(*)f At*) v£(*)f Q( 302), 0(302) ,D{ 3i;?.) ,TQ) FLCAT;
DCL I,J,L;
J=3;
L=0;
TQQ=O.O;
DO 1-2 TO KK, KK+2 TO K; XU)=Y U } + D03*A( I ) ; END;
T=T+D03;
CALL FUNCTTQQ TH!.:N TCC=TQ; END;
IF TQg>l..'; THEN GO TO BORN;
J=l; IF TQQXl.l THEN GO TO NWFN;
J=2S
NWFN: CALL FUNCT(X,F);
BORN: T=T-OT;
END RKMI;
/*
-------
Ui
/* SUBROUTING TO CONTROL PRINTOUT DURING INTEGRATION. */
/* */
/:£;£^;$;£#:^^;$:£ ***##;$ :i=A^-*:^;^:^ ##^
POUT: PPOC;
DCL I;
10=IA;
TT=T;
IF ABS(TPR-T)<,/.01*PRI THEN GO TO REDY;
IF T+DZS«25*OZS THEN DC;
T=T*DT;
IB=IA;
IA=ID;
END;
REDY: TPR=TPR+PRI;
CALL STAPH;
STAPR: PROC;
DCL I,H,L,PCS;
ILC=ILC+I;
IF ILO5 THEN DO;
ILC=O;
PUT PAGF: t.DIT('TIME, HRS ',TT , f DELTA T, HRS» ,D2S, T ICE* , TIDE)
< SK IP (2 ) ,3 (X ( 1 :'i), A (15 J , F {a , 4) ) ) ;
PUT SKIP<2) hOFf{»STATION PQSIT IONS,(XS(I) DO 1=1 TC NS))
(X(20),A,15 (SKIP,16 F( 7,2)));
END;
ELSE PUT SKIPO) EDITCTIME, HRS» ,TT , DELTA T, HRSSCZS,
{ 3(XI 10), AC 15), F(8,4)),);
-------
L=2;
DO 1=1 TO KK;
OZ( I )=GF ( ID, I ) /9*19g+C6;
END;
DC 1=1 TC NS;
CALL INTP(L,KK,XM,OZ,XSm,02U ),ACR);
1:ND;
PUT SKIP(2) EDITCG PROFILE't C02( I ) DC 1=1 TO NS)) (X(2C),A,
15 (SKIP, 16 fi 7,3) j ) ;
*#**#4^^^
/* */
/* PUNCHED CARD OUTPUT OPTITN */
/* */
/* 400 CAN BE REPLACED WITH ANY TIME GREATER Th;AN THE STEACY STATE */
/* TIME. WITH THE PRESENT CARD, PUNCHED CARD OUTPUT WILL Et GIVEN */
/* FOR ALL PRINT INTERVALS GREATER THAN 4«0 HOURS. */
/* */
f*#*4**##**.$+4sf#$*$^tt.X#Xtt#$*%%*:%tt*-.tt3f&%ir.^
IF T>400 THEN DO ; PUT FlLf(PUNCH) ED IT (TIDf , (U2 ( I ) DC 1=1 TO NS),
TIDE) <2(X<8), 9 F(8,3))) ; END :
DO 1=1 TC KL;
M=I+KK;
DZ(I) = GFC ID,M)/9«!9E-K 6;
END;
DO 1=1 TC NS;
CALL INTP{L,KL,XZ,DZ,XSU),D2U ) ,ACR);
END;
PUT SKIPC2) EDITCF PROFILE « , (02 ( 1 ) DO 1=1 TO NS)) (X(Z:),A,
15 (SKIP, 16 Ft 7,3)));
/##**###*#*#*****:£#* **##**#** 3**^*
/* PUNCHED CARD OUTPUT OPTION ---- SAME AS ABCVF */
/* */
********** A* *^.*j^^^:*^***r.k^*^;u**^jfe^^.t**^^
IF T>400 THEN DO ; PUT FILH PUNCH) t:D IT (TIDE, (D? ( I ) DO 1 = 1 TO NS ) ,
-------
vO
TIDE) l2(.Xiait 9 F(8,3))>
END STAPR;
: END POUT;
STORE: PRDC(MfKM,U,DX) ;
DCL U(*)*PnSvACRf If JfNtMfMM
DCL NVS;
NVS=NV;
END ;
DSCRT:
NEXPS:
NfEWTY:
NEXTY:
INTEP:
RETRN:
RETUN:
/*
N=l; XX=XI;
IF IPTX? THEN GO TO INTEP;
IF IPT>-.? THFN GO TO DSCRT;
GET LIST(PGSfNV);
DO I=M TO MM;
U(l)=PGS;
END;
GO TO RETUN;
IF IPT<') THtN DO I = M TO MM; U( !)=?:; END;
GET LIST(POS); IF POSAB?IU(N)-POS)
THEN U(N)=VAL; ELSE U(N-1)=VAL; tNC; GO TO NEXPS;
GS=T LIST«OZ(I),D2( I) DC 1=1 TO IPTM;
PCS=XI;
00 I=M TO MM;
CALL INTPU, IPTf DZf D2tPCJStun)f ACR) ;
END;
GET LIST(NV);
PUT SKIP ^OITI Il)NT(NVS) ,(U(NVS) DO NVS=M TC
(SKIP(2)fX(50)vA*(20) (SKIP ,9F(12,4)));
END STCRE;
fe^*^ * ^#« ^ ^-** * V'>4 *******'****** ***-r^************
*/
-------
oo
/*
/*
/*
/*
/*
/*
/*
/*
/#
/*
INTP
SUBROUTINE TO PERFORM NONLINEAR INTERPOLATION
PARAMETERS ARE AS FOLLOWS:
LN = MAXIMUM POLYNOMIAL ORDER l.» < LN < 7
NP = NUMBER OF PAIRS OF POINTS IN .THE TABLt
X = VALUES OF THE INDEPENDENT VARIABLE ARRANGED IN ASCENDING
ORDER
FX = VALUES OF THE DEPENDENT VARIABLE CORRESPONDING TO X
XX = VALUE OF THE INDEPENDENT VARIABLE FOR WHICH A VALUE OF THE
DEPENDENT VARIABLE IS RBJUIRtiD
FXX * VALUt OF THE DEPENDENT VARIABLE FCUKfl
ACC a DESIRED RELATIVE ACCURACY OF FXX
*/
*/
*/
*/
*/
*/
*/
*/
*/
*/
*/
*/
ENIT:
STRT:
********#^***si.****"
PROC ( LN, NP,X,FX,XX, FXX, ACC) ;
DCL LN,NP,I,J,K,L,LL,MM,NN,X(*),FX{*),XX,FXX,Y(7 ),FY{7),ACC,FYY
IF ACC<1E-06 THEN ACC=1E-06;
L=0;
Kl;
MM=l;
DO 1=1 TO NP;
IF XUKXX THEN GO TO ENIT;
IF A8S(X(I)-XXX = (ACC+ABS{XX) )*ACC THEN DO;
FY<1)=FX(I);
GC TO GOIT;
END;
J=i;
GO TO STRT;
END;
J=NP;
L=-l;
Yd)=x(j)-xx;
FY(1)=FX(J);
FYY=FYM);
-------
AITl: IF L-»*0 THEN DC;
H
NP THEN DC;
J=J+K;
L=-l;
GO TO REOY;
END;
IF J<1 THEN DO;
J=J+K;
L=I;
END;
REDY: MK=MM+l;
Y«MMJ=X(J)-XX;
FY(MM)=FX(J);
LL=MM-l;
DC NN=1 TG LL;
FY«MM)=(FY(NN)*Y(MH)-FY(MM) *Y(NN1 )/ (Y ( MM)-Y (NN ) ) I
END;
IF LN=LL THEN GO TO GOI7;
IF ABSiFYY-FYt^H) )6 THEN GO TO GOIT;
FYY=FY(MM);
GO TO AITl;
GGIT: FXX-FY(MM);
END INTP;
FUNCT: PROC(X.XD);
OCL(X{*),XO(^) ) FLOAT, L,I;
CALL FRSTDt JJ,KK,X,DZ) ;
CALL SCNDD(JJfKK9XfD2);
CALL FRSTD(J,K,X,D2);
CALL SCNDDC J,K,X,02);
-------
SNT=OM£GA*T;
SNT=SIN(SNT);
XAES=ABS(SNT) ;
SFT=UMEGAF*T;
3j:r-:'.;^-:#:^^^^ ^ 4 * ******
/* */
/* VARI/RLE FFtD SATES */
/* */
/4 SFT IS THc RATIO CF THE CURRENT FEED RATE TO THE AVERAGE f'-.EO */
/* RAT6. ANY NhFDF.D MODIFICATION TO THE FUNCTIONAL FORK OF FF4;;-^
/* */
/* CORRECTICN FACTCR FOR K2 (X ) */
/* */
/* IN THE FHLL OWING CARD REPLACE XK5IN WITH K2(I) IF SIMULATING */
/* A RIVER. */
/* */
/****#*#**:>****jJ:*:ie-is«:*:*****K*$*#^
XOII)«EG(I)*D2(I)-U*DZCI)-C XKSIN )*X ( I )+Kl C I ) *X( M)+D3( I ) ;ENO;
RETRN: END FUNCT;
/* */
/* EVALUATION OF THE FIRST DERIVATIVE WITH SIXTH CRDtP ACCURACY */
-------
/* */
/ a*****'
FRSTD:
DCL I,J
IF *I>XK THEN OX=DXF; F.LSE OX=OXG;
JX:-. ...=6-j*OX;
r)X.; ,: = 12*OX;
DC N ) = .'.;
I=y;
DU)=(Y( I)-
DCI1=(Y( I+1)-Y(I-1) )/(
I=M-2;
0( I ) = ( -Y ( H-2 ) +8*Y { 1 + 1 )-8*Y ( 1-1 ) +Y < 1-2 ) )/OXl 2 ;
DCI )=(-Y(I-f2) + 8*Y( I + 1)-8*Y(I-1)+Y( 1-2) )/DX.12;
DC l-N+3 TO M-3;
0(I)=(Y( I+3)-Y(I-3)-9*( Y(I+2)-Y(I-2) )^5^{ Y( 1+1) -Y{ 1-1 ) ) )/DX60;
END;
END FRSTD;
^ ** ********* ********* ^iA***'***^*-**********.****-**^***^****!:;*/
/* */
/* EVALUATION OF THE SECOND DERIVATIVE WITH SIXTH QHDER ACCUKACY */
/* */
/*** 4-*. ***** i; ^ -«*:)! A. .}:^ '.-.-: . : . 4**3»****************- ********* ****** ***
S.CNOD:
IF '>:<: ih-:,N -)i.-=r>xF; ELSE DX=DXG;
0X21-;' -:3^ox->nvif '=;
DX2J.2 = CX*OX12;
I=N;
D{I)=(Y(I+2)-2*YCI-H)+Y(I))/(DX*OX);
-------
DU) = (Y(I-2)-2*YU-l)+Y(I))/(DX*DX);
L=N+l;
D(L)=(Y-2*Y(L)+Y(L-1))/(DX*DX);
L=M-l;
D
-------
DATA FOR PL/1 PROGRAM
6012003005001 .5067.262
16 0 3 4.8 6 8 9 10 11 11.8 13 14 15 16 17.8 20 22
-2 1 02 05 0.10*2 6 0.1042 7 0.020 9 0.020 11 20000 0 28 8
.673 .00208 2.02 0.00208 3.212 .00375 4.255 .00375 5.217 .00708 .09 .0071 6*w»8
.0154 7.5 .0154 8.307 .01290 9.3 .01290 10.237 .0163 11.29 .0163 12.463 .02292
13.75 .02292 14.937 .0133 16.03 .0133 17.19 .01040 18.41 .01040 19.535 .01333
20.565 .01333 21.643 .00958 22.77 .00958 24.318 .0108 26.29 .01083 28.015
.01083 29.48 .01083 30.955 .01166 32.42 .01166 0 28 10 .673 0 2.02 0
3.212 149004.255 14900 5.2171507006.091507006.858301400
O 7.5 301400 8.307 273500 9.3 273500 10.237 347300 11.29 347300 12.463 385500
w 13.75 385500 14.937 279700 16.03 279700 17.19 256800 18.41 256800 19.535 211500
20.57 211500 21.643 159900 22.77 159900 24.318 154100 26.29 154100 28.015
137600 29.48 137600 30.955 15150032.42151500 0
16,4,0,0,1.23,0.3863
3.735,.4421,5.655,.4812,7.185,.568,8.775,.805,10.765,1.042,13.105,1.12
15.485,1.144, 17.8,1.168,20.05,1.19,22.205,1.2,25.305,1.2,28.75,1.112,31.68500
,0.97,35.355,0.9233, 0,14,3, 0, .507, 2.69 ,.078 ,4.78, .096 ,6.53, .0807
7.84 .0682 9.71 .0715 11.82 .0524 14.39 .0510 16.58 .0572 19.02 .0423
21.08 .0375 23.33 .0294 27.28 .02245 30.22 .0192 0
-1 12 9 1.507E+06 10 1.120E+07 12.2 .728E+0
6 19.6 .376*05 22 .18E+05 -1 -1
-------
c
C DIFFERENTIAL EQUATIONS PROGRAM
C
C PROGRAM TO DETERMINE BOD AND OD PROFILES IN AN ESTUARY WITH
C BOTH FRfcSH WATER AND TIDAL VELOCITIES.
C
C THIS PROGRAM USES RUNGE-KUTTA-MERSEN INTEGRATION IN TIME.
C
:^$:$*;*:$4t $4$*£#*;$:£**$$$
REAL KlfK2tKD,LR
COMMON DZ < 302)»D2< 302), DGF1(302)fOGF2(302)t
IDB(151)V EF( 151), £G<151 ),FF( 151) VGF1( 302) vGF2(3(!2)f Kl( 151)
2K2(151) ,Ki;(lf>l)*LR(151 ) ,XM(151) , XZC200 ) tXS ( 50 > ,UFC 151 ), US( 151) ,
3ABSE,D03,D02fD015tDT,r)ZS,DX,DXF,DXGtDX6f,DX12fOX2l8 >,DXZ12,IA,IBf
4ILCfJJ,JtKKfKfKLtNSfNGFtOMEGA,OMEGAFfTtTTDE,TPRtRKLEfPRIt
5IPT,NVtXI
CALL ERRSETf 2U8,26<1,-1, 1,0)
A8SE=10.
RELE=.OG01
1 READ «5»2tENO=999) NGtNF,XI,XO,TItTM,PRI, GMFGA,OMEGAF
2 FORMAT (2I5,(7F10.4)}
WRITE(6,3) NG*NF9yifXOfTI9TM,PRIf CKEGA.CMEGAF
3 FORMAT(il«/////5nX,'INPUT DATA»//20X,
1'NO. G INCKFKENTS »tM*V/2tiX,
2»NO. F INCREMENTS », I1.U//2-JX, «UPSTREAM X',I'iX,E2 ).5//2'SX,
3«OOWNSTREAM X» ,BX, E20.5//20XT INITIAL T IME , 8X,e;-!(.., 5//2CX,
4«FINISH TIMEl,9X,t2r»o5//2^X,'P^INT INTERVAL ' ,6X, E2«U5//2iiX,
5»TIOAL FREQUENCY«,5X,£20.5//23Xf'POLLUTION FREQUENCY «, E2:5.5)
NGF=NF/NG
TPR=TI
T=TI
DT=P
JJ=1
-------
DXF=(XC!-X! )/NF
OXG=(XO-X1)/NG
KL=NF-H
XM(1)=XI
00 4 I=2,KK
4 XMU )=XV(I-11 +DXG
XZ(1)=XI
DO 5 I=2,KL
5 XZ(I)=XZ(1-1) + BXF
REAj (5,6,END=v99) NSt(XS)
NV= NV + i-
GO TO (^1,3,9, ?''M1, 12, 13, 14, 15, 16,17, 18,19, ?2),NV
9 CALL STORtCJJfKKtGFlfDXG)
DO 72 1=1,KK
22 GF1{I)=GFI(1) * o,19E*6
GO TO (71,8,9,10,11,12f 13,14,15,16,17,18, 19,2-1),NV
10 CALL STORF(J,K,GF1,DXF)
DO 23 1=J,K
23 GF1(1)=GF1(I) * 9.19E+6
*^: :):**** *#**********^*******;***"-v:**
c
C UPSTREAM BOUNDARY CONDITIONS
C
C REPLACE 3.6 IN THF FOLLOWING TWO STATEMENTS WITH THF. APPROPRIATE
C UPSTREAM BOD CONCENTRATIONS IN PPM.
C
^ 7;;*£:f::fc:*#i:^ #*A-#* :£ # 4*:^^
GFKJ) =3
GF2(J) =
C-f**t,*">3m- «A.^.- -« << .»* -jj> >.v -',.
-u*^--" ll' -JF'f-f-^"--,- 3p-i- «,.
-------
c
C REPLACE 1.0 IN THE FOLLOWING TWO STATEMENTS WITH THE APPROPRIATE
C UPSTREAM OD CONCENTRATIONS IN PPMo
C
£#£#4. #$*£##**:$! *.##**:T$:K£$#$^
GFH 1) =1. *S
GF2(1) =1, *9
GO TO (21,6,9,115,II,12,13,14,15,16,17,IS,19,2;»,NV
11 CALL STORE (JJ,KL,UF,DXF)
GO TO (21,8,9,1*>,11,12,13, 14,15,16,17,18,19,2,NV
15 CALL STORE(JJ,KK,KlfDXG)
GO TO (21,8,9,10,11,!2,13V14,15,16,17,18,19,20),NV
16 CALL STGRn(JJ,KK,K2,DXG)
GO TO (21,8,9,1'?,11,12,13,14,15,16,17,18*19,2U),NV
17 CALL STORE(JJ,KL,KD,OXF)
GO TO (21,B,9,10,11,12,13,14,15,16,17,18,19,2f3),NV
IS CALL STORE(JJ,KK,DS,L)XG)
GO TO (21,8,9,10,11,12,13,14,15,16,17,18.19,20),NV
19 CALL STOR£(JJ,KL,LR,DXF)
GO TO (21,8,9,10,11,12,13,14,15,16,17,18,19,2«),NV
2C CALL STOREUJ,KL,FF,DXF)
DO 30 I=1,KL
30 FFU )=FF( I)/DXF
GO TO (21, 3* 9,10,11,12,13, 14*15, 16, 17, 18, 1.9, 2i'),NV
21 WRITE(6,31)
31 FORMATt1!1)
-------
35 IA=1
IB=2
CALL FUNCTCGF1»DGF1)
GO TO 39
36 D02=DT/2.
003=DT/3.
D015=OT/15,
37 IF(T+OT.GT.TM) GO TO 40
GO TO (112tl21)t IA
112 CALL RKMI{GF2,GF1,OGF2,DGF1,I£R)
GO TO 123
121 CALL RKMI(GFI,GF2,DGF1,DGF2, IER)
123 IF (IER.NE.3) GO TO 41
DT=DT/2.
GO TO 36
41 1C=IA
IA=IB
I8=IC
IF ( IER.EQ.1) GO TO 39
DT=4.*OT/3.
IF(DT,GT,PRI) DT=PRI
39 DZS=DT
TIDE=T/12.4
CALL POUT
DT=DZS
GO TO 36
40 WRITE(6,42)
42 FORMATt/X'SOLUTION IS COMPLETE')
GO TO 1
999 STOP
END
-------
SUBFsOUTINE RKMI ( X, Y,E, A, Jl}
**4$::V$ $*$**£$*$$ **^
c
C SUBROUTINE TO CARRY OUT CNE STEP OF THE RUNGF-KUTTA-KERSEN
C INTEGRATION. CALLS SUBROUTINE NAMED "FUNCT".
C
C #.**.#*#:£i;:*^>:;*:4:;)e^
DIMENSION X(i),Y(l),A(!),£<1J,B{302),C{3O2),D(302)
REJ»L KI,K2,KD,LS
COMMON DZ( 3U?) ,D2(3C2) ,DGF1(302) ,0(5FH(302 ),
lDB(151)f cF<151)i EGM51!tFF(151)tGFl(302)f GF2(3f*2)fKl(151) »
2K2C151)tKD(I51),LR(15i),XM(151),XZ(2?"» »XS<5
-------
CALL FUNCT(XtD)
00 7 1=2, KK
7 Xd)-X(I) + U03*(1.125*A(I)-5.625*C(I) +6.*D«I>)
DO 8 I=KK2,K
8 X(n = XU) + DQ3*(1.125*A
-------
C SUBROUTINE TO CONTROL PRINTOUT DURING INTEGRATION.
C
C*«#:M:*##********^***********^^
REAL Kl»K2tKDfLR
COMMON 0 Z { 302 ) , D2 ( 302 ) , OGF 1 C 3U2 ) , DGF 2 ( 302 ) »
10B < 1 51 ) t EF ( 151 ) f EG < 151 ) t FF < 151 ) i GF1 ( 302 ) , GF2 ( 3«2 ) , K 1 ( 15 1 ) ,
2K2(151),KO(151),LR<151) , XM{ 151) , XZ(200) ,XS (50) ,UF( 151 ) ,US (151 ) ,
3A8SEfDC3fDC2,D015t DT,DZSf DX,DXFtDXGtDX60,DXi2fDX213i ,DX212f IA,I8f
4ILC,JJ,J,KK,KfKLfNS,NGF,CMEGAf OMEGAF,TtTID£,TPR,RELtfPRI,
SIPT.NVfXI
ID=IA
TT=T
IF(A65(TPR-T).LT. «01#PRI) GO TO 21
IF(T + OZS .LT. TPR) GO TO 22
OTaTPR-T
TT=T+CT
D03=HT/3.
0015=01/15.
GO TO (112,i;il),IA
112 CALL RKHI (GF2,GF1, DGF2,DGF1, JER)
GO TO 123
121 CALL RKMI(GFltGF2fDGFi,OGF2,J£R)
123 ID=IB
IF(JE7;.LT. 3 .AND. 13T.GT. .25*DZS) GO TO 23
GO TO 21
23 T=T+DT
IB = IA
IA=ID
21 TPR=TPR -l-PRI
ILC^ILC +1
IF( ILC.LF..5) GO TO 3
ILC=0
WRITE(6,1) lT,DZS,TIDt
1 FORMAT (! / l^'Xf^TIMEt HRS" ,6Xf F8.4flOXf DSLTA T, HRS f,F8.4f
-------
3
101
llOXt 'TIDES 11X,FB.4)
WRITEC6.2) l ) TT,DZS,TIDE
FORMAT*
// UVX,»TIME, HRSt,6X,F8.4,10X,«D£LTA T, HRS VF8.4V
301
303
302
304
3U5
5
110X, tTIDE',HX,F8.4)
L=2
GO TO (301,3^2),ID
DO 303 1=1,KK
QZU)=GFl(I)/9.19E + 6
GO TO 305
DO 304 1=1,KK
DZ(I)=GF2(I)/9,L9F+6
DO 5 1=1,NS
CALL INTP(L,KK,XM,DZ,XS(I),D2{I),ACR)
WRITE{6,6) (0?(I),I=1,NS)
FORMAT! /20Xf*GPROFILE«,/<16F7.3))
E^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^t^^^^^^^^^^^^^^^^-v:^^
c
C
C
C
C
C
C
8
2
GO TO (20 If 2^2 )v ID
DO 203 I = 1,KL
M=I + KK
DZ(I)=GFl(M)/9«].9E+6
GO TO 205
DO 204 1=1, KL
-------
M=I + KK
204 DZ(I) = GF2(M)/<3.19t+6
205 DO 10 1*1, NS
10 CALL INTP(L,KL,XZ,CZ,XSU),D2(I),ACR)
WRIT£<6,11) (02( I),I=1,NS)
11 FORMAT! /20X,»F PROFILE* ,/( 16F7.3 ))
c
C
C
to
H
to
PUNCHED CARD OUTPUT OPTION ---- SAME AS ABOVE
*******************^^^
IFIT.GT.400) WRITE(7,8) TIDE, ( D2( I ) t I=1»NS It TIDE
22 RETURN
END
SUBROUTINE STOftf.:( M,MM,U,OX1)
DIMENSION IDNT(60), U(l)
REAL K1,K2,KD,LK
COMMON DZ (302 ) t 02( 30'.?), DGF 1( 302 ) ,DGF2( 3C2 ) ,
10B(151),EF(151),nG(151),FF(151),GFl(3«>2),CF2(3?2)fKl(151),
2K2(151),KD(151),LR(151),XM(151),XZ{20^),X5(5»:.),UF{J51),US(151),
3ABS G, 1303,002, D015 ,OT,DZS, DX,OXF,DXG,DX60,DX1"2, 0X2180,0X212,1 A, 18,
41 L, JJ,J,KK,K,KL,NS,NGF,OMEGA,OMEGAF,T,TICE,TPR,Rt-LE,PRIi
5IPT,NV,XI
II AT A IDNT( 1),IDNT'( 2) IDNT( 3),IDNTt 4),IONT( 5),IDNT( 6),
JDNT( 9) ,IONT(10),IONTU1 ),IONT(12),
IDMT( 15) , I DNT ( 16) , I DNT ( ?. 7) , I DNT (18),
ICNT(21),IONT(22)f IDNT(Z3), IDNT(2^}),
I ONT( 27) , IDNT ( ? S) , I DNT ( 29) , I DNT ( 3?> )
5
6
7
8
IDNT< 1),IDNT( 2)
IDNTi 7),IONT( 8)
I DNT (13), I DNT (14)
IDNT(19),IDNT(20)
IDNT(2S),IONT(?6)
/ 'G PR1
'F PR'
»FRES»
T I CA
OFIL1,fP
CFIL',1E
H W.A«,«TER
«L
«,«VELO«,*CITY«,
VE«,fLOCI«,'TY
-------
IDNT
IDNT
ID NT
IDNT
! ONT
(31),
(37),
(43),
(49),
(S3),
/
G
F
IDNTC
01%
DIS
32),
IDNTC38),
IDNTC
IDNT(
IDNTC
Kl
l<2
»KD
OB
LR
F
44) ,
50 ) ,
56V,
PS
P1,
PS
PS
PS
FES,
FFUSS '
FFUSS*
IDNTO3)
IDNT (39)
IDNT(45)
IDNTt 51 1
I ONT (57)
RQFI S1
ROFIS1
ROFIS'
ROFIS'
ROFIS1
EO R1,'
IVIT*
IVIT*
,IONT
,IDNT
tIDNT
iIDNT
f IONT
LE
LE
LE
LE
LE
ATES1
t'Y
f *Y
(34),
(40),
(46),
(52),
(58),
,'
»
t f
t*
,'
,'
S»
S1
IONT(
IONT(
t
i
35),
41),
IDNT (47),
IDNT*
IDNTt
i
f
§
t
i
i
i
i
*
i
t
t
53),
59),
t
t
i
i
t
i
,
/
IDNTC
IONTC
36),
42),
IDNT (48),
IONT<
IONTC
,
,
,
>
,
/
54),
60
DATA
1
3
4
5
6
7
8
9
*
NVS=NV - 2
ACR=.Of)01
IF( IPT.GT, s) GO TO 11
IFCIPT.GT* -2) GO TO 3
R£ADC 5,1) PCS,NV
1 FORMAT (FU'.4,I5)
NV= NV + 2
00 2 I=M,MM
2 U(I)=P05
GO TG 17
3 IFCIPT.GE. i-) GO TO 5
00 4 I=M,.MM
4 u( I )=»;»
5 N=l
XX=0.
6 READC5,7) PCS
7 FORMATCFJ0.4)
IF(POS,LT. XI) GO TO 13
READ (5,1?.) VAL
12 FORMATCE1--.4)
Q IFCPHS.LT. XX) GO TO 9
IFdPT.EQ, C) UCN)= VAL
-------
N=N+1
XX=XX+DX1
GO TO 8
9 IFUPT.GE. 01 GC TC 6
IF(ABS(U(N-1I-POS).GT.A8S(U(N)-POSM GO TO 10
U(N-1)= VAL
GO TO 6
10 U(N)=VAL
GO TO 6
11 READ (5t25) (OZ(I),02(11,1=1,IPT)
25 FORMAT (8F10.4)
POS=XI
Jl=2
DO 15 I=M,MM
J2 CALL INTPU1, IPT,DZ,D2,POS,um,ACR)
* 15 POS=POS «- 0X1
13 READ (5f16) NV
16 FORMAT (15)
NV= NV + 2
17 NVS=(NVS -1) * 5 + 1
NVS4= NVS + 4
WRITE(6,19) (IDNT(II),JI=NVS,NVS4),(U(I),I=M,MM)
19 FORMAT(//50X,5A4,20(/9E12.4))
RETURN
END
SUBROUTINE FUNCT(X,XO)
RF:AL K1,K2,KD,LR
DIMENSION X(1),XO(I)
COMMON DZ'(302 ) , C2 { 3u2 ) , OGF1 ( 3vJ2 ) , DGF2( 3C2 ),
10B(151)« E F(151)* EG(151)t FF(151)v 6F1(302),GF2(3* 2),K1(151),
2K2(151),KD(151)»LR(151),XM(151),XZ(200),XS(5« ),UF(151),US(151),
3AOS i:,D03, 002,0015, DT,DZS, OX, DXFtDXG,DX6«),DX12,nX?13u, 0X212, I A, IB,
-------
SIPTfNVtXI
CALL FRSTC(JJ,KK,XtDZ)
CALL SCN9D( JJ,KK,X,02)
CALL FRSTDCJ,K,X,DZ)
CALL SCNCe(J,KfX,C2)
SNT=OMFGA -T
SNT=SIM(SNT)
XAeS=ABS(SNT)
SFT=OMEGAF * T
SFT=«P01 * COS(SFT) + 1.0
C **************** *#**###*#*#***:$****^
c
C VARIABLE FEEL RATES
to c
in C SFT IS THE RATIO OF THE CURRENT FEFD RATE TC THE AVERAGE FEED
C RATE. ANY NEEDED MODIFICATION TO THE FUNCTIONAL FORM OF FF ( T)
C IS PERMITTED.
C CURRENTLY FF(T) = FF *( 1.0 + 0.001*CQS( OMf GAF*T) )
C
C ********************************** *********************** 4***^ **********
L=l
M=KK+1
DO 1 I=2fKK
00 2 MK=1,NGF
L=L+1
U=UF(L) + US(L) * SMT
2 XD(M)=EF(L) * D2(K) -U*D2(M) -KO(L)*X
-------
C
C
A RIVER.
*4^$*:***#$*:M**«^
XDm=tG
-------
(I )=( Y(I-H)-Y( 1-1) )/(2.*DX)
= M-2
(I)=<-Y< 1+2) 48,*YU + 1) -8.*YCI-1) +Y { 1-2 ) )/OX12
=N+?
-8,*Y-(I-l) +YH-2H/DX12
DO 3 l=N3i.Y!?
3 DC I )=(Y( 14.3 )-Y( I-3)-9.*( Y< I42I-YC 1-2) )445, *C Y( I+D-YC I- I ) M/DX60
^&TUKN
cND
SUBROUTINE SCMDD(N,M,Y,O)
f -A- ij,*l. >*.. -1. .t* *>.. J* -V ..( .». ^ .... ^-* -c. v,- -,i- V .*. wV 4?< :»,?.. -J^ ,f. A- .V -,*, -*.\ »*--**-<- ""- * '-* "^-V^ ,<- «V -V ** * -? J- ~* *>* ""l -J^
^-?- -;',- V -f **' >; "> *- -v- -: ' V T "!* -T -' - - - *< --^- -V1 -i*.--" '.' -? »:* * 7,--'j-' 7,- ^ ++.%£7f~ XI ^f..;C -^ ^. 7£ -+ -^--^ *? .?.
c
C EVALUATION OF- THE SFCOND OEKIVATIVE WITH SIXTH ORDER ACCURACY
C
CSV * & ''- *V *L' V- -' "1* %J- *-' *-' '* -*- JV>L-<' «-*- >.< a..,;. »'. «& ot-*,v Jj «i^ .'.« *j....x. «v ' ^ ^-- *2« *' >'' ^ "'- -''"'sL1 ^ Hr * 4 * -J- ii ₯ 4* ** '-T Jt -* '' £. 5L u
*r .5. ^"- *,. '# ^ .^-- -*,- --.- -;- «- - .-. -,. --. -_ +-" -' "i.~ >*-.* ^- -,- -.- --y *- fyf t'-'v »* -f -> T» "» ^.^f» ^s .*r i* ^ ^f> ^i* -r *r f *? -T ^-r- ".* 'i'- -* -?* -' -T rr *
REAL K1tK2fKD,LR
DIMENSION C(1),Y(1)
COMMON OZ(3? ?} i 02(302) ,OGF1(3''J2) ,OGF2<30^ ) t
10el), tG( }.51),FF(151)fGFH3o2),GF?{3v'2)tKl(157) »
2K2U.f-!) ,KD(.lv?. )TLR(151. ) ,XM (151) , XZ (200 ) ,XS ( 5O ) ,UF( 1 51) , US (151) ,
3ABSE,Dn3,D02,D015,DT,;:)ZS,OX,DXF,DXG,DX6s),DX12,DX2iS^»OX^].2tIAf IB,
VILC,JJ,J,KK,KtKLtNi;,NGF,G
5IPT,NVfXI
IF(M.GT.KK) GO JO 1
DX=OXG
GO TO 3
1 DX=DXF
3 DX2180=3.*DX#DX60
DX212=DX*DX12
-------
Dm=***^************^*******ft**************^**
c
C SUBROUTINE TC PERFGBW NCNLINEAR INTERPCLATICN
C
C PARAMETERS ARE AS FOLLOWS:
C LN = MAXIMUM POLYNOMIAL ORDER 0 < LN < 7
C NP - NUMBER OF PAIRS OF POINTS IN THE TABLE
C X = VALUF.S OF THE INDEPENDENT VARIABLE ARRANGED IN ASCENDING
C DROPS
C FX = VALUtS OF THE DEPENDENT VARIABLE: CCRRESPQNUING TO X
C XX = VALUE OF THE- INDEPENDENT VARIABLE FOR WHICH A VALUE CF THE
C DEPENDENT VARIABLE IS REQUIRED
C FXX = VALUE CF THF DEPENDENT VARIABLE FOUND
-------
C ACC = DESIRED RELATIVE ACCURACY OF FXX
C
C**:J::t:^#^,.j:*#^4:*#4*-;:^
DIMtNSION FY<7), Y(7), X(101), FX(iOl)
L=0
K=-l
MM=1
DO 9<:> 1=1, NP
IF{XU)-XX) 90,91,91
91 1F
-------
O RETURN
END
101 IF(J-l) 102,99,99
102 J=J+K
99 MM=MM+1
Y(MM)=X(J)-XX
FY(MM)=FX(J)
LL=MM-1
DO 104 NN=1,LL
1U4 FY(MM) = (FY(NN)*Y{MM )-FY(MM)*Y(NN)»/(Y(MM)-Y(NN))
IF(LN-LL) 105,94,105
105 IF(ABS{FYY-FY(MM))-ACC*{ACC+ABS(FY{MM))» 94 ,106,106
106 IF(MM-6) 107,107,94
107 FYY=FY(MM)
GO TO 96
94 FXX=FYiMM)
-------
DATA FOR FORTRAN 4 PROGRAM
to
to
60 120
16
11.
20.
-2 1
0.
0.
0.1042
0.1042
0.020
0.020
20000.
28 8
.673
5.217
8.307
12.463
17.19
21.643
28.015
0
28 10
.673
5.217
8.307
12.463
17.19
21.643
28.015
0.
0.
11.8
22.
2
5
6
7
9
11
0
.00208
.00708
.0129
.02292
.0104
.00958
.01083
0.
150700.
273500.
385500.
256800.
159900.
137600.
30.
3.
13.
2.02
.09
9.3
13. 75
18*41
22.77
29.48
2.02
6.09
9.3
13.75
18.41
22.77
29.48
0.
4.8
14.
.00208
.0071
.0129
* 02292
.0104
.00958
.01083
0.
150700.
273500.
385500.
256800.
159900.
137600.
500.
6.
15.
3.212
6.858
10.237
14.937
19. 535
24.318
30.955
3.212
6.858
10.237
14. 937
19.535
24.318
30.955
1.
8.
16.
.00375
.0154
.0163
.0133
.01333
.0108
.01166
14900.
301400.
347300.
279700.
211500.
154100.
151500.
.5067
9.
17.8
4.255
7.5
11.29
16.03
20.565
26.29
32.42
4.255
7.5
11.29
16.03
20.57
26.29
32.42
.262
10.
.00375
.0154
.0163
.0133
.01333
.01083
.01166
14900.
301400.
347300.
279700
211500.
154100
151500.
-------
to
10
to
0
16 4
0*
7.185
15.485
25.305
0
14 3
0.
7.84
16.58
27.28
0
-1 12
9.
1.5070E06
10.
1.1200E07
12.2
7280E06
19.6
3700E05
22.
.1800 EOS
-1.
-1
0.
.568
1.144
1.2
.507
.0682
.0572
.02245
1.23
8. 775
17.8
28. 75
2.69
9.71
19*02
30.22
.3863 3.735 .4421
.805 10.765 1.042
1.168 20.05 1.19
1.112 31.685 .97
.078 4.78 .096
.0715 11.82 .0524
.0423 21.08 .0375
.0192
5.655 .4812
13.105 1.12
22.205 1.2
35.355 .9233
6.53 .0807
14.39 .0510
23.33 .0294
-------
NC. G INCKtHENTS
NL. I- INCREMENTS
tPSTRt** X
OQNNSTKtAH X
INITIAL TIME
HMSH TINE
PRINT IMtKVAl
T1GAL FREQUENCY
F-CLLLUCN FJECUtNCY
INPUT 0»T»
60
120
0.0
0.3000CE 02
0.0
o.sooGce, oi
0.100OOE 01
0.5067CE 00
0.2620CE PO
0.0
0.9
0.0
0.0
0.0
0.0
0.0
U.U
0.0
c.c
U.U
0.0
O.U
u.O
0.0
I'.-J
c.o
'. .0
O.O
C.O
n.o
0.0
o.g
o.o
o.o
o.o
o.u
6 PROFILE
0.0 0.3
0.0 0.0
O.O 0.0
0.0 J-1
0.0 C.J
O.C 0.0
0.0 0.0
u.O
o.u
o.o
0.0
o.a
0.0
0.0
0.0
C.O
C.O
0.0
0.0
O.C
0.0
0.0
O.C
o.o
0.0
0.0
0.0
0.0
o.a
o.a
0.0
0.0
0.0
0.0
0.0
0.0
O.C
0.0
c.c
c.o
o.o
o.o
0.0
o.o
0.0
o.a
0.0
0.0
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3.0
J.O
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0.0
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0.0
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t).'.'
Cr.O
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u.U
o.a
0.0
<-.u
0.0
-.0
0.0
0.0
C.O
0.0
o.a
c.c
O.C
o.o
0.0
0.0
C.O
U.O
o.o
c.c
f PROFILE
0.0 0.0
0.0 0.0
0.0 0.0
o.o c.o
0.0 0.0
o.o o.o
0.0 0.0
0.0 LI.1
0.0 0.0
0.0 0.0
0.0 0.0
o.o o.o
o.o o.o
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.a
0.0
0.0
0.0
0.0
0.0
0.0
e.c
0.0
0.0
c.c
0.0
0.0
0.0
0.0
0.0
c.c
0.0
O.C
0.0
a.o
0.0
0.0
0.0
0.0
0.0
o.o
0.0
0.0
o.a
o.o
0.0
0.1042E GO
0.10*26 CC
C. 10*26 CC
0.10*26 CO
C. 10426 Oii
0.1U42E CC
0.1042E OC
C.1042E
0.1042F
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:UI
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0.1042E
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cc
CO
no
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DO
^.l-.426 DO
U.1042E 00
C.1..42E 00
U.1U42E JO
0.1042E UO
C.T042E OC
L.1042E CO
6 DIFFUSIVI
0.1042E CC
0.1042E OC
0.1C42E OC
C.1042E OC
0.1042E OC
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0.1042E OC
rr
0.1042E
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(j. 104 2E
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Ct
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0.1042E 00
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0.10426 00
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C.1042E 00
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0.104ZE 00
e iriFFll'STSTTY
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O.K.42E CO
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C.1042E CC.
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O.K42E «
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C.1O42E
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DO
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C.2KOOE-01
C.200CE-C1
0.2000 E-C1
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0.2000 E-C1
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0.2000 E-01
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C.2C006-U1
0.2000E-O1
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U.2003E-01
C.2000E-01
0.20006-01
0.2000E-U1
0.2000E-01
0.20006-01
0.20006-01
0.2000E-01
C.2000E-C1
0.2uC6E-Cl
C.2000E-01
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0.20COE-01
0.20OOE-C1
U.2000E-01
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C.2000E-01
0.2000E-C1
C.2000E-C1
0.20OOE-01
C.2000t-01
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'J.200OE-01
C.2000E-01
0 .20006-01
C.200UE-C1
0.20COE-01
C.200UE-01
C. 20006-01
0.2(100 E-01
0.2OOOE-01
0.20006-01
0.2000E-01
C.2000E-01
0.2000E-W1
0.2000E-01
0.20006-01
0.2000E-O1
0.2000E-O1
0.20OOE-01
0.2000E-O1
0.2000E-01
0.2000 E-01
0.20006-01
0.2000 E-O1
Kl PROFILE
0.2000 E-01
0.2000 E-01
0.2000E-01
J .20006-0 1
0.2OOOE-01
O^ 000 E-01
0.20OCE-01
KO PROFILE
0.2000 E-01
0.2000E-01
0.2000E-01
0^000 E-01
0.20006-01
0»20OOE-01
0.2000E-01
0.20006-01
0.2000E-01
O^OOOE-01
0.2000E-01
0.2000E-01
0.2000E-01
0.2000E-01
0.2OOOE-O1
0.200OE-01
0.2000 E-O1
0.2OOOE-01
0.2000E-01
0.2000E-01
0.2000E-01
0.2000E-01
O.2000E-C1
0.2OOOE-O1
0.2000E-01.
0 .20006-01
0.2000E-01
0.2000E-C1
O.ZOOOE-01
O.20O3E-01
0.2000E-01
O.ZOOOE-01
0.2000E-01
U.20OOE-01
0.20OOE-01
0.2000E-C1
0.2000 E-01
0.20OOE-C1
0.2000 E-01
0.20 00 E-01
0.20OOE-01
O.20OOE-01
O.2OOOE-C1
0.20 00 E-01
0.2000E-01
0.2000E-C1
0.2000E-C1
0. 20006-01
O.ZOOOE-01
O.ZOOOE-01
O.ZOOOE-01
0.2000E-01
O.ZOOOE-01
0.2000E-C1
C.20COE-01
C.200OE-01
C.20COE-C1
C.2000E-01
C.20COE-C1
0.2OOOE-01
0.2000 E-01
O.ZOOOE-01
C.20COE-C1
0.2000 E-01
0.2COOE-01
0.2000 E-01
0.2000 E-C1
0.2000E-01
O.ZOOOE-01
O.ZOOOE-O1
c.zoooe-oi
O.ZOOOE-Ol
0.2000E-01
O.ZOOOE-01
O.2000E-O1
C.ZOOOE-01
O.ZOOOE-01
O.ZOOOE-01
0.20006-01
O.ZOOOE-01
0.2000 E-01
C.2000E-01
0^000 E-01
0.2000C-01
0.2000 E-01
C.2COOE-01
O.200OE-O1
O.ZOOOE-Ol
O.ZOOOE-01
0.2000E-01
0.20OOE-01
CO'
-------
0.21QCE CS
0.2000E US
C.20COE C5
C.2000E. CS
0.2UOOE OS
C.2UOCE CS
C.200UE CS
C.2UCOE CS
0.2000E OS
C.200CE CS
0.2000E CS
C.20COE CS
C.2C'CUE CS
0.20CCE CS
0.2li«UE-C2
C.4452E-C2
0.1290 E-C-1
0.22f2E-Cl
0.1u4OE-tl
c.
<.,<: IO<;E LS
C.iOOOt P5
0. 20C.lt L5
...2UCJE »5
C.2UOOI: uS
U.20>.0fc 05
0.20CCE CS
L.2000E C5
<;.20UOE 25
V..210UE CS
o.zaoiF -:s
tUZOOiih 05
...iJH-F c5
..i-O8:lrr-i.2
t.l...3t)44E-Ol
0.3O40E-O1
J.2565E-01
0.2215E-01
O.1961E-O1
0.0
U.O
o.c
o.c
o.o
c.c
0.0
0.0
o.o
o.o
o.c
0.0
o.o
0.0
C.2637E CO
0.4263E I/O
U.4665E CO
C.6183E 00
C.9407E DC
C.1090E 01
C.1131E Cl
G.1155E 01
0.11 79E Cl
0.1195E Cl
'J.12OOE Ol
C.11S7E Jl
0.11466 01
J..1040E 01
C.3362E OO
O.8316E-01
0.920SE-U1
0.7027E-01
0.7099E-01
0.5200E-01
U.5083E-01
O.S73v,E-01
0.4346E-O1
0.3773E-01
0.2964E-01
0.2522E-O1
0.2182E-01
C.1939E-O1
O.C
0.0
C.O
0.0
0.0
C.7280E 06
0.0
0.6
C.O
0.0
0.0
c.o
0.0
c.o
O.3320E Ob
O.4317E OC
0.4752E Ot
0.6571E CO
O.96S5E CC
0.1098E 01
C.1134E 01
0.1157E 01
0.1181E 01
0.11S7E 01
0.1200E Cl
C.11S3E 01
U.113EE 01
FRESH W«TER
O.2881E 00
0.8670 E-01
0.899OE-C1
0.6867E-01
0. 6792 E-01
0.5151E-01
0.51 75 E-01
0.5584E-01
n.423EE-01
0.361£E-01
0.2904E-01
C'.247«E-C1
0.21SOE-01
F FEEC PATES
0.0
0.0
0.0
O.O
0.1120E 08
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
C.3868E 00
C.4371E 00
0.4826E OC
U.6943E OC
0.99S7E OC
o.iiasE 01
C.1137E Cl
0.1160E 01
i.llS+E 01
0.1 19 BE Cl
U.1200E 01
O.1189E Cl
C.1130E 01
VELOCITY
0.2444E 00
0.8966 E-01
0.8772 E-01
U.6923t-Cl
0.65O7E-01
0.5112E-01
0.5329E-01
0.5392E-01
C.4189E-01
C.3S76E-C1
0.28S2E-C1
0.2438E-01
0.2120E-C1
C.O
0.0
0.3
O.C
0.0
0.0
0.0
0.0
o.o
0.0
0.0
0.0
0.0
0.3926E 00
0.4421E CO
C.4887E CO
0.73 14E 00
0.1019E 01
0.1112E 01
C.1139E 01
0.1162E 01
0.1186E 01
0.1199E Cl
0.12OvlE Cl
0.1184E Cl
0.1121E 01
0.205OE CO
0. 92066-01
0.85SOE-C1
0.7055E-C1
0.t24SE-Cl
0.5081E-01
0.54S9E-01
0.5211E-01
0.4140 E-01
0.3477E-C1
0.28C1E-01
0.2398E-C1
0.2C90E-C1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o.o
0.3700E OS
0.0
o.o
0.0
0.0
0.3983E 00
0.4429E 00
C.49C5E CO
0.7670E 00
C.1041E 01
C.1118E Cl
C.1142E 01
0.1165E 01
0.1188E 01
C.1199E 01
C.1200E Cl
0.1179E 01
C.1112E 01
0.1701E 00
0.9390 E-01
C.8326E-C1
0.7154 E-01
C.60C6E-C1
0.5059E-01
C.S564E-01
0.5041E-01
C.4089E-01
0.3382E-01
0.2752E-C1
0.23S9E-01
0.2062E-01
0.0
C.O
0.0
0.0
o.c
0.0
0.0
o.c
o.c
C.1800E 05
0.0
0.0
0.0
0.4040E 00
0.4450E 00
O.S12CE 00
0.8016E 00
0.10S2E 01
C.1121E 01
0.1144E 01
0.1167E Ol
O.IMOE 01
C.1200E 01
C.12COE 01
0.1173E 01
0.1096E 01
0.1395E 00
0.9517E-O1
C.8098E-01
0.7218E-O1
C.5790E-01
0.5046E-01
0.5646E-01
0.4881E-O1
C.4C33E-01
0.3291E-O1
C.2703E-01
0.2321E-O1
C.2035E-O1
0.0
0.0
O.O
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
224
-------
TIME, HAS C.O DELTA Tt HRS 0.2500 TIDE 0.0
STATION POSITIONS
0.0 3.00 4.80 6.00 8.00 9.CO 10.00 11.OC 11.80 13.00 14*00 15.00 16.00 17*80 20*00 22*00
GPROFILE
l.OCC C.C 0.0 0.0 6.0 C.O 0.0 0.0 G.O C.O 0.0 0.0 0.0 0.0 0.0 0.0
FPROFILE
3.400 0.0 0.0 0.0 0.0 O.C 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
TIME, HRS 1.0000 DELTA T, HRS I).0741 TICE 0.0774
GPROFILE
l.OOC 0.001 O.C10 0.017 0.031 0.032 0.048 0.041 0.040 0.042 0.040 0.032 0.030 0.026 C.023 0*016
FPROFILE
3.tCC O.CC2 0.002 O.C02 C.OC3 0.214 1.500 0.204 0.041 0.016 0.002 0.002 0.002 13.C02 C.005 0.004
TIME, HRS 2.0000 DELTA Tf HRS C.OS88 TIDE 0.1543
GPROFILE
l.OOC 0.004 0.013 0.030 0.062 O.C63 U.073 0.104 'J.095 0.082 0.082 0.074 0.065 C.C57 C.050 C.041
F-^PRCFILE
3.600 0.010 0.004 U.004 O.UC5 0.157 1.098 1.416 0.731 0.115 O.041 O.OC6 0.004 C.C04 C.008 0.006
TIME, HRS 3.0000 DELTA T, HRS 0.09B8 TIDE C.2409
GPROFILE
1.000 0.103 0.012 0.035 O.C81 0.090 0.098 0.119 0.144 0.158 0.133 0.118 0.110 0.092 C.080 0.068
FPROFILE
3.600 0.268 0.007 0.006 O.OC7 0.124 0.834 1.110 1.295 1.099 0.379 0.097 0.030 0.006 0.009 0.011
TIME, HRS 4.0000 DELTA T, HRS 0.0988 TIDE C.3206
GPROFILE
1.000 0.432 0.024 0.036 C.091 0.1C7 0.123 0.142 0.158 0.190 0.215 0.1S8 0.163 0.136 0.112 0.097
FPROFILE
3*600 1.251 0.036 0.009 O.OC9 0.129 0.854 0.949 0.993 1.213 1.273 0.844 C.2S6 0.034 0.011 0.012
TIME. HRS 5.0000 DELTA T, HRS 0.1317 TIDE C.4022
-------
c *
C ESTUARY PROGRAM FOR DELTA VALUES *
C *
C***:^*:******?**********^****^?^
C *
C AN AVERAGE DELTA IS CALCULATED FOR EACH SAMPLING STATION *
C OF INTEREST. *
C *
C DATA INPUT FOR EACH STATION: *
C 1. HEADER CARD GIVING THE STATION NUMBER, THE NUMBER *
C OF OBSERVATIONS TAKEN, NI, AND THE TIME OF *
C HIGH TIDE ON THE FIRST DAY THAT THE SURVEY *
C BEGAN. FORMAT (2IS, FKU4) *
C 2. NI SAMPLE CARDS GIVING THE MONTH, DAY, AND *
C TIME THAT THE SAMPLE WAS TAKEN AND THE DO *
C VALUE. FORMAT<2I5t2F10.4). *
C *
C INTERNAL ADJUSTMENTS REQUIRED* *
C 1, INDICATED STATEMENTS IN MAIN PROGRAM MUST *
C BE CHANGED IF DIFFERENT TIME SEGMENTS IN THE *
C DAY ARE TiJ BE CONSIDERED. NOTE, TIME IS *
C GIVEN IN MLITAMY NOTATION. *
C 2. THE FIRST DAY THAT SURVEY BEGAN FUST BE *
C CODED INTO THE TID12 SUBROUTINE, STATE- *
C MENTS 7 THROUGH 10. JUNE 20 IS THE DAY *
C FOR THIS EXAMPLE AND DATA RUNS FRCK JUNE 2\> *
C UNTIL JULY 20. *
C *
C COMPUTATIONS: *
C. FOR EACH STATION THE NI SAMPLE CARDS ARE R£AO, ONE AT A TIME.-
C A CHECK IS MADL- ON THE TIME OF DAY THAT THE SAMPLE WAS TAKEN.*
C IF OUTS III? THF INTERVAL OF INTEREST THE SAMPLE IS DISREGARD- *
C ED IN THE COMPUTATIONS WHICH FOLLOW. USING THE MONTH, *
C DAY, AND HUUR THAT THE SAMPLE WAS TAKEN, THE TIDAL PH/SE AT *
-------
C SAMPLING IS DETERMINED. THE SAMPLE IS THEN *
C CLASSIFIED INTO ONE OF TWELVE SUBGROUPS *
C ACCORDING TO ITS TIDAL PHASE VALUE. WITHIN EACH SUB- *
C GROUP MEANS, VARIANCES, AND DELTAS ARE CALCULATED. *
C ALL SUBGROUP DELTAS ARE AVERAGED TO GIVE *
C A SINGLE OtLTA FOR THE STATION BEING CONSIDERED. *
C *
C OUTPUT: *
C FOR EACH STATION, MEANS, VARIANCES, AND DELTAS ARE *
C PRINTED FOR EACH SUBGROUP, AND THE OVERALL DELTA *
C VALUE IS GIVEN. *
C *
C SUBROUTINES REQUIRED: *
C TID12 *
N> r *
to L
vj Q:^:^***^*:?:^***:*:^****^^
DIMENSION 00(12), XODC12), XXQUC12) , DELTAIC 12)
1 FORMAT ( 21 5, Fl !. 5)
2 FORMATC22X, 12, IX, 12, lX»F5.i) , 23X,F5.3)
3 FORMATC'ONO. IN SAMPLED* ,F5.«, MEAN= , F5.3, VAR=»,
1F5.3,1 DELTA=«,F5.3)
4 FORMATCISTATION SUf1 WITH ',14, OBSERVATIONS*)
5 FORMAT CODELTA =',F6.4,» USING ',14,' OF THE «,I4, TOTAL UBS
1ERVATIQNS')
6 FORMAT (*1ENC OF FILE CARD READ , J=», 12)
DO 3.1 J = l,4
DO 12 1=1,12
DELTAIC I )=0.
OD(I)=0.0
12
READ( 5,l,fiND=15) ISTAT,NI ,XPHASE
IFCNI) 11,11,18
-------
18 WPITE(6,4) ISTATfNT
00 10 T=1,NI
READ(5f2,ENn=15) IMCNTH, I DAY, TIME, OCX
C4*#£*:£^-:*#^V#*#^:{<#«c^
c *
C OPTION CF DIFFERENT TIKE INTERVAL IS AVAILABLE BY CHANGING *
C THE NEXT TWO CARDS. *
C *
£*$***# .t**:*:,1:^.**^*^^^
IF(TIME- 455.,) 1"»10,21
21 IFJ ~v V- >^ ^- '** %^r-A.^v-:> H.*^ . ..v-.s .*, - 1.1 v^ :-- V--U- >x.^v -*£.?..-. *i. .j,.,*, OL. J'^-.o« ^ v- VSfe*f--^-'' **; \ ^j ^'V^ ^v -I- *v ^- Jr i*« &
Jy% o ^ ^*t» > T*.'1 ^" ,»'- -* r"T* -> > *-..*-ii *n.f -f ^-.-n* -v- *- .^ S^waVr,. ^C ^i^; ^.^. .^^C^^S^^^-^HSpsaSt -*S-r ».--v- -T-^ *?* ^- -r 7 -r--i*-t- -r ->--3- /- -v
-------
WR1TE<6,«>) DELTA ,NN,NI
11 CONTINUE
GO TQ 16
15 WRITE(6,6) J
16 CONTINUE
STOP
END
to
to
VO
-------
STATION 1 WITH 1446
NC. IN SAMPLED 25.
NO* IN SAMPLED 22.
NO. IN SAMPLED 25.
NO. IN SAMPLE* 22.
NO. IN SAMPLE- 22.
NO. IN SAMPLE- 20.
NO. IN SAMPLED 23.
NO. IN SAMPLED 21.
NO. IN SAMPLED 22.
NO. IN SAMPLE= 23.
NO. IN SAMPLED 22.
NO. IN SAMPLED 23.
DELTA =0.2236 USING
OBSERVATIONS
MEAN=2.074
MEAN=1.964
MEAN=1.796
MEAN=1.847
MEAN=1.694
MEAN=1,794
MEAN=2.016
MEAN=2.253
MEAN=2.555
MEAN=2.534
MEAN=2.407
MEAN=2.077
270 OF THE
VAR=0.4Q1
VAR=0.416
VAR=0.274
VAR=0.368
VAR=0.362
VAR=0.429
VAR=0.610
VAR=0.831
VAR=0.530
VAR-0.319
VAR=0.494
VAR=0.548
1446 TOTAL
OELTA=0.193
OELTA=0.212
DELTA=C.153
DELTA=0.199
DELTA=0.214
D£LTA=0,239
DELTA=0.303
DELTA=C,369
DELTA=0.208
OELTA=0.126
DELTA=0.205
DELTA=(3.264
OBSERVATIONS
230
-------
?.«*^:£*#*****^^
C ESTUARY ANALYSIS PROGRAM *
C
C*****#*****#4 EXPLAINATION OF OPERATIONS
C *
C INPUTS: *
C *
C TIDE IS AN ARRAY OF TIDAL PHASE VALUES FROM O.-j TO Q.SS999 *
C AT WHICH SOLUTIONS TO THE MODEL WERE DETERMINED *
C WHEN READ IN VALUES ARS NOT IN CORRECT ORDER. =>
C SUBROUTINE GROOM MUST BE CALLED TO PREPARE TIDE AND *
C CORRESPONDING XX VALUES. *
C *
N C XX(ltPvT) IS AN ARRAY OF THESE SOLUTIONS FOR BOD. THE INDEX *
H C P SIGNIFIES POSITION IN THE ESTUARY FOR SOME SPECIFIED *
C TIME IN THE TIDAL CYCL£. T SIGNIFIES THE TIME IN THE *
C TIDE FOR WHICH THIS WAS DETERMINED. THE ACTUAL T VALUES*
C ARE GIVEN IN THE ARRAY TIDE. *
C *
C XX<2,P,T) IS AN ARRAY SIMILAR TO XX(1,P,T) EXCEPT THAT *
C IT IS A SOLUTION FOR OD AT P JND T. *
C *
C XPHASE IS AN ARRAY OF TIMES AT WHICH HIGH TIDE OCCURED *
C AT SAMPLING STATIONS FOR A FIXED DAY DURING THE *
C SAMPLING PERIOD. *
C *
C NPOINT IS THE NUMBER GP VALUES OF ACTUAL DATA ABCUT TO 8E *
C READ IN. POSIT IS THE POSITION AT WHICH THE flEASUREMENT*
C WAS TAKEN. I POSIT IS THE SAMPLING STATION N00 *
C *
C OUTPUT : *
C *
C 1. BOTH SETS OF CONCENTRATION PROFILES *
C 2. XVALUE, PREDICTED MEAN, CONFIDENCE LIMITS, ETC FOR EACH *
-------
N>
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
c
C
C
C
C
C
C
C
C
c
C
C
C
INDIVIDUAL OBSERVED DATA POINT. *
3. SUMMARY OF DATA OUTSIDE: LIMITS FOR fcACH STATION. *
*
SUMMARY OF COMPUTATIONS: *
*
TIDE AND XX ARE READ IN. TIDL: VALUES ARE CONVERTED FROM TIDE*
NOot 34,273, CYCLES TO PHASE] VALUES, 0.273. THEN TIDE *
IS REARRANGED IN STRICTLY ASCENDING ORDER. XX VALUES *
ARE ALSO REARRANGED TO LINE UP WITH THEIR CORRESPONDING*
TIDE VALUES. CONCENTRATION PF.CFILFS ARc DETERMINES *
THROUGH THE ESTUARY FOR TIDAL PHASES OF 0.0, C.23, *
n.5-Jt AND C.7b AND PROFILES THROUGH TICAL CYCLE FOR *
EACH STATION OF INTEREST. THEN ACTUAL DATA IS READ IN *
BY STATIONS. FOX EACH OBSERVED VALUE, A PREDICTED MEAN *
AND AN ALPHA PSRCtNT POISSON CONFIDENCE LIMITS ARE *
DETERMINED. THE NUMBER OF VALUES WHICH FALL OUTSIDE OF *
THE CONFIDENCE INTERVAL FOR E/»CH STATION IS TABULATED. *
j(!:X--* ********
--'' ****** ^4.
*
SUBROUTINES LENGTH AND TIMEX CALCULATE PROFILES THROUGH THE *
ESTUARY AT DIFFERENT TIDAL PHASES AND THROUGH THE TIDAL*
CYCLE FOR EACH SAMPLING STATION, RESPECTIVELY. *
*
XPOSIT IS AN ARRAY OF POSITIONS, IN MILES, AT WHICH XX *
VALUES ARE GIVEN BY THE DIFFERENTIAL EQUATIONS PROGRAM.*
THESE CORRESPOND TO THE P INDEX OF XX. *
*
/:*T*:M ********** **#*#^
*
ij'-'D":?, .'3NC FORMAT CF INPUT: *
*
).» XX AND TIDE, FORMAT FIXED BY OUTPUT FORMAT CF THE *
-------
C DIFFERENTIAL EQUATIONS PROGRAM, *
C 2. XPHASE. FORMATUOF8.5) *
C 3, XPOSIT. FQRMAT(8F10.2) *
C 4. HEADER CARD FOR SAMPLING STATIONS. THE NUMBER CF *
C OBSERVATIONS, THE STATION NUMBER, AND THE POSITION OF *
C THE SAMPLING STATION IN MILES. FORMAT(215,Flu.4) *
C 5. INDIVIDUAL OBSERVATIONS., MONTH, DAY, AND TIME, AND *
C XVALUE. *
C *
C#*#* **#*##*##*:*##:###***##*****#*#**##*#
C *
C INTERNAL ADJUSTMENTS: *
C *
C 1. THE ALPHA CARDS IN LIMITS SUBROUTINE MUST BE ROTATED *
W C UNTIL OUTPUT IS OBTAINED FOR #LL ALPHA LEVELS. *
U> C 2. THE CORRECTlONSt III, FOR NOT HAVING PHOTOSYNTHESIS, N03 *
C RECYCLE, ETC IN THE MODEL MUST Bt CHANGED FOP DIFFERENT*
C RESULTS FROM THE DIFFERENTIAL EQUATIONS PROGRAM. *
C THIS REFERS TO SUBROUTINES PREOIC AND TIMEX. *
C 3. THE POSITION INDICES, II, RELATING THE STATION NUMBER TO *
C THE POSITION MUST 8F CHANGED IF THE OUTPUT POSITIONS =?
C FROM THfc DIFFERENTIAL EQUATIONS PROGRAM ARt CHANGED. *
C THIS KtFrRS TO SU3ROUTINES PREDIC AND TIMEX. *
C *
C**###**#*#*#*##:**^##^
C *
C SUBROUTINES REQUIRED: *
C *
C 1. GROOM *
C 2. LENGTH *
C 3. TIMEX *
C 4. TIDAL *
C 5. PREDIC *
C 6. LIMITJ *
C 7. COUNT *
-------
C 8. ATSG *
C 9, ACFI *
C *
D I MENS ION XX (2, 16, 100 ) , TIDE ( 10*} ) , XPHAS EC 10 > , XPOSI T { 16 )
COMMON JZX
JZX=10000
C *
C READING IN OUTPUT FROM DIFFERENTIAL EQUATIONS PROGRAM *
C *
C***#****#*******#********#***#*#*^
1=1
It) READCStl) TIDE( I),(XX{l,Jf I), 0=1, 16)
READ(5,1) TIDE( I ) , { XX{ 2, J, I ) , J=l ,16)
1 FORMAT(8X,9F8.3)
IF(TIDECI)) 9,9,8
8 1=1+1
GO TC 10
9 IK=I-1
READ(5,5) (XPHASEII1,I=1,3 )
5 FORMAT (10F8. 5)
READ(5,7)
-------
C IPOSIT - SAMPLING STATION NUMBER *
C PCSIT = POSITION ON ESTUARY, IN MILES, WHERE SAMPLING *
C STATION IS LOCATED. *
C *
C#**#5X*,*r:*V:lrt^**##*#*.1.^
REAU(5f27END=13) NPCINT, IPOSIT, POSIT
2 FORMAT (21 5, F10.4)
IF (NPCINT) 14,14,98
98 WRITE (6, 80) JJ
80 FOKM/iTl'IRESULTS OF STATION NO. , I 3//87X' NO. DBS' /3X,« OBSERVED^ f6X
1, PREDICTED1, 1»X, 'LOWER' ,10X, 'UPPER' , 20X, 'NO. 05S',3X, 'ACTUALLY',
23X, 'NO, OUTSIDE'/4X,2( ' VALUE ' ,M)X) ,2X, 2 (' L IfUT ', 10X ),' PHASE' , 3X,
3»CONS IDGRED',5X, 'KEPT',7X, 'LIMITS' )
DO 11 1=1, NPCINT
to C* ***** ******* *********** **-^***J^*^*********************2f:*****^^*****^.-X**
u? C *
C READING IN ACTUAL DATA VALUES *
C *
4 **#**^
READ(5,3tENO=13) IMONTH, IDAY, TIME, XVALUt
FORM^T(22X,I2,lX,I2,lX,F5aO,23X,F5.3)
#*:«:**$#*:}:*.* *#:*#:fc^
C *
C DISCARDING DATA NOT TAKEN BETWEEN 5 AND 9 AP TC PREVENT *
C DISTORTION DUfc TO WITHIN DAYS VARIATION CAUSED BY PHOTOSYNTHESIS *
C *
C * ************ 3 ***### *#*4********#***#*#^
IFCTIME-455.) 11,11,15
15 IF(TIME-905«) 16,11,11
16 IPGINT=IPOINT+1
CALL TIDAL( IMONTH, I DAY, TIME, XPHA S6 ( IPOSIT) , PHASE)
CALL PREDIC{XX,NKEEP, IPOSIT, TIDE, PHASE,XMEAN)
CALL LIM.ITJ(XMEANtXLIMl tXLIMZt IPOSIT)
CALL COUNT( XVALUfc,XLI M1,XLIM2, ICOUNT)
-------
to
00
ITOTAL=ITOTAL+ICOUNT
WRITE (6, 6) XVALUE,XM£-:AN,XLIM1,XLIM2,PHASE,I, I POINT, ITOTAL
6 FORMAT(IX,5(Flu.4,5X),I 5, 6X, I5.3X, I 5)
11 CONTINUE
12 WRITE(6,4) ITOTAL, IPOINT
4 FORMATC'IS THEKt WERE SIS,1 DATA POINTS OUTSIDE OF CONFIDENCE
1 LIMITS OUT OF',I4,» OBSERVATIONS')
14 CONTINUE
13 STOP
END
-------
OB VALUES ThHU tSTUAKV
I.I 146
1.1 f>?
I. 357!.
1.413?
1.5157
1.5a<<«
1.6(.b7
1.7?35
1.7934
1.S732
2.I2S2
2.1922
2.2469
2.3132
2. 3020
2.4242
2.4911
2.5636
2.643C
2.730*
2.8269
2.S33S
3.0507
3.1792
3.3190
3.4699
3.631)
3.81.22
3.9812
4.1661
4.3639
4.5551
4.7462
4.93SO
5.1200
5.2923
5.4600
5.6324
5.7855
5.9240
6,1307
6.3580
6.3676
6.4644
6.561):.
6.6467
6.7293
6.8C12
6.8656
6.9220
6.9702
7.0116
T.U464
7.075C
7.u>>7a
7.1149
7.1266
T.1331
T.I 344
7.13OO
7.1254
7.1155
7.1-jya
7.0816
7.0580
7.03(12
6.9983
6.9626
6.9232
6.880C
6.8333
6.7831
6.7296
6.6729
6.6130
6.5501
6.4842
6.4118
e.3395
6.2648
6.1S79
6.1CVO
6.0282
$.9460
5.8623
S.7772
5.6912
5.6042
5.5165
5.4283
5.3396
5.2507
5. 1617
5.O729
4.9*40
fOk fuUK I10AL PHAStS
O.9O10
U.IU63
0.8237
0. 8456
0.8CJ3
I .9267
I..*t25
1.J4S6
1.1147
1.1887
1.26C4
1.3471
1.4299
1.S14J
1.S9B6
1.6628
1.7661
1.3474
1.9262
2.0016
2.3731
2.14C2
2.2030
2.2616
2.3168
2.3698
2.4221
2.4756
2.5311
2.593Z
2.66U3
2.7353
2.8161
2.9037
2.9«78
3.0977
3.2C27
J.312C
i.4250
3.54C9
3.6590
3.7788
3.8999
4.0220
4.1448
4.268L
4. 392c
4.5155
4.639U
4.7625
4.8859
5.Q099
5.1335
5.257C
5.38C4
5.5040
5.6269
5.749C
5.8694
5.9868
6.1000
6.2T12
6.3072
6.3990
6.4823
6.5573
6.6245
6.6848
6.7390
6.7877
6.8317
6.8717
6.9C72
6.9390
6.9671
6.9916
7.J126
7.030C
7.0440
7.0547
7.J618
7.0643
7.0637
7.0594
7.U512
7.0391
7.0230
7.0030
6.9787
6.9504
6.9178
6.8808
6.8393
6.7853
6.7340
6.6787
6.6196
6.5570
6.4910
1.0115
1.0247
1.C395
1.05U
1.C743
1.CV43
l.lltO
1.1395
1.1648
l.l«ie
1.22C7
1.2514
1.2840
1.3185
1.3550
1.3935
1.434C
1.4767
1.5215
l;568*
1.6179
1.6696
1.723<
1.7800
1.8387
1.8997
1.9626
2.0272
2.0929
2.1590
2.2246
2.2642
2.1512
2.2462
2.3207
2.3843
2.4598
2.5223
2.5896
2.7110
2.7639
2.81C7
2.8757
2.9352
2.9970
3.0713
3.1444
3.21CS
3.2944
3.3730
3.4420
3.S244
3.6095
3.6S51
3.7830
3.8779
3.9648
4.C584
4.1540
4.2512
4.3500
4.45C5
4.5525
4.6560
4.7610
4.8674
4.9752
5.C841
5.1944
5.3060
5.4195
5.5340
5.6491
5.7643
5.6750
5.9925
6.1C41
6.2140
6.3190
6.4190
6.5132
6.6008
6.6815
6.7551
6.8214
6.8806
6.9329
6.S786
7.0180
7.0515
7.C794
7.1022
7.1200
7.1331
7.1419
7.1465
7.1472
7.1441
7.1373
1.1270
1.0394
1.0807
1.1238
1.1687
1.2152
1.2433
1.3131
1.3641
1.4166
1.4702
1.5251
1.5807
1.6373
1.6945
1.7520
1.8C99
1.8679
1.9296
1.9627
2.0393
2.0952
2.1502
2.2C47
2.2590
2.3140
2.3710
2.4316
2.4977
2.5713
2.6540
2.7464
2.8483
2.9586
3.0757
3.1976
3.3272
3.4521
3.5777
3.7035
3.8290
3.9540
4.0783
4.2019
4.3248
4.4470
4.5682
4.6891
4.8C97
4.93OO
5.0500
5.1694
5.2885
5.4C79
5.5262
5.6440
5.7610
5.8772
5.9928
6.1060
6.2166
6.3241
6.4278
6.5268
6.62O5
6.7080
6.7887
6.8619
6.9272
6.9843
7.0330
7.0733
7.1054
7.1291
7.1462
7.1570
7.1619
7.1615
7.1563
7.1467
7.1330
7.1149
7.0930
7.0677
7.0389
7.O069
6.971*
6.9337
6.8928
6.8490
6.8025
6.7533
6.7019
6.6478
6.5913
6.5324
6.47U
6.4077
6.3420
6.2740
6.2040
237
-------
USTINC OF 00 VAlttS THRU
2.5417
2.4410
2.43*3
2.5245
2.52'.6
2.V'«B
2.4S7C
2.4B26
2.4606
2.44SU
2.432 T
2.4U1
2.39Z8
2. 372'..
2.3)13
2.3241
2.30*5
2.2i?t
2.25V3
2.2347
2.2KH
2.1(i6U
2.1 625
2. 1373
2.111',
2.L-840
2.0562
2.'J273
l.«8t
I.«o9#
1.9417
1.9135
1.8850
1.8*82
1.8324
1.8087
1.7459
1.7641
1.7444
1.7266
1.7108
1.696«
1.6850
1.6755
1.6685
1.6637
1.6009
1.660C
1.6608
1.6637
1.6685
1.6747
1.6825
1.6919
1.7028
1.7153
1.7295
1.7448
1.7614
1.7779
1.7947
1.8139
U8345
1.8564
1.8778
1.8999
1.9224
1.946C
1.9698
1.9934
2.0173
2.0420
2.0631
2.VB84
2.1127
2.1371
2.1614
2.1853
2.2067
2.2317
2.2549
2.2779
2.30J4
2.3221
2.3431
2.3632
2.3628
2.4022
2.4213
2.4395
2.4565
2.4724
2.4870
2.5007
2.5129
2.5221
2.5301
2.5361
2.5404
2.5433
TIOAl PHASE fCK THREE STAT
6.5240
6.53U
6.5347
6.43*7
6.532?
6.5251
6.5134
6.4975
6.4772
6.4534
6.4242
t.3893
6.3492
A.3C3U
6.24S7
6.1883
6.1174
6.0347
5.9414
S.«3«5
5.7271
5.6058
5.4977
5.3*63
5.2374
5.11/90
4.9813
4.8563
4.7342
4.6156
4.5017
4.3«7
4.2890
4.1909
4.0984
4.026U
3.9415
3.86C7
3.8027
3.7437
3.6917
3.6471
3.611C
3.5798
3.5565
3.54IJ3
3.9317
3.5302
3.5352
3.5463
3.5630
3.5854
3.6128
3.6452
3.6843
3.7265
3.7742
3.8271
3.8861
3.936C
4.0C91
4.)611
4.1574
4.2380
4.323C
4.4123
4.5067
4.6044
4.7057
4.B11J
4. 91 36
5.0291
5.1268
5.2417
5.3523
S.4609
5.5664
5.6675
5.7627
5.85C6
5.9313
6.0065
6.0726
6.1314
6. 1826
6.2228
6.2631
6.2967
6.3262
6.3519
6.3746
6.3962
6.4110
6.4275
6.4431
6.4571
6.4715
6.4851
6.4994
6.5126
6.4246
6.4420
6.4658
6.4467
i.!278
(.5(92
6.6136
t.tt!2
6.7121
«.76*5
6.8137
6.8701
(.<26I
6.«840
7.d416
7.C987
7.1542
7.2069
7.2568
7.304U
1.3480
7.3881
7.4213
7.45(7
4.4763
7.4969
7.9123
7,5225
7.5285
7.5310
7.52*8
7.5253
7.5176
7.5083
7.4979
7.4869
7.4T52
7.4633
7.4522
7.4420
7.4327
7.4247
7.4190
7.4142
7.4126
7.4143
7.4190
7.4268
7.4375
7.4512
7.4673
7.4849
7.5038
7.5238
7.5448
7.5661
7.5869
7.(068
7.6253
7.4411
7.6545
7.6655
7.6732
7.6770
7.6758
7.67C3
7.66C5
7.6461
7.626T
7.6C20
7.5733
7.5410
7.5058
7.4667
7.4229
7.3750
7.3237
7.2697
7.2138
7.1959
7.C948
7.0335
6. 9722
6.9116
6.8S22
6.7954
6.7388
6.6153
6.6349
6.587*
6.5438
6.5052
4.4730
6.4440
6.4219
6.4073
«.3956
6.391*
6.3965
6.4099
238
-------
10
U>
VO
c
C
C
tSTUARY LIMITS PROGRAM
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
*
*
*
^
INPUTS:
1.
THE FIRST DATA CARD SHOULD HAVE THE FOLLOWING PUNCHES *
STARTING IN COLUMN 1. .* 123456739 *
2. OUTPUT FROM THE DIFFERENTIAL EQUATIONS PROGRAM. THE LAST *
CARD AND THF THIRD FROM LAST CARD FROM THIS OUTPUT *
DECK SHOULD HAVE THE SAME VALUE FOR THE LAST NUMBER ON *
THE CARD. THE DATA IS LIMITED TO 40..) OR FEWER CARDS. *
THF CARDS SHOULD BE FOLLOWED BY 4 BLANK CARDS. *
3. A SERIES OF INDIVIDUAL CARDS ARE READ. EACH CARD HAS THE #
STATION NUMBER FOR WHICH OUTPUT IS REQUIRED. THE *
STATION NUMBER IS LOCATFD, RIGHT JUSTIFIED, IN CARD *
COLUMNS 1 TO 5. *
OUTPUT: *
1. A TABLE OF ONE-SIDED CONFIDENCE INTERVALS ARE GIVEN FOR *
EACH STATION. THE TABLE LISTS DIFFERENT ALPHA LEVELS *
ACROSS THE TOP AND DIFFERENT TIDAL PHASES DCWK. INSIDE *
THF TABLE, THE CONCENTRATIONS THAT ARE PREDICTED TO BE *
ABOVE ALPHA FRACTION OF THE OBSERVATIONS ARE GIVEN. *
2. A GRAPH SUMMARIZING THE ABOVE TABLE IS GIVEN. *
INTERNAL ADJUSTMENTS REQUIRED: *
1. THE ScT II IN SUBROUTINE PREDIC, WHICH RELATES THE *
STATION NUMBER TG TH£ CORRECT PCS IT ION NUMBERt MUST BE *
CHANGED FOR DIFFERENT ESTUARIES. *
2. THE SFT III IN SUBROUTINE PREDIC, WHICH COPsRECTS FOR NOT *
HAVING PHOTOSYNTHESIS, N03, ETC., MUST BE CHANGED WITH *
DIFFERENT ESTUARIES. *
3. SIMILARLY FOR DELTA VALUES IN SUBROUTINE LIMXXX. *
-------
c *
C SUBROUTINES REQUIRED: *
C 1. GROOM *
C 2. PREXXX *
C 3, LIMXXX *
C 4, ATSG *
C 5. ACFI *
C *
C NOTE: THE LAST TWO SUBROUTINES WERE TAKEN FROM IBM'S SCIENTIFIC*
C SUBROUTINE PACKAGE. *
C *
DIMENSION XX{2,16,100),TIO£(100 ) t IVECTt 19) ,LINF ( 101, 101 )
INTEGER DO T, STAR, BLK, ONE, TWO, THREE, FGUP, FIVE, SIX, SEVEN, EIGHT, NINE
g 1 FORMAT (8Xt9F3. 3)
O 2 FQRMATU5)
3 FORMAT (12A1)
4 FORM AT(« *,F6*4V5X9101A1)
READ (5, 3) DOT,STAR,8LK, ONE, TWO, THREE, FOUR, FIVE, SIX, SEVEN, EIGHT,
1NINE
1=1
10 READ(5,1) TIDt(I),(XX(l,J,I),J=l,16)
READCStl) TIDb{I),(XX(2,J,I),J=l,16)
IFCTICE(I)) 9,9,8
8 1=1*1
GO TO 10
9 1K=I-1
CALL G£OOM(XX,T1DE,IK,NKEEP)
12 READ(5,2,FND=99) IPOSIT
WRIT£<6,2 IPCSIT
200 FORMATCl1'! SSXt'TABLt OF ONE-SIDED CONFIDENCE INTERVALS FOR STATIC
1N«,I3 /6X,«TH£ CONCENTRATIONS WITHIN THE TABLE ARfc ONE-SIDED CONFI
2DENCE LI HITS FOR OXYGEN DEFICIT AS FUNCTIONS OF TIDAL PHASE AND '/
36Xt«CnNFID£NCEt ALPHA) LEVEL* THE FRACTION ALPHA OF ALL CXYGEN DEFI
4CIT OBSERVATIONS WOULD BE EXPECT £0 TO FALL BELOW THE 00 »/6X, 'CON
-------
5CENTRATION SHOWN IN
6
7
8
WITH PHASE=
PHASE
0.45
0.95
0.40
.0 FOR
0.90
0 .35
THE TABLE.
HIGH
0.85
0.30
TIDE
0.80
0.25
TIDAL
0.75
0.20
PHASE
INCREASES DOWN THE
//55X, 'ALPHA-LEVEL'/
0.70
0.15
0.65
0.10
0.60
0.05
y.5 -
«/
PAGE
6X,
0.50
9 6X,124< -)/)
DO 11 1=1,101
PHASE=0,01#FLOAT(I-1)
CALL PRE XXX ( XX, NKEEP, I POSIT, TIDE, PHASE, XMEAN)
CALL LIMXXXUMfcAN, PHASE, IVECT, IPOSIT)
DC 13 J=l,101
13 LINE(I,J)=BLK
DO 14 J=l,ll
14 LINE( I,KK)=DOT
LINE(I,IVECT{ 2))=NINE
LINE(I,IVECT( 4))=EIGHT
LINE( I,IVECT( 6))=SEVEN
LINE(I*IVECT'(18) ) = ONE
LINE(I,IVECT(16) ) =TWO
LINE( I,IVECT(14) )=THRE6
LINE(I,IVECT(10) )=STAR
11 CONTINUE
WRITE(6t2&l) IPOSIT
201 FORMAT (« I1 ,35X,» GRAPHED SUMMARY OF ABOVE TABLE FOR STAT ION1 , I3//
140X, "OXYGEN DEFICIT CONCEiNTRATION,PPM. / PHASE l'.0',7X,
2»1.0',7X,'2.<)',7XT'3.u«,7X,'4.0«,7X, 5.0' , 7X, 6.0* , 7X, 7. C* ,7X,
S'B.O1 ,7X,»9.i^ '; .oXt'lU.O1 /l2X,l(U(*i« ) )
DO 20 1 = 1 tin
X=ti.01*FLCAT(I-l)
20 WRITF(6,4) X«(LINE(ItJ) ,J=1,10U
202 FORMAT! I2X,lvl < ' . )/» PHASE 0.0 ,7X, l.O«, 7X, 2. 0 , 7X, «3.0« ,
27X, '4.t',7X,'5.iM ,7X,'6.0» , 7X, «7.0» ,7X , * 8.0 ' ,7X, » 9.0' , 6X, « 10.0 /
340X,« OXYGEN DEFICIT CONCENTRATION, PPM.1)
GO TO 12
-------
99 STOP
END
(O
-------
to
SAMPLE DATA FOR LIMITS PROGRAM. OUTPUT FRCM DIFFERENTIAL EQUATIONS
PROGRAM HAS BEEN DELETED
* 123456789
1
2
3
-------
lArtlfc Uf ONE-SlOtO COHFICENCe INIiHVttS FOR SIAllCft 1
IHt CLW.;STHTIUSS .UHIN IHt TABLE »Rfc UNE-MOEC CtWflUCNCt IMUS (-CO OXYGEN OEFICI1 AS FUNCTIONS Of 11 DM. MUSE MO
tUnJIUHiCLIAlPml IhVLl. II'r rp»CIILN HfKt Of UL CXVCFN UIF1CII CBSEWAIIUNS HOULC tb UPtCUO 10 FALl MUM TMt OO
tl'NCEMKITU.% SHt.kN IN IHt l»ult. IIUAL PHASI: INdEASES DOHN THE MCE MUM MUSEiO.J fOf HICH TIOE
o.c
( .0201.
Q...300
t.C40(l
0.0580
J..*40C
O.C70C
I..OSOC
c.u»oo
C.ltfOC
4.1 luo
C.I20C
I..I30C
0.140 C
O.I90C
0.160C
...IX 0
>.18CC
i'. Hoi
o,2iH/<>
0.2 IK
JW20V
rJ.230*i
0.24C'ti
r'«2SbO
0.26<-(
C.2K'C
U.I80C
C.290C
0,3000
C.lluC
0.32UC
tt.31oC.
0.3401.
C.3SOO
0.3600
0.1KC
0.18UC
0.1900
U.4OOO
0.410O
U.420C
0.4100
C.440C
C.4900
U.44OO
0.4 701
C.460C
0.4*00
v.5000
".5100
u.92V«)
U.930C
0*.5400
0.84OO
C.9SOO
ol*70d
0.89CO
C.4OOO
0.4100
o.42o'0
C.tlBO
C.4400
v.4500
C.*60<
O.47CC
c»44no
1.0'JO'I
4.1-,
4.19
4. IS
4. la
4.1«
4.17
4.14
4.1i
4.14
4.12
4.11
4.C9
4.C7
4,t)S
4.03
4.01
3.40
3.96
3.43
3.41
3.88
1.8S
3,83
3.90
3,71
3.14
3.71
3.4B
3.64
3.61
3.47
3.54
3.50
3.47
3.43
J.39
3.34
3.32
3.29
3.25
3.22
3.1*
3.16
3.14
3.12
3.11
3.0*
3.08
3.08
9.08
3.J4
3.08
3.09
3.10
3.12
3.13
3.15
3.17
3.1*
3.22
1.25
3,27
3.30
3.33
3.1*
3.3*
3.42
3.45
3.S1
1.54
3.57
3.60
3.63
3.6*
3.68
3.71
3.74
3.77
3.80
3.82
3.8*
9.8*
1,40
3,93
3,95
3.97
4.00
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3.3C
3.36
1.42
3.49
3.56
3*C4
3.72
3.01
3.89
3.99
4.C8
4.18
4.2»
4.38
4.48
4.58
4.68
4.C7
4.t6
5.1-5
5.13
9.21
9.27
5.U
9.39
5.43
5.40
9.91
9.»
5.91
9.6H
9.t2
5.04
5.»6
9.61
9.69
9.7a
9.71
9.73
5.!9
3.59
9.CC
9^0
5.K'
3.60
9.99
5.58
9.S7
9.93
5.93
9.9M
3.47
3.39
5.34
9.28
9.21
9.14
4^96
4. '6
4.76
4.69
4.94
4.42
4.31
3.S6
3.86
3.79
3. 69
3.55
3.43
3.J7
3+?9
3.21
3.14
3.Q8
3.13
2.98
2.54
2.90
2.87
2.89
2.84
2.83
2.83
2.83
2.84
2.85
2.88
2.90
2.93
2.97
3.01
1.09
3.10
3.13
3.21
3.28
1.34
1.42
3*Su
3.38
3.67
3.13
3.89
3.94
4.14
4.13
4.23
4.33
4.43
4.53
4.72
4.11
4.40
4.46
3..' 5
4.12
3.18
5.23
9.2>
5.32
9.19
9.3*
9.41
5.44
4.46
5.4d
4.44
9.91
1.92
5.54
9.99
9.46
S.O
9.43
5.43
S44
5.44
9.43
*.4^
9.39
9.36
9.34
3.31
5.J1
9.23
9.18
9.12
9.06
4.S6
4.9r.
4.81
4.71
4.C1
4.91
4.39
4.28
4.16
3.92
3.6!
3.49
3.34
3*49
3.S9
3.3<
3.21
3.14
3.H7
3.i,t.'
2.44
2. (4
2.84
2.er
2.77
2.74
2.72
2.71
2.7')
2.7C
2.7.,
2.11
2.72
2.74
2.77
2.80
2.83
2. (7
2.41
2.44
3.C1
3.07
3.13
3. If
3.26
3* 34
3.42
3.51
3.34
3.t«
3.78
3. (I
3.98
4. Ot
4.18
4.28
4.2t
4.37
4.66
4.74
4.82
«.8«
4.96
9.1?
3.17
3.12
9.16
9.19
5.22
5.29
4.27
9.2«
9.31
5.33
9.14
9.34
3.37
9.38
9.40-
3.26
3.20
9.27
9.27
9.21
9.21
9.21
3.21
3.26
9.29
9.24
9.22
3.2..
4.11
'-.14
S. 11
9.17
9.-J2
4.46
4.4C
4.82
4.14
4.44
4.94
4.43
4.31
4.20
ll96
jlll
3.62
3.32
1.41
3.23
3.14
3.06
2.99
2! 86
2.8.'
2.79
j.7'.-
2.47
2.43
2.61
2.34
2.47
2.37
2.56
2.37
2.38
2.99
2.41
2.41
2.46
2.69
2.73
2.T7
2.82
2. 87
2.42
2.48
3.04
3.11
3*lV
3.23
3.33
3.42
1.31
3.61.
3.44
3.74
1.84
3.49
4.09
4.14
4.14
4.44
4.98
4.66
4.74
4.81
4.86
4.41
4.46
9.01'
3.03
9.U6
3.0V
9.11
5.13
4.13
3.17
9.18
9.14
4.21
4.2?
4.21
3.L4 4.79
9.04 4.79
9.C9 4.79
4.119 4.76
5.05 4.T6
%C6 4.74
5.05 4.74
5.C5 4.74
4.1)4 4.79
9.01 4.T<
3.»J2 4.73
5.UO 4.TI
4.48 4.64
4.99 4.66
4.92 4.63
4.18 4.60
4.83 4.9*
4.78 4.11
4.72 4.49
4.69 4.14
4.S8 4.12
4.49 4.24
4.40 4.It
4.10 4.J7
4.20 3.97
4.04 3.87
3.48 3.77
3.17 3.67
5.T6 3.9*
1.61 3.44
1.99 1.16
1.44 1.26
3.34 3,16
3.Z4 1.U7
3.19 2.94
3.r6 2.90
2.98 2.83
2.41 2.71
2.84 2.49
2.T7 2.41
2.71 2.17
2.46 2.32
2.41 2.47
2.97 2.43
2.53 2.14
2.51. 2.17
2.47 2.14
2.46 2.12
2.44 2.31
2.41 2.19
2.43 2.10
2.44 2.11
2.49 2.11
2.44 2.11
2.41 2.34
2.50 2.17
2.33 2.14
2.14 2.42
2.54 2.49
2.41 2.49
2.48 2.9)1
2.72 2.38
2.77 2.41
2.U 2.48
2.84 2.74
2.45 2.K>
3.02 2.86
3.C9 2.43
3.17 1.00
3.23 1.01
1.31 3.14
3.42 1."
1.31 3,32
1.40 3.41
1.44 1.4D
3,79 3.48
3.M 1.67
3.48 1.74
4.C7 3.85
4.14 3.44
4.29 4.02
4.14 4.10
4.42 4.17
4.44 4.24
4.14 4.3V
4.42 4.14
4.41 4.41
4.72 4.45
4.76 4.44
4.40 4.52
4.83 4.99
4.84. 4.58
4.8* 4.40
4.40 4.42
4.42 4.64
4.44 4.49
4.44 4.47
4.41 4.68
4.48 4.TO
5.CU 4.71
3.01 4.T2
4.44
4.44
4.44
4.44
4.47
4.47
4.47
4.46
4.44
4.43
4,44
4.42
4.40
4.38
4.19
4.12
4.28
4.24
4.1*
4.11
4.C6
1.44
1.41
3.83
1.74
1.41
1.35
1.44
1.14
3.26
3.17
1.J8
2.44
2.«fl
2.(2
2.74
2.67
2.40
2.34
2.44
2.43
2.18
2.11
2.24
2.24
2.21
2.21
2.14
2.11
2.17
2.17
2.17
2.18
2.19
2.21
2.21
2.24
2.28
2.12
2.13
2.1*
2.41
2.48
2.11
2.9»
2.44
2.70
2.17
2.84
2.41
2.48
1.04
3.14
3.22
3.30
1.11
1.47
1.S9
1.41
1.71
3.74
3.86
J.43
3.94
4.03
4.10
4.14
4.18
4.22
4.24
4.28
4.10
4.12
4.34
4.14
4.17
4.18
4.40
4.41
4.42
4.41
246
-------
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247
-------
C *
C RIVER DELTA PROGRAM *
C *
c *
C INPUTS: DATA CARDS WITH THE FOLLOWING DATA:N,I,ITIME,IMINS, *
C X AND Y *
C WHERE: N=A POSITIVE INTEGER NUMBER *
C 1=STATION NO.,(INTEGER). *
C ITIME=HGUR OF DAY,(0 TO 24)v(INTEGER). *
C IMINS=MINS,(INTEGER). *
C X=DISSOLVED OXYGEN CONCENTRATION IN PPM. *
C Y= BOD CONC.IN PPM. *
M C FORMAT(4I5,2F10.4) *
a C *
C NOTE: THE PROGRAM IS CURRENTLY SET UP FOR THE OHIO RIVER*'
C USING A TOTAL OF SEVEN STATIONS RUNNING FROM 2 TO *
C 8 . THE PROGRAM WOULD HAVE TO BE CHANGED TO RUN *
C OTHER DATA. SPECIFICALLY THE INPUT FORMAT, THE DC *
C LOOP LIMITS,REMOVE THE X=(Xl+X2)/2 AND Y=(Y1+Y2I/2 *
C CARDS AND DIMENSION. *
C *
c OPERATIONS: *
C THE PROGRAM CATAGORIZES ACCORDING TO TIME OF DAY AND *
C STATION NUMBER AND THEN CALCULATES DELTAS IN EACH *
C SUBDIVISION. THE NUMBER OF SAMPLES FALLING INTO EACH *
C CELL, THE DELTA IN EACH CELL, THE AVERAGE DELTAS FOR *
C STATIONS AND TIME OF DAY AND THE OVERALL DELTA ARE *
C PRINTED. *
C *
C SUBROUTINES REQUIRED: NQNF. *
C *
*$ :5r* *:*£-!## :J ### ^ ^
DIMENSION SUM(2,8,8 ),SS(2,8,8 ),ICOUNT(8,8 )yDELTA(2,8,8 ),D{2,8)
-------
DO 1C 1=2,8
DO 10 J=l»8
ICOUNTCI, J)=0
DO 10 K=1T2
SUM0+50.P)/300«0>
IF(J) 8,8,7
8 J = 8
7 SUM (It It J) = SUM(1VI,J)+X
SSC1,I,J>=SS(1,I,J)+X*X
SUM(2,I , J)=SUM<2,1 ,J)+Y
SS(2f If J)=SS(2t It J)+Y*Y
ICOUNT(I,J)=ICOUNT( I,J)+1
-------
GO TO 11
9 WRITE(6t63)
63 FORMATC1TA8LE OF SAMPLES FALLING INTO EACH SUBGROUP. /'OTABLE IS
1ARRANGED WITH THG TIME OF DAY CLASSES IN'/' COLUMNS ACROSS THE PAG
2E WHILE THE STATIONS ARE'/' ARRANGED IN RCWS DCWN THE PAGE.'J
DO 12 1=2,8
WRITE<6,4) (ICOUNTU,J),J=1,8 )
4 FORMATCQ', 816)
DO 12 J=l,8
IF(ICOUNTU,J)-1) 13,13,14
14 DO 15 K=l,2
Z=FLCAT(ICOUNTU,J))
XM£AN=SUM(K,I,J)/Z
VAR=(SS(K,I,J)-SUM
-------
DO 17 I=2,8
DO 16 J=l,8
16 D(K,I)=D(K, I)+DELTA(K9I»J)
D(K,I)=D(K,I)/e.O
DD=DD+n(K, I )
17 WRITE(6t2.} I ,(DELTA(K, I,J),J=l,8),D
-------
TABLE OF SAMPLES FALLING INTO EACH SUBGROUP.
TABLE IS ARRANGED WITH THE TIME OF DAY CLASSES IN
COLUMNS ACROSS THE PAGE WHILE THE STATIONS ARE
ARR/NGED IN ROWS DOWN THE PAGE.
17
17
17
17
17
17
17
16
16
16
16
16
16
17
17
17
17
17
17
17
16
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
252
-------
TABLE OF 00 DELTA VALUES
10
THE TABLE HAS TIME CLASSES IN THE COLUMNS ACROSS THE PAGE
THE LAST COLUMN IS STATION AVERAGES, THE LAST ROW IS TIME
ELEMENT IS THE OVERALL AVERAGE 00 DELTA.
WITH THE STATIONS IN THE ROWS DOWN THE PAGE,
CLASS AVERAGES, AND THE BOTTOM RIGHT HANC
2
3
4
5
6
7
8
0.10684
0.11227
0.20586
0.25796
0.24212
0.13038
0.08673
0.16317
0.
0.
0.
0.
0.
C.
13987
15200
18348
20405
18482
09461
D.08389
0.
14896
0.
0.
0.
.
0.
0.
0.
0.
10159
26731
28394
21712
20211
11483
U9721
13344
0.20556
0.30881
0.24677
C.I 81 03
0.19517
0.09758
C. 09997
0.19070
0.09897
0.24161
0.26886
0.11832
0.19194
0.12373
0.1U2C7
0.16364
0.1C232
C. 26792
0.22250
0.20020
0.22502
0.19821
C.13370
0.19284
J. 10422
0.15555
0.18215
0.25466
0.1922C
0.17734
0. 14000
0.17230
0.14223
0.10246
3.10362
0.27930
0.22329
0.10243
0.09736
0.15010
0.12520
0.20099
0.21215
0.21408
0.20709
C. 12989
0.10512
0.17064
-------
TABLE OF BOD DELTA VALUES
THE TABLE HAS TIME CLASSES IN THE COLUMNS ACROSS THE PAGE
THE LAST COLUMN IS STATION AVERAGESt THE LAST ROW IS TIME
ELEMENT IS THE OVERALL AVERAGE BOD DELTA.
WITH THE STATIONS IN THE BCfcS DOWN THE PAGE.
CLASS AVERAGES* AND THE BOTTOM RIGHT HAND
CO
Ui
2
3
4
5
6
7
8
0.04873
0.13983
0.19956
0.06374
O.C8953
0.03149
0.03547
0.08691
0.08523
0.10719
0.17195
0.18122
0.23712
0.04110
0.04855
0.12462
0.12389
0.09664
0.17117
0.34519
0.23592
O. 08868
0.05641
0.15970
0. 12389
0.14282
0.15249
0.25478
0.30691
0.06859
0.06223
0.15882
0.
0.
0.
0.
0.
0.
0.
0.
07581
13786
14747
14325
13289
06181
03887
10542
0. 04 47 8
0.13515
C.213C8
0.15689
C. 13105
C.08737
0.07322
C.I 2 022
O.C616C
0.17621
0.15931
O.C9484
0.08705
O.C6656
0.05454
C. 10002
0.03022
0.14521
0.11106
0.07876
0.07698
0.08891
0.06298
0.08488
O.OT427
0.13512
0.16576
0.16483
0.16218
0.06681
0.05403
0.11757
-------
RIVER ANALYSIS PROGRAM *
***.*4***^
C *
C INPUTS: *
C 1. PRED. PREDICTED MEAN CONCENTRATIONS AT EACH *
C SAMPLING STATION. FQRMATC8F10.4). *
C 2. HEADER CARD FOR EACH SAMPLING STATION, STATION *
C NO. AND NO. OF OBSERVATIONS TAKEN. *
C FGPMAT(2I5)« *
C 3, OBSVATION CARDS. XVALUE. FORMAT(F1Q«4) *
C COMPUTATIONS: *
C 1. THE PREDICTED MEAN AT EACH STATION IS *
C TAKEN AND USED IN DETERMINING ALPHA Z *
g C CONFIDENCE LIMITS ABOUT ITSELF. *
Ui C 2. THE OBSERVATIONS ARE READ AND COMPARED *
C WITH CONFIDENCE LIMITS. *
C 3. THE NO. OF OBSERVATIONS OUTSIDE OF CONF- *
C IDENCE LIMITS FOR EACH STATION IS *
C DfcTERMINED AND READ. *
C SUBROUTINES USED: *
C 1. LIMRIV *
C 2. COUNT =5=
C *
#:^*##:£#:#:*##iV*:^
DIMENSION PREO(6)»LIMITX<2,6)
REAL LIMITX
READ(5tS) (PRIED ( I ),I = 1,6)
5 FORMAT(3Flu.4)
DO 1C 1 = 1,6-
10 CALL LIMFIV(PRED(I),LIMITX(1,I),LIMITX(2,I),I)
11 R£AD(5,2tEND=99) ISTAT,NI
2 FORMAT(2I5)
ITOTAL=y
IF(NI) 11,11,12
-------
12 J=ISTAT-2
WRITE<6,6) I STAY
6 FORMAT (fl RESULTS FOR STATION NO.',I3//« SAMPLE ,9X, f LOWER' ,7X,
1« OBSERVED* flnx," UPPER* ,3X, NO. CUTS IDF* ,3X, » PREDICTED V3X, 'NG.',10X
2, LIMIT1, 8X, 'VALUE', 12X, 'LIMIT' , 5X, ' LIMITS' ,7X, VALUE-'/ )
DO 13 1=1 » NT
READ ( 5 , 1 , If ND=99 ) fv , K , I T I ME , I MI NS , XI ,X2 , Yl , Y2
1 FORMAT ( 21 5t 2-^Xt 2 J 5t 1«X, ^F5. 1)
4^*:^^
c *
C THE NEXT TWO CARDS SHOULD BF. INTERCHANGED IF BOO DELTAS ARE TO *
C BE CALCULATED. *
C *
-*^^
CALL CCUNT(XVALUl£,LIMITX(ltJ)»LlMITX(2,J),ICOUNT)
ITOTAL=ITCTAL-HCOUNT
IF(ICOUNT) 13,13,1A
14 WRITE(6,A) I,LIMITXIlf J), XVALUEtL IMITX( 2, J ) , ITOTAL ,PREO(J)
4 FORMAT! ',15,3(3X,F1 i«4) ,5X, I5,5X, F10.4)
13 CONTINUE
WRITE{6,3) 1ST AT f ITOTAL, MI
3 FORMAT{ '>', 'STATION SUMMARY'//' STATION NO, ' ,10X, Ili/ ' NO. OUTS
1IDE LIMITS »tI5/« TOTAL NO. OF DBS, »,I5)
GO TO 11
99 STOP
END
-------
RESULTS FOR STATION NC. 3
SAMPLE
NO.
4
10
12
13
20
22
23
26
27
28
29
30
32
34
35
36
37
38
39
50
51
52
53
57
58
61
62
63
64
65
71
72
74
75
76
79
81
82
87
68
93
105
106
IC7
112
113
118
119
120
121
122
123
124
128
129
130
131
132
133
134
135
LONER
LIMIT
2.7117
2.7117
2,7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7117
2.7T17
2.7117
2.7117
OBSERVED
VALUE
1.7000
2.7000
2.4000
2.5000
2.3000
4.4COO
4.5500
2.2500
2.2500
2.1500
2.20OO
2.5000
2.65f)U
2.5000
2.5UOO
1.7COO
1.8000
2.5000
2.60CO
1.70CO
2.2000
1.8500
2.3000
4.2000
4.4000
4.3000
4.4500
4.6000
5.2500
5.5000
4.7000
4.2500
2.2500
2.4OOO
2.5000
4.5500
4.3000
4.CCOO
4.1500
4.7OOO
4,1000
2.7000
2.6500
2.60CO
4.4000
5.4500
4.0000
4.O500
4.9500
5.0500
5.6000
5.3500
4.0500
4.O5OO
5.2000
4.8000
4.9000
4,7500
+.0500
4.3000
4.5500
UPPER
LIMIT
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3. 9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3.9269
3*9269
3.9269
NO.OUTSIDE
LIMITS
1
2
3
4
5
6
7
a
9
10
11
12
13
14
15
16
17
IB
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59 ,
60
61
PREDICTED
VALUE
3.4000
3.4000
3*4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4CCO
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.40CC
3.4000
3.4000
3.4COO
3.40CO
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.40CO
3.4COC
3.4000
3.4COO
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4O)tJ
3.400C
3.4000
3.40CO
3.4000
3.4000
3.4000
3.40OO
3.4000
3.4000
3.4000
3.40CO
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.40CO
3.4000
3.4000
3.4000
3.4000
STATION SUMMARY
STATION NO. 3
NO. OUTSIDE LIMITS 61
TOTAL NO. OF DBS. 135
257
-------
RESULTS FCR STATION NO.
SAMPLE
NC.
7
9
15
18
20
22
23
26
27
28
29
32
34
35
36
37
39
48
49
50
51
53
57
56
59
60
61
62
63
64
65
66
70
71
72
74
75
76
19
86
67
68
106
107
112
113
114
115
118
119
120
121
122
122
124
125
126
127
128
129
130
131
132
134
135
LONER
LIMIT
2.6932
2,6932
2. 6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2. 6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.4932
2.6932
2.693i
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2. 6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
ZT6932
2.6932
2.6932
2.6932
2.6932
2.6932
2.6932
OBSERVED
VALUE
2.4500
2.3000
4.1000
2.6CGC
2.6000
4.1COO
4.9500
2. 3 500
2.1500
2.45CO
2.2000
2.65CO
2.4500
2.35OO
1.650C
1.2000
2.5500
2.6500
2.3500
2.0500
2.6500
2.5000
4.05CO
4.1000
4.05OO
4.0500
4.5500
4. 6001)
4.8500
5.0500
5.20CO
4.0500
4.1500
4.3500
4.2500
2.3500
1.6500
2.4000
4.0500
3.9500
4.60OO
4. 7C:OU
2.5500
4.95CO
5.3000
4.4000
4.3000
4.3500
5.1500
4. 8OOO
5.2000
4. 8COO
5.2000
4.2000
4.1500
4.5OOO
4.7000
478500
5.1000
4.7500
4. 8000
5.3000
4.3500
4.8000
UPPER
LIMIT
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
379312"
3.9312
3.9312
3.9312
3.9312
3.9312
3.9312
NC. CUTS IDE
LIMITS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
19
60
61
62
63
64
65
PREDICTED
VALUE
3.4000
3.4COC
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
9.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4COO
3.4000
3.4000
3.4000
3.4000
3.4CUO
3.4000
3.4CCO
3.4000
3.40CO
3.4CfaO
3.4COO
3.4CCO
3.400C
3.4000
3.4CCO
3.4000
3.4000
3.4COO
3.4000
3.4000
3.4000
3.4000
3.4000
3.4COC
3.4000
3.4COO
3.4000
3.4000
3*4000
3.4000
3.4000
3.4000
3.4000
3.4000
3.4COO
3.4000
3.4000
3.4000
r.40co
3*4000
3.4000
3.4000
3.4000
3.4000
3.4000
STATION SUMMARY
STATION NC. 4
NO. OUTSIDE LIMITS 65
TOTAL NO. OF DBS. 135
258
-------
RESULTS FDR STATION NO.
SAMPLE
NO.
1
2
3
4
25
27
28
29
30
31
32
3*
35
36
37
39
40
41
42
44
52
54
55
61
62
63
64
65
66
67
ta
69
70
71
77
78
64
85
86
87
88
92
93
54
95
106
1C7
116
117
118
119
120
121
124
125
126
127
128
T29
130
131
132
133
134
135
S1ATICN SUMMARY
STATION NO.
NO. OUfSIOE LIHITS
TOTAL M0« OF DBS.
LOWER
LIMIT
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.232-4
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
3. 2324
3.2324
3.2324
3.2324
3.2324
3.2324
3T2324
3.2324
3.2324
3.2324
3.2324
3.2324
3.2324
C8SERVEO
VALUE
2.1500
1. 9000
2.5000
2. bCJO
5.0500
3.00OO
2. 5CCO
2.7000
2. 8 JOO
3.05CO
3.0500
2.8500
2. 8000
3.2000
2.7000
3.1UOO
3.2OOO
2.9500
2.8000
3. 15OO
2.8500
3.0500
3.2000
4.8COO
5.1000
5.1500
5.2009
5.30CO
4.9UOU
4.8COO
5. 1OOO
5.7QOO
5.9000
5.15CO
3.1uDO
3.2000
4. 8COO
4.t>000
5.1000
4.5500
5.6OQO
4.7500
4.9500
5.2500
5.3500
3.2000
3.O500
4.8000
5.1500
5.4500
5.3000
5.3000
4.9500
4.9500
5.2500
5,7500
6.05GO
6.4000
5T9CC6
5.3000
4.7000
5.1000
5.8500
6.5000
6.5000
UPPER
LIMIT
4.5360
4. 538(1
4.5380
4.5380
4.5380
4. 5380
4.5380
4.5380
4.5380
4. 5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380.
4.5380
4.5380
4.5380
4.5380
4.5380
4.538O
4.538C
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.S38G
4.5380
4.5380
4.538O
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.5380
4.538O
4.5380
4.5380
4.5380
4T5380-
4.5380
4.53BO
4.5360
4.53BO
4.5380
4.5380
NO. OUTS IDE
LIMITS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
PREDICTED
VALUE
4.0000
4.0000
4.0000
4.0000
4.0000
4.00OO
4.0000
4.0000
4.0000
4.0000
4.0CCO
4.0000
4.0COG
4.0000
4.0000
4.0000
4.0000
4.0000
4.0COC
4.0000
4.0000
4.0COC
4.0000
4.0000
4.0000
4.0COO
4. 0000
4.0000
4.0000
4.0000
4.0000
4.0COO
4.0000
4.OOOO
4.GQOO
4.0000
4.0000
4.0COO
4.0000
4.0000
4.00OO
4.0000
4.0000
4.0000
4.0000
4.0COO
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.OOOO
4.0000
4.0COC
4.0000
4.0000
4.0000
4~.oo6o
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
5
65
135
259
-------
RESULTS FOR STATION NO. 6
SAMPLE
NO.
1
2
3
4
14
22
25
27
28
29
30
31
32
34
35
36
37
40
41
42
43
51
52
57
61
62
63
64
65
66
67
68
69
70
71
72
84
86
87
ee
89
92
93
94
S5
110
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
LOWER
LIMIT
3.2442
3. 2442
3.2442
3. 2442
3.2442
3.2442
3.2442
3.2442
3.2442
3. 2442
3.2442
3. 2442
3. 2442
3.24*2
3. 2442
3.2442
3.2442
3.2442
3.2442
3. 2442
3.2442
3.2442
3.7442
3. 2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3. 2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3.2442
3. 2442
3.2442
OBSERVED
VALUE
1.9000
2.CCGO
2.4000
2.8500
4.6500
4.5500
5.1500
2.5500
2.7500
2.7500
3.0500
3.1000
3.2000
3.0COO
3.1500
2.8500
3.0000
3.1500
3.1000
2.9500
3.1000
3.2CUO
2.5500
3.1500
4.6500
5.1000
5.2COO
5.3000
5. 10CO
4.9500
5.3500
5.4000
4.9000
5.8500
6.2500
4.5500
4.7500
5.1000
S.luOO
5.25CO
4.7500
4.90OO
4.9500
5.2500
4.85OO
3.2C-00
5.0000
4.9500
4.9000
4.8500
4.7500
4.6500
4.7000
4.70CO
5.5000
5.5000
5.9000
6.1000
6.4500
5.6500
5.7000
5.1500
5.000O
6.1000
6.6500
6.5500
UPPER
LIMIT
4.5374
4.5374
4.5374
4.5374
4. 5374
4. 5374
4.5374
4.5374
4.5374
4.5374
4.5374
4.5374
4.5374
4. 5374
4. 5374
4. 5374
4.5374
4.5374
4. 5374
4.5374
4.5374
4.5374
4.5374
4.5374
4.5374
4. 5374
4. 5374
4.5374
4.5374
4.5374
4.5374
4. 5374
4. 5374
4.5374
4. 5374
4.5374
4.5374
4. 5374
4.5374
4. 5374
4.5374
4.5374
4.5374
4.5374
4.5374
4. 5374
4.5374
4.5374
4.5374
4.5374
4.5374
4. 5374
4.5374
4.5374
4.5374
4.5374
4. 5374
4.5374
4.5374
4.5374
4.5374
4.5374
4.5374
4.5374
4.5374
4.5374
MO. OUTSIDE
LIMITS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
16
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
6.2
63
64
65
66
PREDICTED
VALUE
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.0CCC
4.0000
4.0000
4.0000
4.000X3
4.0000
4.0COO
4.0000
4.000C
4.0000
4.0000
4.CCCO
4.0000
4.0000
4.CCOO
4.0000
4.0000
4.0COO
4.0000
4.0QCO
4.0000
4.0000
4.0000
4.0000
4.000PO
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.000O
4.0000
4.0000
4.0COO
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.CCOO
4.COOO
4.0000
4.0000
4.0000
4*0000
4.0000
4.0000
4.0000
4.0000
4.0000
4.0000
STATION SUMMARY
STATION NO. 6
NO. OUTSIDE LIMITS 66
TOTAL NO. OF DBS. 135
260
-------
RESULTS FOR STATION NO. 7
SAMPLE
NO.
1
2
3
4
5
6
7
8
9
10
11
21
22
29
30
31
34
35
36
37
39
40
42
50
SI
52
53
54
55
72
13
74
76
77
78
79
8C
81
82
83
84
85
88
93
94
95
96
97
98
99
100
101
102
103
1C4
105
1C8
110
131
132
133
134
135
LOWER
LIMIT
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3*9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
3.9566
OBSERVED
VALUE
2.9CGG
3.4000
2.3500
2.1500
2.9000
3.1000
2.5500
3.2000
3.1500
3.7000
3.7500
5.4000
5.2000
5.6500
5.75CO
5.3000
3.8000
3.9500
3.3500
2.9000
3.6000
3.80OO
3.5500
3.5500
3.4500
3.3000
3.80OO
3.8500
3.9500
5.2000
5. 3000
5.2OOO
5.8500
6.0COC
5.3500
5.5500
5.50CO
5.2000
5.2500
5.3CCO
5.4000
5.2SCO
5.7000
5.1500
5.2000
5.3000
5.3500
5.50CO
5.3OOO
5.2000
5.4500
5.2500
5.5000
5.75CO
5.350U
5.3000
5.1500
5.2000
5.2000
5.1500
5.6500
5.400O
5.4000
UPPER
LIMIT
5.1105
5.1105
5.1105
5.1105
5.1105
5* 1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.11C5
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.11C5
5.11C5
5.11U5
5.1105
5.1105
5.1105
5.11C5
5.1105
5.1105
5. 11C5
5.1105
5.1105
5.1105
5.1105
5.1105
5.11C5
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
5.1105
NC. OUTSIDE
LIMITS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
4C
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
PREGICTEC,
VALUE
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6COO
4.6000
4.60OO
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.60CO
4.60CG
4.6000
4.6CCO
4.6COO
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6060
4.6000
4.6000
4.6COO
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
4.6000
STATION SUMMARY
STATION NO.
NO. OUTSIDE LIMITS
TOTAL NO. OF DBS.
7
63
135
261
-------
RESULTS FOR STATION NO. 6
SAMPLE
KC.
I
2
3
4
8
9
10
11
12
13
14
15
16
17
18
19
20
30
35
36
37
38
39
40
49
50
51
52
53
54
55
56
66
74
75
79
80
81
82
63
84
85
86
67
88
89
90
91
«
93
94
106
115
116
117
118
119
120
LOWER
LIMIT
A.2380
4.2380
4.238C
4.238C
4.238U
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2330
4.2380
4.238C
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.238C
4.2380
4.2380
4.2380
4.2380
4.238C
4.2380
4.238U
4.2380
4.2380
4.238U
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.2380
4.238C
OBSERVED
VALUE
3.5500
3.9500
3.6000
3.4000
4.2000
3.5000
3.3500
3.2500
2.9500
3.25CO
3.4500
3. 7000
3.55CO
3.8500
3.5500
3.7500
4.0500
5.4000
5.4500
5. 4000
5.5500
5.550v>
5.65CO
5.61)00
4. 2OUO
3. 8000
3.7000
3.80OO
4.0000
4.0000
4.0500
4.050O
4. U5UO
4.2000
3.8500
5.4500
5.60GO
5.5000
5. 350u
5.7500
5.7000
5.95CC
6.2500
6.35UG
5.8000
5.5500
5.9000
5.8500
5.6500
5.5UOO
5.4500
5.3500
5.4000
5.6000
5.5500
5.5000
5.4000
5T45THT
UPPER
LIMIT
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3066
5.3068
5.3068
5.3068
5.3068
5.3068
5. 3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3C68
5.3C68
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3066
5.3066
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3C68
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
5.3068
ST37J68-
NC. OUTSIDE
LIMITS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
~59~
PRECICTED
VALUE
4.8300
4.8300
4.8300
4.8300
4.83,00
4.8300
4.8300
4.830C
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4.8300
4*8300
4*8300
4.8300
STATION SUMMARY
STATION NO. 8
NO. OU7SICE LIMITS 59
TOTAL NO. OF OBS. 135
262
-------
C FIRST STAGE PROCEDURE FOR PREDICTING DELTA *
C
C NVAR= THE NUMBER OF VARIABLES READ IN OFF THE DATA CARDS,
C ONE DEPENDENT VARIABLE(FROM WHICH DELTA WILL BE COMPUTED)
C AND NVARM1 FACTORS
C NVARM1= NVAR - 1
C NDATA= THE NUMBER OF DATA CARDS
C NFMT= THE NUMBER OF FORMAT CARDS
C XYZ= 1 IF TH& DELTAS ARE TO BE COMPUTED AND PUNCHED
C =0 OTHERWISE
C NMIN= THE MINIMUN NUMBER OF OBSERVATIONS NEEDED TO COMPUTE THE
C DELTAS (GREATER THAN OR EQUAL TO 2)
C NLEV(I)= THE NUMBER OF LEVELS OF THE I TH FACTOR C A FACTOR IS AN
N c INDEPENDENT VARIABLE) 1=1,2, ... .NVARM1
£ C RANGE(I,J)= THE SORTING BCUNDRIES FOR THE I TH FACTOR
C 1=1,2, ... ,NVARM1 J=l,2, ... ,NLEV(I)-1
C
C
DIMENSION FMT{40),ICOUNT(l,10,5,5,5,51,DA7A(6),ID<6),YU),NLEVI5l,
lNLEVMl<5),RANGEI5,9),L(6),S(l,10,5,5,5,5),Sq
-------
READ(5f15) (NLEVdltl = 1.NVARM1)
15 FORMATC5I5)
NLEV1 = NLEV(l)
NLEV2 = NLFV(2)
NLGV3 = NLEVO)
NLEV4 = NLEV(4)
NLEV5 = NLEV(5)
C
C READ IN THE RANGE NUMBERS FOR EACH INDEPENDENT VARIABLE
C
DO 20 I = ItNVARMl
NLEVMHI) = MLEV(I) - 1
Ml = NLEVMKI)
20 READ (5,25)(RAHGE(I,J),J=i,Ml)
25 FORMAT(8F10.0J
C
C READ THE FORMAT CARD
C
DO .30 I = 1,NFMT
K = I * 21.}
J = K - I
-------
40 Y(J) ~ DATA(ID(J))
C
C LOOP TO SORT INDEPENDENT VARIABLE OR FACTORS INTO LEVELS OR RANGE
C
DO 50 J=2,NVAR
JM1 = J - 1
L(J) = 1
IF (NLEV(JM1)0EQ»1) GO TO 56
M2 = NLEVMHJM1)
DO 45 K=ltM2
IF (Y(J) .GT, RANGEt JM1,K) ) GO TO 45
LU) = K
GO TO 50
45 CONTINUE
L(J) = NLEVUM1)
50 CONTINUE
ICOUNT(ltLC2)fL(3)f L(4)rL(5)tL(6M = ICOUNT( 1, LC 2) ,L( 3) ,L(4) ,L(5) ,
C
C DC LOOP TO COMPUTE THE TOTALS FOR EACH VARIABLE SO THAT THE LEVEL
C AVERAGES CAN BE CCMPUTED
C
DO 51 M=2fNVAR
MM1 = M - 1
JI= L(M)
TQT(MM1,JI)= TOTCMMlfJIH Y
-------
S <1,L<2),L(3),L(4),L(5),L(6)) = S (1,L(2),L<3),LC4),L<5),L(6)) +
1 Yd)
C
C COMPUTE SUM OF SQUARED DEPENDENT VARIABLES FOP EACH CELL
C
SQ<1,L(2),L<3),L(4),L<5),L<6)) = SO (1, L 12 ) ,L ( 3) , L ( 4) , L ( 5 ) , L ( 6) ) +
1 Y(l)*#2
52 CONTINUE
DO 55 I=ltNVARMl
K = NLEV(I)
DO 55 J=lfK
IF (ICNT(I,J) .NE. 0) GO TO 54
WRITE(6,53) I,J
53 FORMAT(//,10X,«NO OBSERVATIONS FOR FACTOR»,12,«, LEVEL,12,///)
GO TO 55
54 R = ICNT(I,J)
C
C COMPUTE LEVEL AVERAGES
C
A(I,J)= TOTtI,J) / R
55 CONTINUE
IF(XYZ .EQ. 0.0) GO TO 75
WRITE«6,999)
999 FORMAT!!)
DO 70 16 = 1,NLEV5
DO 70. 15 = 1,NLEV4
DO 70 IA * 1VNLEV3
DO 70 13 = 1,NLEV2
DO 70 12 = 1,NLEV1
C
C CHECK TO SEE IF THE NUMBER OF OBSERVATIONS IN A CELL ECUALS OR
C EXCEEDS THE SPECIFIED MINIMUM NUMBER
C
IF (ICOUNTd, 12,13tI4,15,16) .LT. NMIN) GO TO 60
RN = ICOUNT(1,I2,I3,I4, 15,16)
-------
c
C COMPUTE THE SAMPLE VARIANCE FOR EACH CELL
C
SSQ = (SQ(1,I2,I3, 14,15,16) - ( ( S( 1, 12, 13, 14, I 5, I 6) **2) /RN> ) /(RN -
1 1)
C
C COMPUTE THE DELTA FOR THIS CELL
C
DELTAU2,I3,I4,I5,I6) = (RN*SSQ) / S(l, 12 , 13, 14, 15, 16 >
JN = RN
8(1) = Ad,121
B(2) = A(2,I3)
8(3) = A(3,I4)
B(4) = A(4,I5)
ai B(5) = A(5,I6)
^ WRITE(6,59) JNfDELTA(I2,I3,I4,I5,I6),(BU),I = l,NVARMl)
WRITE (7,59) JN,DELTA(I2,I3,I4,I5,I6),(B(I),I=1,NVARN|I)
59 FORMAT(I5,F1C.5,5X,5F12.4)
C
C
C IF YOU DESIRE TO WRITE AND PUNCH THE LEVEL NUMBERS INSTEAD OF THE
C LEVEL AVERAGES, REPLACE THE CARDS WITH AVE IN COLUMNS 75-77
C WITH THE FOLLOWING 8 CARDS DELETING THE C IN Tht FIRST COLU
C IB(1) = 12
C IB(2) = 13
C IB(3) = 14
C IB(4) = 15
C IB(5) = 16
C WRITE(6,59) JN,DELTA(12,13,14,15,16),(IB(I),1=1,NVARM1)
C WRITE(7,59) JN,DELTA(I 2,13,14,I 5,16),(IB(I),1 = 1,NVARM1)
C 59 FORMAT(I5,F10.5,5X,5I12)
C
C
GO TO 70
-------
C IF THERE ARE NOT ENOUGH OBSERVATIONS IN THE CELL TO COMPUTE DELTA
C THE CELL NUMBER IS WRITTEN ALONG WITH THE NUMBER OF 08SERVA
C IN THE CELL
C
60 WRIT£(6,65) 12, 13 , 14, 15, 16 , ICOUNTM, 12, 13, 14, 15, It)
65 FORMAT!/,2GX,«ICOUNT C 1,»,12,,,12,,,12,,,12,,,12,) = «,
112,/)
70 CONTINUE
75 CONTINUE
WRITE(6,999)
WRITE(6,76)
76 FORMAT(?.0(/),3GX,'AFTER THE DATA HAS BEEN SORTED ACCORDING TO THE
1PREVIOUSLY GIVEN FACTOR ',/,27X,'RANGES, WE HAVE THE FOLLOWING FRE
2QUENCY OF SAMPLE SIZES FOR COMPUTING THE DELTAS*',///)
W DO 78 I = 1,21
B 78 IHIST(I) = C
C
C COMPUTE A HISTOGRAM SHOWING THE NUMBER OF TIMES THAT WE HAVE CERT
C SAMPLE SIZES IN THE CELLS TO COMPUTE THE DELTAS
C
DO 80 16 = 1,NLEV5
DO 80 15 = 1,NLEV4
DO 80 14 = 1,NLEV3
DO 80 13 = 1.NLEV2
DO 80 12 = 1»NLEV1
j = ICOUNT<1,I2,I3,I4,I5,I6)
IF (J .GT. 2«) J = 20
JP1 = J * 1
80 IHIST(JPl) = IHIST(JPl) + I
WRITE(6,82) (IHIST{K),K=1,21),(KK,KK=1,20)
82 FORMAT(19X,»FREQUENCY»4X,21(13,IX),//,9X,'NUMBER OBSERVATIONS1,6X,
110«,20(2X,I2))
WRITE(6,999)
C
C COMPUTE A HISTOGRAM FOR INDEPENDENT V/>RI£BLt 1 FCR EACH OF ITS
-------
C LEVELS SHOWING THE OCCURANCE FREQUENCY OF THE SAKPLE SIZES
C IN THfc CELLS FOR FACTOR 1, THIS IS DONE SEPERATELY FOR EAC
C CF ITS NLEV(l) LEVELS.
C
IJ = 1
WRITE<6,87) IJ
87 FORMAT*/////,2X,'FACTOR NUMBER',12,/)
WRITE(6,91)
91 FORMAT<34X,«GREATER THAN',5X,'LESS THAN OR EQUAL 70S 10X, "AVERAGE
1WITHIN LEVELS5X,'NO. DBS. PER LEVEL*)
WRITE (6., 92) RANGE ( JJ,1),A(IJ,1),ICNTCIJ,1)
92 FORMATC20X,'LEVEL 1,25X,FI2.3,19X,F12.4,16X,lo)
Ml = NLEVMKIJ)
IF (NLEVUJ) .EQ. 2) GO TO 96
DO 93 1=2,HI
IM1 = I - 1
93 WRITE (6, 94) I ,RANGE (IJ, IM1), RANGE ( IJ,I ),A{ IJ,I ),ICNTUJ,I)
94 FORMAT(20X,'LEVEL ',12,5XVF12«3,8X,F12.3,19X,F12.4f16X, 16)
96 NL = NLEV(IJ)
WRITE(6,97) NLEV(IJ),RANGE
-------
95 CONTINUE
IF CNVAR .EQ. 2) GO TO 160
C
C COMPUTE THE HISTOGRAM FOR FACTOR 2
C
IJ = 2
WRITE<6,87) IJ
WRITE<6,91)
WRITE(6,92) RANGE< IJ, 1),A(JJ,1),ICNTtIJ,1)
Ml = NLFVMIUJ)
IF (NLEV(IJ) .EQ. 2) GO TO 99
DO 98 1=2,Ml
I Ml = I - 1
98 HRITE<6,
-------
WRITEC6,91)
WRITE(6*92) RANGE(IJ,1),A
M.1 = NLEVMKIJ)
IF (NLEVCIJ) .EQ, 2) GO TO 112
00 111 1=2,Wl
IM1 =1-1
111 WRITE(6,94} I,RANGE
-------
127 NL = NLEV(IJ)
WRITE (6, 97) NLEV UJ), RANGE
DO 135 14 = IfNLtVB
DO 135 13 = 1,NLEV2
DO 135 12 = lyNLEVl
J = ICQUNT(1,12,13,14, 1,16)
IF (J .61. 20) J = 20
JP1 = J + 1
135 IHIST(JPl) = IHIST(JPi) + 1
WRIT(6,90) I,(IHIST(K),K=1,21),(KK,KK=1,20)
140 CONTINUE
IF (NVAR .EQ. 5) GO TO 160
C
C COMPUTE THE HISTCGRAM FOR FACTOR 5
C
IJ = 5
WRITE(6,87) IJ
WRITE(6,91)
WRITE (6, 92) RANG(IJ,1 ),/*( IJ,1 ), ICNT< IJ, 1)
Ml = NLEVMKIJ)
IF (NLEV(IJ) oEQ. 2) GO TO 142
DO 141 1=2,Ml
IM1 =1-1
141 WRITE(6,94) I,RANGE{IJ,IM1),RANGECIJ,I),A(IJ,I),ICNT(IJ,I)
142 NL = NLEVUJ)
WRITE! 6, 97) NLF.VC IJ ) , RANGE* I J,M1) , A( IJ ,NL) , ICNTCI J, NL)
DO 155 I = 1,NLEV5
DO 145 11= 1,21
145 IHISTCII)= 0
DO 150 15 = 1,NL£V4
DO 150 14 = 1,NLEV3
-------
30 150 13 = 1,NL£V2
00 150 12 = LfNLFVl
J = ICCUNTU,I2,I3,I4, 15, I)
IF (J *GT. 20) J = 20
JP1 = J + 1
150 IHIST(JPl) = IHIST(JPl) + 1
URITE<6990) I9(IHIST(K)fK=l ,21
155 CONTINUE
160 CONTINUE
WRITE!6,959)
998 STOP
END
to
-4
10
-------
20 J.05461 2.09PO 263889.4375 23.JOSS
ICOUNT I 1. 2t 1, 1. 1, 1) . I
1.6027
I COUNT I 1, 3, 1, 1, 1, It « (>
10 0.1940S S.iKiiO 2«388S.4375 23.5055 1.6U2T
* 0.17906 6.00JO 26368^.4375 23.5055 1.602T
2t O.CS967 7.00OO 263889.4375 23.5O55 1.6027
28 0.05371 8.000? 263889.4379 23.5O55 1.6027
21 O.OT712 2.0(100 868852.3750 23.5O55 1.6027
ICOUNT I 1. 2, 2. 1. 1, 1) - 0
ICOUNT
1)
16 0.20879 S.OilOO 8688*2.3750 23.5055 1.6027
14 0.19610 6.(JO(VI 868852.375ti 23.5^55 1.6(<27
.17 0.04n5 7.0000 8*8852.3750 23.5P55 1.6027
23 O.G5419 8.011X1 868852.3750 23.SOSS 1.6027
13 0.06619 2.00im464Zfc6.M.jO 23.5055 1.6027
ICOUNT < 1, 2, 3, 1, lt 1) » 14«4266.»<)!^ 23.5055
6.0Oim4«4266.l >'Jv 23.5M55
7.00Q01464266.C ton 23.SO55
8.00'JUl4642t>6.0.)VJ 23.505!
2.0OU02063333.U hill 23.5155
3.00UU2063833.C30O 23.5O55
ICOUNT I 1, 3. 4, 1. 1, 1) - o
5.0 J'I'I2"63S33.IJ'>J.> 23.SC55
6.0dj02l'oi833.'.My', 23.51155
7.OOr<)2v63S33.lV.i'> 23.5OS5
8.00')')2U63833.U,)i'l' 23.5355
2 .OOP i 263839.4375 74.67.'<4
ICOUNT ( It 2t It 2t It II '
1.6C-27
I.6u27
1.6027
1.6"27
1.6^27
1.6V27
1.6027
1.6,127
l.A"27
1.6417.7
1.6027
5 C.23566
6 0.04058
2 0.00054
ICOUNT I It 3t It 7, It II
ICOUNT < 1, 4, 1, 2t It II
ICCUNT ( It 5. 1. 2. 1, It
7.GOO) 2«3A«9.437S 24.6TC4
8.1/UOO 263889.4375 24.6704
2. '"Ml £68852.3750 24.67C4
ICOUNT < It 2t 2, 2, 1- 1) )
1.6027
1.6027
1.6 '27
2 O.n0132
4 0.05555
14 0.12667
7 0.03857
14 0.13248
ICOUNT I 1, 3. 2t 2. If II O
5.001) 66B85J.375U 24.6704
6.0000 868852.3750 24.6704
7.00O1 668852.3750 24.6704
8.0000 868852*3750 24.6704
2.00001464266.0.100 24.6704
ICOUNT « lf 2t 3, 2t It 1) - 0
1.6027
1.6O27
1.6027
1.6427
1.6027
ICOUNT I It 3t 3, 2. It II O
6
4
IT
19
3
0.15267
0. 18250
0.10067
0.12871
0.06748
5 .00001464266. OOOO
6.00001464266. 0000
7.00001464266.0000
8.000014642 66. OOOO
2.00O02063833.0000
ICOUNT 1 It 2. 4, 2. 1. 11
ICOUNT « It 3t 4t 2t It Ik
ICOUNT 1 It 4t 4t 2t It 11
ICOUNT « It * 4, 2t It 11
ICOUNT 1 It At 4. 2t It 11
24.6704
24.6704
24.6704
24.6 T04
24.6764
0
0
0
O
1
1.6U27
1.6027
1.6027
1.6027
1.6027
274
-------
3
5
21
14
19
2C
2
0.161*5
0.00642
0.10391
0.1*382
0.24511
0.71632
J.OC354
2 0.04716
IS 0.14419
18 0.23397
S C.28385
« 0.32131
e.cino-j2.i638.,J.n)j<,
2.0000 263884.4375
3.(ll)0i) 263*84.4375
4.0(100 263889.437*
5.POO') 263884.4375
6.0000 263889.4375
7.0000 263RH9.4375
24.67>OO 868852.3751. 23.5055
4.0000 868852.375i- 23.5U55
5.om-:) 668852.3750 23.5055
6.UOJ> 868852.3750 23.5055
ICOUNT I 1. 6, 2. 1. 2. II 0
2.6431
2.6431
2.6431
2.6431
2.6431
ICOUNT I 1, 7, 2. 1. 2. II . 1
1. 1. 3. 1, I, 1)
f
11
6
8
2
20
21
22
19
3
5
3
5
6
5
2
e
7
2
2
7
16
11
1C
1C
4
3
4
6
3
5
5
3
2
4
10
0.11903
0.19582
0.22522
0.14981
0.20769
0.17214
0.16163
0.25C-46
0.24118
0.01409
0.27069
O.OO4O2
U. 10376
0.07355
O.C8533
0.0214T
0.03138
0.03955
0.21038
0.17536
O.OP035
0.08636
A. 16684
0.20C56
3.10015
0.20821
0.34868
O.C597O
0.40133
O.C5690
Q.G4C15
O.C8543
0.10922
0.38208
0.03189
0.03180
0.02315
3.0UO')1464266.0.)UI,
4.0')09146426A.O>001464266. OQ:jl>
6.00001*6*266. OLl'H.
ICOUNT 1 1. 6, S, 1, 2, 11
ICOUNT 1 1, T, 3, 1, 2. It
2 .00002063833. O'JUO
3.000.12063833. OUOC
4.0'J002063833.000n
5.00uJ2C63833.0Uo<>
6.00092063H3. 0 I0:>
7.0^0^2063833.0000
2.041)0 263839.4375
3.i'OuU 263889.4375
ICOUNT ( 1, 3. 1. 2, 2, 11
5..IOO.) 263889.4375
6.0 W.) 263889.4375
ICOUNT 1 1, 6, 1, 2, 2, 11
ICOUNT 1 1, 7t It 2t 2t 11
2.0flOO 868852.375,1
3.000-1 1 68852. 375.-
4.0OOO 868852. 375i>
S.lhH'!) 868852.375')
6.0'in.-) 568852.375-'
7.t»)MO 808852. 375.)
8.';o:lf' 96a852.375'~"
».0>J031464 266.00 GO
3'.U'I'I 114642 06. DO'IO
*.0»)'.i>l*64266. i. J'^c;
5.0C")v/1464266..VlOa
6. CO' 014642 66.'." .U
7. HO Oo 14 642 66. '^'1')'-
8 ."Oi)l 1 1 464266 .no uM
2.'j')002f63833.C'J-.J
3.0CI002f'638i3.C .nil)
4.or>ro2t.<63d33.i^if)
5.C''C'02C63833. CJOO
6.OQ002t'63833.0i' 0
0
- 0
m O
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
/.6431
2.6431
2.o4Jl
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
2.6431
7.6431
2.6431
2.6431
3'. 9642
3.9642
0.12949
0.07*87
3.000O 868852.3750 23.5055
4.0000 868852.3750 23.5O55
3.9642
3.9642
275
-------
* 0.10*10
9 o.csin
S O.T76»6
5 0.2320*
7 0.061*7
7 o.CTaoo
3 O.S4M2
2 0.05(90
0*21707
11 0.204*5
4 0.13213
9
ICOUNT I 1. 4. ?. 1. 3, II
COUNT i. s. t. i. j. ii
ICUUNT I 1, t. 2. 1, !, 1|
ICOUNT I 1. 7. I, I, 3. II
I COUNT I I. 1. 3. 1, 9, II
ICOUNT 4 1. 2. 3. 1. 3. II
ICOUNT « 1. 3. 3, 1. 3. II
ICUUNT I 1. 4. 3. 1. 3, II
ICOUNT I 1, 5. 3, 1. 3. II
ICOUNT | 1, 6. 3, 1. 3, II
ICOUNT I 1, 7. 3. 1. 3. II
ICOUNT I 1. 1. 4. 1. 3, II
3.uO(U20t38S3.COOC
23.5055
Z3.VSS
24. 6TC4
74.6TU4
ICOUNT | 1. *. 4. l, 3, i| . o
ICOUNT I 1. 5. 4. 1. 3. II . a
ICOUNT I 1. &. 4. I. 3, 1> . 0
ICOUNT « 1. T. 4. 1, 3. II - n
ICOUNT I 1. 1. 1. 2, 3. O 0
3.Ol»0 2638B«.4375
4.0OOO 263889.4375
ICOUNT t li 4. 1, 2. 3. II
ICOUN1 t 1. ». 1. 2. 3, i.
ICOUNT I 1. 6. 1. 2. 3, II
ICOUNT I 1. 7. 1. 2. 3. II
'.'JUmr I 1. 1, 2. 2. 3. II
3.OOCJ 868852.3790
4.0000 868852.375C
5.OOOO 8«8852.37SU
t.OOOil (68852.3751.'
ICOUNT I It 6. 2. 2. 3, II
ICOUNT I 1. 7. 2, 2, 1, t.
ICOUNT I 1. 1. 3, 2, 3. II
3.000014642' ». Or,i,f.
4.OOOO1464266.000U
5.000314642*6.0100
6.00O01464266.00(.0
ICOUNT I 1« 6, 3, 2, 3, 1|
ICOUNT I 1. Tt 3, 2. 3, II
ICOUNT I 1, 1, 4. 2, 3t II
» 0
24.67C4
24.67C4
24.6704
24.6764
.0
24.67C4
24.6T04
24.6704
24.6704
* O
3.9642
3.9642
3.9642
3.9642
3.9642
3.9642
3.9642
3.9642
3.96*2
3.96*2
3.46*2
3.4642
2 0.005** 3.OOOJ2063833.OOOO
5 O.O4V2 4rfO0020«3*33.0000
ICOUNT
ICOUNT
KMNT
t COUNT
1
1
1
1
It
It
1*
It
*t
>t
kt
7.
4.
*t
»t
*.
2,
2t
2,
2t
3.
3t
3t
3.
11
It
11
11
24.6704 3.9A42
24.6T04 3.9642
1
1
0
. -
276
-------
K, AFTER TttE DATA HAS BEEN SORTED ACCORDING TO THE PREVIOUSLY GIVSN FACTOR
O RANGES, ME HAVE THE FOLLOWING FREQUENCY OF S4MPLE SIZES FOR COMPUTING THE OFLTAS.
-0
FREQUENCY 57 11 12 98 13 10 53443? 131 22 1413
NUMBER OBSERVATIONS 0 1 2 3 4 5 6 7 3 9 10 11 12 12 14 15 16 17 13 IS 2>
-------
FACTOR NUMBER 1
GREATER THAN
LESS THAN OR EQUAL TO
LEVEL 1
LEVEL 2
LEVEL 3
LEVEL 4
LEVEL 5
LEVEL 6
LEVEL 7
LEVEL NUMBER 1 FREQUENCY
NUMBER OBSERVATIONS
LEVEL NUMBER 2 FREQUENCY
NUMBER OBSERVATIONS
to
00 LEVEL NUMBER 3 FREQUENCY
NUMBER OBSERVATIONS
CttCI feMIMftCD A. KDEnilCttf V
LCVcL NUfVBcK % rKtwUtNvT
NUMBER OBSERVATIONS
I CUCI UtIMBCB K CDCmiCUI*W
LEVEL NUnocK 5 rKEBUcNCY
NUMBER OBSERVATIONS
LEVEL NUMBER 6 FREQUENCY
NUMBER OBSERVATIONS
LEVEL NUMBER 7 FREQUENCY
NUMBER OBSERVATIONS
2*000
3.000
4.000
5.000
6.000
7.000
9
0
6
0
9
0
0
0
9
0
11
0
2. 000
3*000
4.000
5,000
6.000
7.0CC
0
1
2
1
1
1
1
1
3
1
2
1
3
2
2
2
1
2
2
2
2
2
2
2
1
3
1
3
1
3
3
3
2
3
2
3
2
4
2
4
0
4
4
4
1
4
0
4
2
5
2
5
3
5
5
5
1
5
0
5
1
6
2
6
1
6
6
6
0
6
1
6
1
7
1
7
1
7
7
7
0
7
1
7
u
8
1
8
0
8
3
8
0
8
C
e
0
9
1
9
0
9
9
9
0
9
0
9
0
1C
{
10
1
10
10
10
0
10
0
10
AVER ACE WITHIN LEVEL
2.0000
3.00UO
4,0000
S.uO'M
7. IK' 00
8*0000
NO. DBS. PER LEVEL
135
135
135
135
135
135
135
ociiocooaa
11 12 13 14 15 16 17 18 19 20
OUOU110U02
10 11 12 13 14 15 16 17 IB 19 20
3000 II 'J 0111
10 11 12 13 14 15 16 17 18 19 20
0000010011
11 12 13 14 15 16 17 18 19 20
0001000011
10 11 12 13 14 IS 16 17 18 19 20
0101002002
10 11 12 13 14 15 16 17 IB 19 20
0100000013
10 11 12 13 14 15 U 17 18 1* 20
-------
FACTOR mum t
LEVEL.
LIVfL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
LEVEL
1
I
3
4
CHEATER
6JUUHO
1200000
NUMBER 1 FREQUENCY
NUMBER OBSERVATIONS
NHNtER 2 FREQUENCY
NUMBER OBSERVATION
UMBER 1 FREQUENCY
NUMER OBSERVATIONS
NUHBER 4 FREQUENCY
NUMBER OBSERVATIONS
THAN
OUO
.Ju'.»
18 1
0 1
12 2
14 3
0 1
13 4
0 1
LESS THAN OR tUUAL TC
12W)Gu.lK>«
laouoco.ii'ij
I 1 2 7 1 t
P 2 3 b 2 1
2 3 4 5 t 1
4 5 2 4 2 C
234541
AVfAACE ItlTNlN ItVCL
B68IJ2.3TSO
1464266 .(WOO
2063a33.UOOu
1-12
322
B 9 10
0 1 ft
8 9 1O
O
11
11
11
0
11
0
12
12
12
0
12
000
13 14 IS
13 14 It
13 14 IS
13 14 IS
NO. OBI. MA LEVEL
tlB
Ml
til
2*1
i> 0 0
16 IT IB
1 1 1
16 IT IB
16 IT IB
16 '.. 1»
t »
IV tO
B t
i« to
1* M
IV tO
MCICai NMMKA. 3
LEVEL 1
LEVEL 2
CHEATER THAN
LESS THAN OR EQUAL TO
24.OLO
AVERACE WITHIN LEVEL
23.SOSS
24.6M*
NO. oss. re* JLCKL
411
111
LEVEL MMER 1 FREQUENCY
NUMBER CBSERVAT IONS
2121111111 I*
10 11 12 < 13 14 IS 16 IT U It M
NIEft 2 FREOUENCV
NUMBER OBSERVATIONS
2B4BB610SS1O22002011O1O
0 1 Z 3 4 t 6 T > 9 1O 11 12 13 14 IS 16 IT 18 IV M
FACTOR RWMR 4
LEVEL 1
LEVEL 2
LEVEL 3
CHEATER THAN
2.0OO
3.500
LESS THAN OR EOUAl TO
2.OCO
3.500
AVERA6E WITHIN LEVEL
l.MZT
2.4431
3.9642
NO. OBS. FER LEVEL
44*
394
10 Z
LEVEL NUMBER 1 FREQUENCY 1< 2 3
NUMBER OBSERVATIONS O 1 2
1021301201B
10 11 12 1% 14 IS 16 IT 1* IV tO
LEVEL MHBER t FREQUENCY 6 4
NUMBER OBSERVATIONS 0 1
122O0011O13S
1 10 U It U 14 IS 16 IT IB IV tO
LEVEL NUMBER * FREQUENCY 33 5 2
NUMBER OBSERVATIONS a I 2
O110000000OO
V 10 11 12 n 14 M 14 IT IB 1* M
279
-------
SUBROUTINE GROOM ( XX,T! OH, IK,NKEfr P)
C4******************#**.**#*#*4###*#**#*^
c *
C SUBROUTING GRUOH ARRANGES THIE TIDE VALUC-S AND THE CORRESPCNCING *
C XX VALUES IN STRICTLY ASCENDING ORDER. *
C *
f **-#jMs*#*****#*##*#*#*^*######=^^
DIMENSION XX(2fl6v100) * TIDE(IOO), lAHAY(lOn)
101 FORMATC1TIDAL VALUE CUT CF ORDER* >
DO 11C 1=1, IK
110 TIOE( I)=TIDE{ 1)-FLOAT(IFIX(TIDE( I) ))
DO 111 J-19IK
XLOW=1.1
DO 112 I=J,IK
IF(TIDg(I)-XLOW) 113,112,112
113 XLOW=TIOE(I)
ILOW=I
112 CONTINUE
SAVE=T1DE(J)
TIDECJ)sTIOE(ILOW)
TIDEl ILOW)=SAVE
DO 114 1=1,16
SAVE=XX(1,I,J)
XX(1, IVJ)-XX(1«!,ILOW)
114 XXIlt It ILOW)=SAVE
111 CONTINUE
KAWAY=0
DO 22U 1=2, IK
IF(TI!JE(I)-TIDE
-------
to
00
H
un 3i-.-:; I=I,NKE;PP
IMH-ICOUNT-IAWAY(JAWAY)) 30 lf 302,302
302 JA«;\Y = JAHAY+1
IC;rUNT=tCOUNT+l
301 HUH i)=TID£(l + ICCUNT)
Ufl ?24 JI-1,16
X X ( 1 , J I , I ) =XX ( 1 , J 1 1 1+ 1 COUNT )
'
300 CrV4T
GC TO
-------
(0
00
ro
SUBROUTINE COUNTC XVALUE,XLIM1,XLIM2,ICOUNT)
C***# **##**#**:* *#:fr4^^
c *
C SUBROUTINE COUNT COUNTS TH£ NUMBER OF DATA VALUES THAT *R£ *
C OUTSIDE OF THE PREDICTED CONFIDENCE LIMITS. ICUUNT=1 IF OUT OF *
C LIMITS. ICCUNT=w» IF WITHIN LIMITS. *
C *
*****#*****#*#*****#****#**###^
ICC)UNT = 0
IF(XVALUE-XLIMl) 1C,10,11
11 IF(XLIM2-XVALUE) 1M,12,12
10 ICOUNT=1
12 RETURN
END
-------
SUBROUTINE LENGTH(XX,TIDE,XPOSIT ,NKEEP >
c
C
C
C
S
c
C
C
C
C
SUBROUTINE LENGTH CALCULATES 00 PROFILES THROUGH THE ESTUARY
FOR TIDAL PHASE OF 0.0, (>. 25, 0.50, AND 0.75.
*
#**^
DIMENSION XX{2, 16,100) , TIDEC .100) ,XPOSIT(16) ,SAVE(4,100) ,
1XX1<16),XX2<16),XX3<16),XX4{16),WORK{1<>0),ARG(10),VAL<1)
1 FORMATS *,4F2>}.4)
2 FORMAT C«iaD VALUES THRU ESTUARY FOR FOUR TIDAL PHASES1)
WRITE(6,2)
ACOO.C001
DO 10 1=1,16
*
*
THE THIRD INDEX, AN INDEX ON TIDAL PHASE, NUST BE CHANGED WITH
DIFFERENT XX SETS IN THE FOLLOWING FOUR STATEMENTS TO
APPROXIMATE TIDAL PHASE VALUES OF 0.0, 0.25, 0.5d, AND b.75.
*^^
10
11
XX2(
XX3(
XX4(
DO 1
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
I)=XX
I)=XX
I) = XX
11 = 1
(
(
(
A
2.^r L0«
ATSG(
ACFI
ATSG
ACFI
ATSG
ACFI
ATSG
ACFI
(
{
1
1
1
T
1
X
X
X
(X
(
(
X
X
(X
(
X
,
f
,
f
»
»
»
1,16)
1,33)
1,48)
tj
X POSIT,
ARG,VAL
X POSIT,
XXI,
,SAV
XX2,
WORK
Ed,
WORK
ARG,VAL,SAVE(2f
, XPOSIT,
»
»
,
ARG,VAL
XPOSIT,
ARG,VAL
XX3,
WORK
,SAV£(3,
XX4,
WORK
,SAVE<4,
T
I
,
I
»
I
»
I
16
)f
16
)t
16
),
16
),
,1
10
fl
10
.1
l(j
f 1
10
,ARG,VAL,10)
,ACC,IER)
,ARG,VAL,10)
,ACC,IER)
,ARG,VAL,10)
,ACC,IER)
,ARG,VAL,10)
tACCtIER)
-------
DO 12 1=1,100
12 WRITF<6,1) (SAVECJ,I),J=1,4)
RETURN
END
to
oo
-------
SUBROUTINE TI MFX < XX ,TID£, NKEEP )
##**# ###**#^
c *
C TIMEX CALCULATES CD PROFILES THROUGH THE TICAL PHASE FOR *
C STATIONS 1, 2, AND 3, *
C *
C $***$######*##£**:$**#:##*
DIMENSION XX(2,16tl')U) , T IDE ( 1-HU fSAVh ( 3 ,!(**) f XXXd'K-) iXXY (ItKO t
IXXZdOO), 111(3) fWGRK(100)vARG
2 FORMAT (!» 'LISTING OP OD VALUES THRU TIDAL PHASE FOR THRF.H STAT« )
WRITE(6,2)
ACOG <)'>:> 1
f* J- *Af *^ -.!» -JU -V 9,- -.V '*r ^f '** -V -V-V -^ »*' -^' **** -.'. .d- Jf JO -7s,vJ, ..J, .A, .1,-!' J» A ^- >.:.- Jj iju -J. -3L -.t. ^t, ,«, .,&, ^V -V -t A. .,1. *JU ».^ -**. .-v, ,.*,..^,», ^, ^L, *«, *. w\ -A -*. .C -^---1- -V
\j 3r;'V^**i» ;;- T1 ".,**# -i^3!*-.- -!? -3S-? 't- >.- ^--".. .(->». -r-.^ ^- -^- -F T..T**,* -r ^r -<* -v -r ^ -» -.-.'»- W -v -? -:;- -v- V -v *?-?^ -f --v- -^-^ -r- f- -> j- -, -r -^k -v v-3jr. V',- *, -r- V *t ^^ -v-'V^ -9s
C *
C III MUST BE CHANGED FOR DIFFERENT XX SETS #
C *
1 1 1(1 )=->.! f
1 11(2) =-0.5 5
C-V & ~f*~if ** V- "^f *" -J1- *^ -A"*- "** Vr O. t.«J,, .L ^V - <-. .J*+.\. .', .j^ »i, «A. ^V.' ^ JU »r *'' S1 "A'V* -A- -A- -. V -Vt -^' <>* s*-"-f- 'V-" -A- «i- -Ur ^- WU -V- .&. -Oi -O- *v>- ^> -*- J.- *
^- 5?.^. V gt X^ ^^s^ -S--1* -v -^ -3-* V- ' ,* -v- r- -^ *v- ^-'.- 'j- -v '.y f -»-"* ? -A. -.v**- «t- -t- -»' -v ^v -; ' -A- -*-*u j, ~, J. ..>-u. -A- sV *' *Ar .* v-^ »*--* «.v-a *j- -^ i- -.v-J, .4--vV > -^-v -,t*.L *V -*' -X--*.- ^>. < -
***»'>(- -T--5- -"?'/-« *-«-* -v j- -^ -? *%- -v i*--*1- *,'-*. -t- !/ -^ i--i*-i- ^-v V*-*"-.*-"*-3*- -. -.' ^ -* / ..... ->-;' '- *.* -T- -,--'f > -> ? -' «*-' * -y- V
ini)=3
II(2)=9
II(3)=14
DC)" 11 I = 1,NKE£P
XXX{I)=XX(i,II(l ),I)
XXY( I) = XX( It IH?) ,1)
11 XXZ(I)=XX(1,I1(3), 7.1
-------
DO 10 1=1,100
X=0.01*FLOAT(I)
CALL ATSGCX,TID£,XXX,WORK,NKEEP,ItARG,VAL,1C)
CALL ACFI(X,AR6,VAL,SAVE<1,I),10,ACC,IER)
CALL ATSG(X,TIDE,XXY,WORK,NKEEP,!,ARC,VAL,10)
CALL ACFI(X,ARC,VAL,SAVE(2,1),10,ACC,IER)
CALL ATSG(X,TIDE,XX2,WORK,NKEEP,1,ARC,VAL,10J
10 CALL ACFI(X,ARG,VAL,SAVE(3,I),10,ACC,IER)
DO 13 1=1,100
SAVE (1, I ) =SAVt (1. M + III < 1)
SAVE(2,I)=SAVE(2,I)+III(2)
13 SAVe{3,I)=SAVE<3,I)+III<3i
on 12 1=1,100
12 WRITEC6,!) (SAVE(J,I),J=1,3)
RETURN
END
-------
SUBROUTINE PREDICC XYZ, NKEEPf J,TI DE , PHAS E,XMEAN)
::fc#*###t***x*#*##*#:Mt^^
C *
C SUBROUTINE PREOIC TAKES THE OUTPUT FROM THE DIFFERENTIAL *
C EQUATIONS PROGRAM AND DETERMINES A PREDICTED VALUE AT THfc SAME *
C TIME AND POSITION AS THE OBSERVED VALUE WHICH HAS JUST BEEN READ *
C IN. AN INTERPOLATING ROUTINE IS USED TO DC THIS. XX, NKEEP, *
C IPOSIT, TIDE, AND PHASE ARE PASSED. XMEAN IS RETURNED. *
C *
C**$#*$* 4 **.##*#*** #*#4*****^
DIMENSION XYZ(?tl6t liK»tXZZ(K<0) , TIDE < 100 ), 1 1 { 3 ) , 1 1 1 1 3 ) ,
lWr)RK
-------
18 CALL ATSG< PHASE,TIDE,XZZ,WCRK,NKEEP,1,ARG,V/>L,JC>)
CALL" ACFK PHASE,/me, VAL,XMEAN,IO,ACC,IFR)
XMEAN=XMEAN+III(J)
JJ=J
RETURN
END
to
00
00
-------
SUBROUTINE PREXXX(XYZf NKFEP,J , TIDE, PHASE, XMFAN )
DIMENSION XYZ(2,16,liH» tXZZ(lDG) TIDE (IOC) » IK3 ) f IIII3 ) t
1 WORK < IOC > ARC ( 3»> ) » VAL < 30 )
REAL III
ACO0.050C
C^4***4c***^*.*** ************ *4*X-^-********* ******** £
c *
C II MUST BC CHANGED FCR DIFFERENT ESTUARIES. *
C *
****** *****^-*-^
IItl)=3
II(2)=9
****** ********** ****TT********:* ******
c *
C III MUST BE CHANGED FCR CIFFERENT ESTUARIES. *
C *
4******44* 4 ****
U.i«001) 8f8tl8
B DO 9 I=l»NKF-eP
9 XZZ(I)= XVZ(1,II(J) ,1)
18 CALL ATSG( PHASE, TI DE ,XZZ » WORK,NKEE P,l ,ARG,VAL,3D )
CALL ACFK PHASIF« ARG« VALf XMEAN, 3U,ACC ,1 ER)
- XMEANsXMEAN+IlHJ)
11 X=0.50
XHFAN=X*XMtAN-K1.0-X)*RESI
lij RESI =XMi;A!\i
RFTURN
FND
-------
SUBROUTINE LIMXXX (XMEAN, PHASE, IVECT,L)
DIMENSION PP(30) ,XLIM( 20) , IVECTC 19) ,RESID(19) , PAC3Q ) ,DELTA(4)
COMMON PESIDfRESI
FORMATC 9FlQ.4tl9F6*2)
SAT=8.i)
JHIGH**IFIX(SAT*10.3+l«5i
XR=1.0
XR-0.5
c *
C DELTA MUST BE CHANGED FOR DIFFERENT ESTUARIES. *
C * *
C******#***#*****###^*#*:?**£:*#^
DELTA(1)=0«275
DELTA (2 1=0. 275
OELTA< 3) =0.0475
PARA=XMeAN*DELTA
-------
IF(ADO-XMASS) 11,11,10
10 CONTINUE
11 1=1
00 70 J=J,19
XL=Q.f)5*FLGAT( J)
52 IF(PPm-XL) 50,51,51
50 I a 1*1
GO TO 52
51 IFU-U 53,53,54
54 X={XL-PP(I-1))/ PACI)
GO TO 55
53 X=XL/ PA (1) -0.5
55 XLIM(J)=XMEAN~(PARA-X)*C
to IFIPHASE-4I.JJCKJ1) 22,22,23
H 23 XLIM(J)=XR*XLIM(J)*{1*-XR)*RESID(J)
22 RESIDi J)=XLIM(J)
JJ=IFIX{XXX)
IF(JJ) 7,7,6
7 JJ=1
GO TO 12
8 IF{JJ-JHIGH) 12,12,9
9 JJ=JHIGH
12 IVECT(J)=JJ
70 CONTINUE
00 71 J=l,9
JKEEP=rVECT(J)
J)aIVECT(20-J)
)=XLIM(^G-J)
IVECT{20-J)=IKEEP
71 XLIM{20-J}
WRITE(6,1) PHASE,(XLIH{J),J=1,19)
99 RETURN
-------
END
(0
NO
to
-------
SUBROUTINE LI MRI V (XMEANf XI ,X2» J)
DIMENSION DtLTA(6) t PP( 30) ,PA(30)
c *
C VARIOUS ALPHA LEVELS *
C *
C WHEN DOING THE ANALYSIS RUTATi" THRU THE CYCLE UNTIL ALL LEVELS *
C HAVE 8F EN CONSIDERED. *
C *
ALPHA=fj.3*:
ALPHA=0.2 !
ALPHA0.15
ALPHAS. 1
= UO-XL
*.***.* *^*t--*******^-^-r .V '?.*** VV*********^-*
c *
C BOD DELTA VALUES FCP THE OHIO *
C "
C THE TWO DELTA SETS SHOULD UE INTERCHANGED IF BUD DELTAS ARF TO *
C B& CALCULATtO, *
C *
*^** -:- -4 *s *********** *******************************************
DFLTAl 1)='1. 135D-M.1.
**^
C OD DELTA VALUES FCR THE OHIO
C *
-------
D£LTA(1)=0.201
DELTA<2)=».2i2
DELTA(3)=0.214
DELTA<4)=0.2C7
DELTA{ 5)«0
PAPA=XMEAN*DF:LTA**^5^*^^.tA**«^**^^^^^*$*^4:^**^
91 O1«0-(0.5-PARA)*0«6
92 XMASS*C«Ot;l
PR08=7».0
AOD=1.0/EXP(PARA)
DO 10 1=1,30
X=FLOAT(I )
PR08=PROB+ADD
PA(I)=ADD
PP(I )=PROB
IF(ADD-XMASS) 11*11,10
10 CONTINUE
11 1=1
52 IF{PP(1)-XL) 50,51,51
50 1=1+1
GO TO 52
51 IFU-1) 53,53,54
54 X=(XL-PP( !-!))/ PACI)
X=FLOATII)+X-l.b
-------
to
vO
Ui
GO TO 55
53 X=XL/ PA(1)-G.5
55 Xl=XMEAN-fPARA-X)*C
56 IF(PPd)-XH) 57,58,58
57 1=1+1
GO TO 56
58 X=1.0-PP(I)
X=(XL-X)/ PA(I)
X=1.0-X
X=FLOAT( D + X-1.5
X2=XKEAN+(X-PARA)*C
RETURN
END
-------
SUBROUTINE LIMIT J< XMEAN, XI t X?,J )
**#***A***%****^^
c *
C SUBROUTINE LIMITS TAKES THE PRFDICTED KEAK />ND DETERMINES FCISSON^
C CONFIDENCE LIMITS. THE POISSON VARIANCE IS CALCULATED BY THE *
C FORMULA VAR= PEAK*DELTA. *
C *
OIMHNSION Oh-LTAdO) ,PP (30) , PA(3'»
^***:**^**^^^^^^:;^.^^**********
C *
C ALPHA CARDS SHOULD 3E ROTATED UNTIL ALL LEVELS HAVF BEEN RUN. *
C *
************* 4*4* ***************************************
ALPHA=*>.40
ALPHA=0,30
ALPHA='.)*25
ALPHA =0.20
ALPHA=0.15
ALPHA=H.05
ALPHA=0»1
ALPHA=0.35
XL=ALPHA/2.u
XH=1,0-XL
C ************ A******************:#*****A******^*< ******** **
c *
C PCTDM4C ifSTUARY DELTA VALUES. *
C *
^ ***********;>***« ***************************:{: **************:*
DELTA(l)=n.275
DELTA(2)=Ue275
DELTA (3)= /o'
-------
PROB-G.O
AOD=1.0/EXP(PARA)
DO 10 1=1,30
X=F LOATH)
PROB=PROB+ADD
PA(I)=ADD
PP(I)=PRCB
ADD=ADD*PARA/X
IFtADD-XMASS) 11,11,10
10 CONTINUE
11 1=1
52 IF(PPU)-XL) 50,51,51
50 1=1+1
GO TO 52
51 IFCI-1) 53,53,54
54 X=(XL-PP(I-1))/ PA(I)
X=FLQAT(I)+X-1.5
GO TO 55
53 X=XL/ PA(1)-0,5
55 X1=XWEAN-(PARA-X)
56 IF(PPd)-XH) 57,58,58
57 1=1+1
GO TO 56
58 X=1.0-PP(I)
X=(XL-X)/ PA(I>
X=1.0-X
X=FLOAT(I)+X-1.5
RETURN
END
-------
c
C
C
C
C
C
C
C
C
C
C
2
3
SUBROUTINE T IDALC IMONTH, IDAY, TIME, XPHASE, PHASE)
*####^
*
SUBROUTINE
MONTH, DAY,
TIDAL DETERMINES THE POINT IN TIDAL CYCLE USING THE
AND TIME OF DAY. TIME IS PASSED HAVING MILITARY
VALUES, SUCH AS
0.0 TO 0.99999.
1459 OR 1600. PHASE IS PASSED BACK RANGING FROM
*
*
*
#**;£;£***
X=FLOATCIFIX(TIME))
TIME=(X-HTIME-X)#li>0./6Ci.)/lGO.
#*###*#****#***###*#*#^
*
THE NEXT FOUR CARDS MUST BE CHANGED WITH DIFFERENT SURVEYS. *
THE PRESENT CARDS ARE CODED FOR JUNE 20 AS THE FIRST DAY OF THE *
SURVEY BEING CONSIDERED. *
*
****^***********^^
IFIIMONTH-6 ) 1,1,2
IDAY=IDAY-20
GO TO 3
IDAY=IDAY+10
PHASE=(FLOAT(IDAY)*24.+TIME-XPHASE)/12.4
PHASE=PHASE-FLOAT( I FI X ( PHASE) )
RETURN
END
-------
SUBROUTINE T1D12CIMONTH,IDAY,TIMEtXPHASE,PHASE)
ITIME=TIME
XTIME=TIME-ITIME
XTIME=XT1ME*100./6U.
TIME=ITIME
TIME=TIME+XTIME
C THE FOLLOWING FOUR STATEMENTS MUST BE CHANGED IF THE FIRST DAY *
C OF THE SURVEY OF INTEREST IS DIFFERENT FROM JUNE 20. *
IFUMONTH-6 ) 1,1,2
1 IDAY=IDAY-20
GO TO 3
2 IDAY=IDAY+10
3 PHASE=(FLCAT(IDAY)#24.+TIM£-XPHASE)/12.4
IPHASE=PHASE
PHASE=PHASE-IPHASE
PHASE=PHASE*12.
RETURN
END
-------
10
8
C
c
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
SUBROUTINE ATSGJX,Z,F,WCPK,IROWtICCLtAPG,VAL,NDIM)
SUBROUTINE ATSG
PURPOSE
NDIM POINTS OF A GIVEN GENERAL TABLE ARE SELECTED AND
GROUPED SUCH THAT A8S(ARGCD-X).G£»ABS(ARG(J)-X) IF I.GT.J.
USAGE
CALL ATSG ( X, Z,F , WORK, IROW, ICCL t ARG.VAL, NDIM)
DESCRIPTION
X
Z
F
CF PARAMETERS
THE SEARCH ARGUMENT.
THE VECTOR OF ARGUMENT VALUES (DIMENSION IPCW).
IN CASE ICOL=1, F IS THE VECTOR OF FUNCTION VALUES
(DIMENSION IRQW).
IN CASE ICOL=2t F IS AN IRGW BY 2 MATRIX.-THE FIRST
COLUMN SPECIFIES THE VECTOR OF FUNCTION VALUES AND
THE SECOND THE VECTOR OF DERIVATIVES.
A WORKING STORAGE (DIMENSION IROW).
THE DIMENSION OF VECTORS Z AND WORK AND CF.EACH
COLUMN IN MATRIX F.
THE NUMBER OF COLUMNS IN F (I.E. 1 OR 2).
THE RESULTING VECTOR OF SELECTED AND ORDERED
ARGUMFNT VALUES (DIMENSION NDIM).
THF RESULTING VECTOR CF SELECTED FUNCTION VALUES
(DIMENSION NDIMl IN CASE ICOL=1. IN CASE ICCL=2,
VAL IS THE VECTOR OF FUNCTION AND DERIVATIVE VALUES
(DIMENSION 2*NDIM) WHICH ARE STORED IN PAIRS (I.E.
EACH FUNCTION VALUE IS FOLLOWED 3Y ITS DERIVATIVE
VALUE).
NDIM - THL: NUMBER OF POINTS WHICH MUST flE SELECTED OUT OF
THF. GIVEN TABLE (Z,F).
WORK
IROW
I CO I.
ARG
VAL
-------
c
C REMARKS
C NO ACTION IN CASE IROW LESS THAN 1,
C IF INPUT VALUf NDIM IS GREATER THAN IROW, THE PROGRAM
C SELECTS CNLY A MAXIMUM TABLE OF IROW POINTS. THEREFORE THE
C USER OUGHT TO CHECK CORRESPONDENCE BETWEEN TABLE (ARG,VAL)
C ANC ITS DIMENSION BY COMPARISON OF NDIM AND IROW, IN CROER
C TO GET CORRECT RESULTS IN FURTHER WORK WITH TABLE (£RG,VAL).
C THIS TEST MAY BE DONE BEFORE OR AFTER CALLING
C SUBROUTINE ATSG.
C SUBROUTINE ATSG ESPECIALLY CAN BE- USED FOR GENERATING THE
C TABLE (ARG,VAL) NEEDED IN SUBROUTINES ALI, AHI, AND ACFIo
C
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIREu
C NONE
C
C METHOD
C SELECTION IS DONE EY GENERATING THE VECTOR WORK WITH
C COMPONENTS WORK(I)=ABS(Z(I)-X) AND AT EACH OF THE NDIM STEPS
C (OR IROW STE»S IF NDIM IS GREATER THAN IROW)
C SEARCHING FOR THE SUBSCRIPT OF THE SMALLEST COMPONENT, WHICH
C IS AFTERWARDS REPLACED BY A NUMBER GREATER THAN
C MAX(WORK(I)).
C
C
C
c
DIMENSION Z(IROW),F(IROW),WORK(IROW),ARG(NOIM),VAL( NDIM)
IFUROUUlfllffl
1 N=NDIM
C IF N IS GREATER THAN IROW, N IS SET EQUAL TC IRUW*
IF(N-IROW)3,3,2
2 N=IROW
-------
C GENERATION OF VECTOR WORK AND COMPUTATION OF ITS GREATEST ELEMENT.
3 B=0.
DO 5 I=1,IROW
OELTA=Ae$
-------
SUBROUTINE ACFIfXtARG,VAL,Y,NDIM,EPS,I£R)
C
C r...
C
C SUBROUTINE ACFI
C
C PURPOSE
C TO INTERPOLATE FUNCTION VALUE Y FOR A GIVEN ARGUMENT VALUE
C X USING A GIVEN TABLE (ARGtVAL) OF ARGUMENT AND FUNCTION
C VALUES.
C
C USAGE
C CALL ACFI (X,ARG,VAL,Y,NDIM,EPS,IER)
C
U) C JESCRIPTION OF PARAMETERS
S C X - THE ARGUMENT VALUE SPECIFIED BY INPUT.
C ARG - THE INPUT VECTOR (DIMENSION NDIM) OF ARGUMENT
C VALUES OF THE TABLE (POSSIBLY DESTROYED).
C VAL - THE INPUT VECTOR (DIMENSION NDIM) OF FUNCTION
C VALUES OF THE TABLE (DESTROYED).
C Y THIF RESULTING INTERPOLATED FUNCTION VALUE.
C NDIK - AN INPUT VALUE WHICH SPECIFIES THE NUMBER OF
C POINTS IN TABLE (ARG,VAL).
C EPS - AN INPUT CONSTANT WHICH IS USED AS UPPER BOUND
C FOR THE ABSOLUTE ERROR.
C IER - A RESULTING ERROR PARAMETER.
C
C REMARKS
C (1) TABLE (ARG,VAL) SHOULD REPRESENT A SINGLE-VALUED
C FUNCTION AND SHOULD 8E STORED IN SUCH A WAY, THAT THE
C DISTANCES ABS
-------
C THAN 1.
C <3) INTERPOLATION IS TERMINATED EITHER IF THE DIFFERENCE
C BETWEEN TWO SUCCESSIVE INTERPOLATED VALUES IS
C ABSOLUTELY LESS THAN TOLERANCE EPS, OR IF THE ABSOLUTE
C VALUE OF THIS DIFFERENCE STOPS DIMINISHING, OR AFTER
C (NDIM-1) STEPS (THE NUMBER OF POSSIBLE STEPS IS
C DIMINISHED IF AT ANY STAGE INFINITY ELEMENT APPEARS IN
C THE DOWNWARD DIAGONAL OF INVERTED-DIFFERtNCES-SCHEME
C AND IF IT IS IMPOSSIBLE TO ELIMINATE THIS INFINITY
C ELEMENT BY INTERCHANGING OF TABLE POINTS).
C FURTHER IT IS TERMINATED IF THE PROCEDURE DISCOVERS TWO
C ARGUMENT VALUES IN VECTOR ARG WHICH ARE IDENTICAL.
C DEPENDENT ON THESE FOUR CASES, ERROR PARAMETER HER IS
C CODED IN THE FOLLOWING FORM
C IEK=0 - IT WAS POSSIBLE TO REACH THE REQUIRED
C ACCURACY (NO ERROR)*
C IER=1 - IT WAS IMPOSSIBLE TO REACH THE REQUIRED
C ACCURACY BECAUSE OF ROUNDING ERRORS.
C ItR=2 - IT WAS IMPOSSIBLE TO CHECK ACCURACY BECAUSE
C NDIM IS LESS THAN 2, OR THE REQUIRED ACCURACY
C COULD NOT BE REACHED BY MEANS OF THE GIVEN
C TABLE, NDIM SHOULD BE INCREASED.
C IER=3 - THE PROCEDURE DISCOVERED TWO ARGUMENT VALUES
C IN VECTOR ARG WHICH AR? IDENTICAL.
C
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
C NONE
C
C METHOD
C INTERPOLATION IS DONE BY CONTINUED FRACTIONS AND INVERTF.D-
C DIFFERENCES-SCHEME. ON RETURN Y CONTAINS AN INTERPOLATED
C FUNCTION VALUE AT POINT X, WHICH IS IN THE SENSE OF REMARK
C (3) OPTIMAL WITH RESPECT TO GIVEN TABLE. FOR REFERENCE, SEE
C F.B.HILDEBRAND, INTRODUCTION TO NUMERICAL ANALYSIS,
C MCGRAW-HILL, NEW YORK/TORONTO/LONDON, 1956, PP.395-406.
-------
c
C ............... .......a... ..«.
C
c
c
DIMENSION £RG(NDIM),V£L(NCIM)
!ER=2
IF(NDIM)2U, 20,1
1 Y=VAL<1)
C
C PREPARATIONS FOR INTERPOLATION LOOP
2 P2=l.
l*> P3=Y
g 02=0.
Q3=l.
C
C
C START INTERPOLATION LOOP
DO 16 I=2,NDIM
11 = 0
P1 = P2
P2=P3
01=02
Q2=Q3
Z=Y
DtLTl=DELT?
JEND=I-1
C
C COMPUTATION OF INVERTED DIFFERENCES
3 AUX=VAL(I)
60 10 J=1,JEND
H=VAL(I)-VAL(J)
IF(APS(H)-1.E:-6*ABS(VAL( I) ) )4,4,9
-------
4 IF(ARG(I)-ARG
-------
C END OF INTERPOLATION LOOP
C
C
RETURN
C
C THERE ARE TWO IDENTICAL-ARGUMENT VALUES IN VECTOR ARC
17 IER=3
RETURN
C
C TEST VALUE DELT2 STARTS OSCILLATING
18 Y=Z
IER=1
RETURN
C
W C THERE IS SATISFACTORY ACCURACY WITHIN NDLM-1 STEPS
3 19 IER=0
20 RETURN
END
-------
POTOMAC DATA INPUT
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
82.399
82.240
82.099
82.299
82.399
82.699
82.699
82.690
82.699
82.699
82.699
82.500
82.599
82.640
82.699
82.399
82.599
82.390
82.199
82.199
82.000
82.000
82.000
82.000
82.099
82.199
82-.000
81.699
81.899
81.899
81.599
81.540
81.500
81.899
81.899
81.699
81.630
81.560
81.500
81.399
4.919
4.820
4.739
4.739
5.559
5.359
5.919
6.030
6.159
6.519
6.019
6.039
6.059
6.300
6.559
6.699
6.559
6.490
6.439
6.339
6.179
6.259
6.039
5.859
5.699
5.679
6.399
5.959
5.339
5.319
5.000
5.030
5.059
4.939
4.959
4.159
4.650
5.150
5.650
5.939
308
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
i
i
i
i
i
i
i
i
i
i
i
i
i
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
21
22
22
22
22
22
22
22
22
22
22
22
22
22
22
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
81.500
81.399
81.599
81.699
81.699
82.199
82.599
82.699
82.399
82.299
81.899
81.699
82.199
82.699
82.599
82.399
82.500
82.599
82.799
82.599
82.899
82.899
83.000
82.899
83.199
82.799
82.599
82.899
83.000
82.899
82.899
83.000
82.299
81.899
81.799
81.699
81.899
81.899
81.899
82.399
5.959
6.259
6.439
6.559
7.539
7.259
8.439
8.819
8.659
6.979
7.639
7.159
7.559
7.939
7.939
7.579
6.879
7.919
7.959
7.859
7.899
7.639
7.599
7.500
7.719
7.039
7.139
8.039
8.179
8.379
7.899
7.779
7.399
6.839
6.139
5.579
6.399
6.179
6.659
7.259
3O9
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
I
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
23
23
23
23
23
23
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
82.299
82.299
82.099
82.199
82.500
82.299
82.299
82.399
82.500
82.500
82.399
82.599
82.599
82.899
82.899
82.699
83.000
83.199
82.899
82.899
82.299
82.399
82.599
82.699
82.699
82.699
82.599
82.500
82.299
82.399
82.500
82.699
82.599
82.399
82.199
82.099
82.099
82.199
82.000
82.000
7.339
6.459
6.139
7.179
7.259
6.859
7.339
7.639
7.719
7.859
7.859
8.000
7.879
8.500
8.199
7.159
7.899
6.479
7.579
7.759
7.000
7.199
7.219
7.579
7.279
6.079
7.079
6.819
6.559
6.000
6.279
6.579
6.639
6.479
5.259
6.279
6.339
5.379
6.279
6.259
31O
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
23
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
81.799
81.799
81.799
81.799
81.799
81.899
81.799
81.699
81.699
81.799
82.000
81.799
81.899
83.399
81.699
82.099
82,099
82.500
82.599
82.399
82.899
83.000
83.199
83.500
83.500
83.199
83.699
84.099
83.699
83.000
82.599
82.199
82.500
82.899
82.899
82.899
82.899
83.000
82.799
82.500
6.279
6.259
6.239
6.039
5.879
5.739
5.699
5.459
5.399
5.599
5.699
5.719
5.419
7.899
5.039
5.079
6.519
6.779
6.779
6.679
6.899
7.039
7.139
5.659
7.659
7.539
8.319
8.179
7.699
6.559
6.119
4.659
6.059
6.239
6.479
6.799
6.579
5.259
6.419
6.099
311
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
23
23
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
82.500
82.699
82.599
82.500
82.500
82.399
82.699
82.599
82.799
82.699
82.699
82.899
82.899
82.699
82.899
82.699
82.500
82.799
82.699
82.799
82.899
82.899
82.699
82.899
83.099
83.199
83.199
83.399
83,299
83.699
83.799
83.599
84.199
83.899
83.899
83.500
83.199
83.199
83.299
83.099
6.079
6.939
7.219
7.159
7.039
5.799
7.159
7.339
7.439
7.459
7.439
7.419
7.359
7.259
7.299
7.019
7.779
6.759
6.639
5.639
7.000
6.839
6.739
6.579
7.139
7.199
5.159
7.259
7.519
8.339
8.819
8.559
8.979
9.299
8.919
8.779
7.799
8.039
8.299
8.000
312
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
24
24
24
24
24
24
24
24
24
24
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
83.099
82.899
83.299
83.399
83.299
83.500
83.699
83.500
83.299
82.799
82.899
83.000
83.299
83.199
83.500
83.299
83.399
83.500
83.699
83.299
83.699
83.799
83.500
83.299
83.199
83.199
82.899
82.899
83.199
83.500
83.699
84.299
83.899
83.799
84.099
84.500
84.699
85.199
85.000
85.299
7.679
7.539
8.079
8.459
8.439
8.559
8.699
8.399
7.879
6.579
7.819
7.859
6.659
7.859
7.779
8.719
8.000
7.539
7.359
7.159
7.319
7.179
6.779
6.959
6.139
5.839
6.439
6.539
6.419
5.539
6.079
6.739
6.179
5.899
5.939
6.479
6.379
6.659
6.399
6.699
313
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
85.399
85.699
85.500
85.399
84.899
85.199
85.199
84.699
84.299
84.000
84.000
84.199
83.899
83.799
83.899
83.599
83.399
83.299
83.299
83.500
83.199
83.399
83.099
83.399
83.299
83.299
83.099
83.299
83.399
83.399
83.399
83.500
83.299
83.099
83.000
83.000
82.899
83.000
83.099
83.199
7.000
7.119
6.899
7.039
6.639
7.079
7.639
6.459
5.739
5.779
6.019
6.059
5.959
5.859
5.859
5.739
5.619
5.839
5.619
5.539
5.779
5.899
5.699
5.779
5.799
5.759
5.859
5.979
5.959
5.979
6.039
5.979
5.979
5.879
5.859
5.679
5.859
5.779
6.799
5.659
314
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
27
27
27
27
27
27
27
27
27
27
27
27
27
27
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
83.500
83.799
84.199
84.000
84.399
84.299
84.399
84.399
84.450
84.500
84.450
84.399
84.399
84.299
84.399
83.899
83.699
83.500
83.500
83.299
83.500
83.500
83.299
83.099
83.000
82.799
82.699
82.500
82.500
82.299
82.299
82.199
82.199
82.199
82.440
82.699
82.699
82.699
82.699
82.899
5.759
5.939
6.299
6.539
5.739
6.579
6.139
5.699
5.850
6.019
6.710
7.419
7.319
7.759
8.019
8.419
8.259
6.299
6.399
6.239
6.359
6.639
6.500
6.039
6.299
6.419
6.379
6.279
6.879
7.439
6.579
6.539
6.519
6.459
6.370
6.299
6.219
6.159
6.179
6.099
315
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
27
28
28
28
28
28
28
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
82.699
82.899
82.799
82.799
82.899
83.000
83.099
82.899
82.799
83.099
83.199
83.099
82.899
83.099
82.799
82.899
82.899
82.899
82.699
82.500
82.399
82.699
82.399
82.199
82.000
82.000
82.000
82.000
81.899
81.899
81.699
81.500
81.500
81.399
81.399
81.199
81.199
80.899
80.899
80.699
6.059
6.059
6.139
6.099
6.039
6.079
6.019
5.939
5.939
6.059
5.939
6.000
5.699
5.739
5.679
5.659
5.699
5.919
6.039
6.239
6.219
6.739
6.539
6.559
6.439
6.539
6.610
6.699
6.279
6.419
6.239
6.339
6.879
6.859
6.839
6.819
6.779
6.739
6.599
6.359
316
-------
Sta. Mo. Day Time Tenp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
28
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
80.899
80.599
80.699
80.599
80.799
80.699
80.799
80.899
81.299
80.899
81.000
81.299
81.299
81.299
81.000
81.099
81.500
81.500
81.500
81.699
81.500
81.599
81.899
81.500
81.500
81.500
81.500
82.099
82.000
82.000
81.899
81.899
81.500
81.500
81.299
81.500
81.399
81.199
81.199
81.399
6.619
6.759
6.539
6.419
6.419
6.539
6.439
6.439
6.439
6.279
6.359
6.259
6.479
6.279
6.099
6.299
6.839
6.759
6.579
6.279
6.299
6.439
6.739
6.000
6.000
5.879
5.899
7.259
7.000
7.739
7.939
8.000
6.959
7.500
6.899
6.799
6.699
8.639
6.439
6.399
317
-------
Sta.
Mo.
Day
Time
Temp.
D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
28
28
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
29
2300
2330
30
100
130
200
230
300
330
AOO
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
80.899
80.799
80.899
80.899
80.599
80.699
80.599
80.299
80.399
80.500
80.000
80.099
79.899
80.000
80.000
80.199
80.000
80.199
80.199
80.199
80.199
80.199
80.000
80.199
80.099
80.199
80.199
80.099
80.199
80.399
80.500
80.590
80.699
80.699
80.500
80.699
80.899
81.000
81.099
81.199
6.299
6.279
6.079
6.000
6.500
5.939
6.039
6.079
6.099
6.099
5.919
5.959
5.939
6.079
6.379
6.539
6.559
6.599
6.479
6.519
6.459
6.399
6.639
6.699
6.419
6.859
6.699
6.659
6.739
6.859
6.759
6.750
6.759
6.279
6.299
6.259
6.299
6.339
6.359
6.299
318
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
29
29
29
29
29
29
29
29
29
29
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
80.899
80.799
80.699
80.799
80.799
80.599
80.699
80.699
80.500
80.599
80.500
80.399
80.500
80.199
80.199
80.199
80.199
80.299
80.000
80.000
80.199
80.000
80.000
80.000
80.099
79.799
79.799
79.699
79.899
79.699
79.500
79.699
79.799
79.799
79.799
79.899
79.699
79.699
79.699
80.199
6.099
5.919
6.419
6.199
6.019
5.779
5.819
5.839
5.779
5.779
5.679
5.659
5.599
5.579
5.399
5.619
5.679
5.739
5.579
5.199
5.199
5.379
5.419
5.419
5.279
8.359
5.459
5.139
5.479
5.500
5.519
5.619
5.479
5.099
5.239
4.959
5.139
5.159
5.059
5.819
319
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
79.799
80.000
80.000
79.899
80.399
80.000
80.000
80.199
80.299
80.500
80.299
80.000
80.000
80.000
80.000
80.000
79.699
79.799
79.899
80.000
80.000
79.799
79.699
79.799
79.799
79.899
79.899
79.500
79.799
79.500
79.699
79.799
79.799
79.899
79.699
79.699
79.599
79.500
79.500
79.699
5.779
6.000
5.659
5.639
5.859
5.339
5.339
5.419
5.500
5.699
5.379
5.079
5.079
4.979
4.879
4.879
4.639
4.699
4.939
4.879
4.859
4.779
4.679
4.959
4.539
4.359
5.079
5.159
4.899
4.979
5.039
4.979
4.539
4.679
5.159
4.899
4.939
4.979
5.500
5.819
320
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
79.690
79.699
79.699
79.699
79.799
79.699
79.799
80.000
80.199
80.199
80.899
80.699
80.699
80.799
80.500
81.199
80.799
80.799
80.699
80.799
80.599
80.599
80.500
80.500
80.399
80.000
80.000
80.000
80.399
80.500
80.500
80.399
80.500
80.599
80.399
80.299
80.299
80.199
80.299
80.199
5.680
5.559
5.019
5.019
5.699
5.379
5.839
5.359
6.199
5.279
5.979
5.879
5.719
5.739
5.379
5.959
5.619
5.439
5.359
5.399
5.259
5.379
5.319
6.000
5.059
4.619
4.279
4.399
4.479
4.639
4.659
4.639
4.619
4.479
4.399
4.359
4.399
4.279
4.379
4.379
321
-------
Sta.
Mo,
Day
Time
Temp,
D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
80.299
80.199
80.399
80.299
80.299
80.500
80.699
80.899
80.699
81.000
81.199
80.899
81.299
81.299
81.699
81.699
81.899
82.000
81.899
81.699
81.699
81.599
81.599
81.500
81.899
81.820
81.7AO
81.660
81.599
81.899
81.599
81.599
81.199
81.500
81.299
81.299
80.699
80.699
80.699
80.599
4.500
4.779
4.879
4.899
5.099
5.279
5.319
5.559
5.639
6.159
5.919
5.619
5.779
5,879
5.939
5.899
5.939
6.099
5.779
5.599
5.500
5.439
5.139
5.259
5.219
5.140
5.070
5.000
4.939
5.199
4.979
5.139
5.319
5.699
4.639
4.719
4.179
3.779
3.359
3.359
322
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
80.590
80.599
80.699
80.399
80.399
80.799
80.899
80.500
80.599
80.599
80.799
80.399
80.000
80.199
80.299
80.500
80.699
80.699
80.399
80.899
80.699
80.299
80.299
80.799
80.399
80.599
80.699
80.899
80.899
80.799
81.299
81.299
81.299
81.199
81.399
81.299
81.399
81.199
81.199
80.899
3.630
3.919
3.979
4.159
4.359
4.579
4.619
4.539
4.439
4.639
4.839
6.459
6.379
6.399
6.619
6.699
5.899
5.979
6.500
6.719
6.459
5.659
5.579
6.279
5.799
5.379
5.639
5.759
5.579
5.599
5.639
5.639
5.679
5.739
6.299
5.739
5.759
5.699
5.579
5.559
323
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
3
3
4
A
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
80.899
80.899
80.599
80.699
80.599
80.699
80.640
80.599
80.490
80.399
80.500
80.399
80.299
80.199
80.000
80.000
80.199
80.399
80.199
80.199
80.399
80.599
80.699
80.699
80.899
80.699
80.899
81.000
81.099
81.199
81.299
80.899
80.899
80.799
81.299
81.299
81.199
81.299
81.299
81.099
5.579
5.559
5.419
5.539
5.119
5.299
5.280
5.279
5.220
5.179
5.059
5.039
4.939
5.679
5.779
5.699
5.659
5.699
5.699
5.899
6.199
5.599
5.679
5.759
5.839
5.699
5.619
5.579
5.779
5.539
5.519
5.359
5.099
5.239
5.759
5.639
5.679
5.559
5.839
5.500
324
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
I
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
80.799
81.000
80.899
80.899
80.799
80.699
80.699
80.699
80.699
80.500
80.599
80.399
80.399
80.399
80.399
80.399
80.299
80.199
80.099
80.299
80.000
80.000
79.899
79.799
80.000
80.880
80.750
80.620
79.500
79.500
79.500
79.799
79.740
79.699
80.000
80.299
80.699
80.699
80.500
80.590
5.519
5.459
5.399
5.259
5.299
6.439
6.139
6.139
6.099
6.079
6.039
6.019
5.979
6.019
5.859
5.839
5.779
5.739
5.679
5.639
5.599
5.679
5.719
5.819
5.779
5.930
6.100
6.270
6.439
6.699
6.739
7.039
7.030
7.039
7.239
7.359
7.539
7.619
7.379
7.450
325
-------
Sta. Mo. Day Time Temp. D.O.
175
175
175
175
175
175
175
175
1 75
175
175
175
175
175
175
175
175
175
176
176
176
176
176
176
176
176
176
176
176
176
176
176
176
176
176
176
176
176
176
176
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
AOO
430
500
530
600
630
700
730
800
830
900
930
1000
1030
80.699
80.500
80.299
80.340
80.399
80.500
80.399
80.390
80.399
80.000
79.899
79.799
79.699
79.399
79.500
79.399
78.899
78.599
78.500
78.340
78.199
78.099
78.199
78.099
78.299
78.299
78.199
78.000
78.030
78.060
78.099
78.399
78.399
78.399
78.500
78.599
78.699
78.899
78.899
78.899
7.539
7.259
7.139
7.250
7.379
7.259
6.939
7.120
7.319
7.000
6.939
7.039
7.119
7.079
7.279
7.299
7.299
7.099
7,039
7.090
7.159
7.039
7.039
7.039
6.879
6.859
6.839
6.819
6.790
6.770
6.759
6.779
6.839
6.799
6.919
6.919
6.879
7.000
7.079
6.859
326
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
7
7
7
7
7
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
79.000
79.000
78.899
79.000
79.000
78.899
79.000
79.199
78.899
78.599
78.500
78.500
78.699
78.699
78.799
78,699
78.399
78.500
78.250
78.000
78.199
78.199
78.000
78.199
78.099
77.799
77.799
77.699
77.399
77.199
77.490
77.799
77.500
77.500
77.500
77.500
77.500
77.500
77.299
77.399
7.019
6.899
6.979
7.139
7.259
7.239
7.699
7.779
7.639
7.379
7.099
7.219
7.339
7.159
7.259
7.579
7,319
7.199
7.180
7.179
7.239
7.519
7.559
7.679
7.799
7.559
7.459
7.619
7.179
7.059
7.100
7.159
7.039
7.000
6.939
6.919
6.859
6.759
6.759
6,759
327
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
77.599
77.699
77.599
77.699
77.899
77.899
78.000
78.199
78.299
78.299
78.299
78.500
78.500
78.699
78.599
78.500
78.599
78.699
78.599
78.699
78.599
78.699
78.699
78.599
78.500
78.500
78.099
78.199
78.199
78.199
78.099
78.199
77.899
78.000
77.799
77.899
77.699
77.599
77.699
77.699
6.659
6.739
6.859
6.679
6.879
6.779
6.959
7.139
6.899
6.919
6.859
7.259
7.299
7.739
7.599
7.500
7.439
7.599
7.539
7.659
7.539
7.699
7.619
7.579
7.399
7.299
7.139
7.179
7.139
7.079
7.199
7.239
7.299
7.259
7.359
7.199
7.179
7.079
6.959
7.000
328
-------
Sta,
Mo.
Day
Time
Temp.
D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
77.699
77.799
77.699
77.740
77.799
77.799
77.699
77.599
77.500
77.699
77.799
77.899
77.950
78.000
78.000
78.099
78.099
78.199
78.299
78.299
78.199
78.299
78.299
78.099
78.199
78.199
78.199
78.000
78.199
78.299
78.199
78.099
78.000
78.099
77.899
77.840
77.799
77.799
77.799
77.699
6.959
7.099
6.879
6.850
6.839
6.799
7.259
6.779
6.759
6.779
6.879
6.879
6.820
6.779
6.759
6.739
6.739
6.779
6.779
6.739
6.739
6.779
6.839
6.879
6.939
6.859
6.819
6.879
6.759
6.879
6.639
6.619
6.399
6.659
6.379
6.360
6.359
7,479
6.539
6.479
329
-------
ta.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Mo.
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
Day
8
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
Time
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
Temp.
77.699
77.699
77.599
77.500
77.399
77.699
77.699
77.899
77.799
77.899
77.899
77.899
77.799
77.799
77.799
77.799
77.799
77.699
77.899
78.099
77.899
78.099
78.299
78.199
78.500
78.699
78.699
78.899
79.000
79.000
79.399
79.299
79.899
79.799
79.500
79.299
79.500
79.099
78.899
78.599
D.O.
6.539
6.579
6.479
6.359
6.239
6.299
6.319
6.379
6.159
6.199
6.239
6.339
6.159
6.139
6.179
6.059
6.099
6.159
6.279
6.239
6.299
6.179
6.219
6.279
6.339
6.379
6.599
6.739
6.439
6.500
6.699
6.579
7.079
7.059
6.539
6.659
6.679
6.059
5.959
5.619
33O
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
9
9
9
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
78.799
79.299
79.299
79.399
79.299
79.299
80.000
79.699
79.500
79.699
79.899
79.799
80.099
80.000
80.199
80.000
80.000
80.099
79.699
79.399
79.199
78.899
79.000
79.199
78.899
79.000
78.899
79.199
79.399
79.299
79.299
79.290
79.299
79.599
79.500
79.600
79.699
80.399
80.540
80.699
5.979
6.459
6.419
6.379
6.359
6.339
7.099
6.659
6.500
6.659
6.939
7.039
7.399
7.239
7.459
7.199
7.379
7.399
7.119
6.519
6.079
5.899
6.359
5.939
5.759
5.939
5.599
6.059
6.139
6.739
6.979
6.850
6.739
6.939
6.699
6.720
6.759
7.379
6.860
6.359
331
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
80.399
80.699
80.760
80.820
80.899
80.799
80.500
80.290
80.099
80.490
80.899
81.199
81.099
80.699
80.899
81.199
80.899
80.500
81.000
81.199
81.799
81.399
81.500
81.699
81.699
82.199
82.199
81.500
80.699
80.399
80.799
80.699
80.399
80.590
80.790
80.990
81.190
81.399
81.199
81.290
7.679
5.899
5.860
5.840
5.819
8.299
6.439
5.900
5.379
6.400
7.439
6.419
6.000
6.159
6.079
6.319
6.059
6.079
6.259
6.979
6.659
6.959
7.299
7.079
8.179
8.059
6.539
7.339
5.739
5.579
6.859
6.099
5.659
5.810
5.970
6.130
6.290
6.459
6.359
6.090
332
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
81.399
81.799
81.599
81.699
81.899
81.899
82.399
82.199
83.000
82.899
82.399
82.399
82.199
82.199
81.899
81.899
80.899
81.299
81.399
81.699
82.099
82.099
82.299
82.000
81.899
82.099
81.799
81.699
82.399
82.199
82.000
82.000
82.000
82.000
82.000
82.000
82.000
82.399
82.299
82.399
5.839
6.079
5.939
6.239
5.959
6.139
6.179
6.379
5.439
5.419
5.199
5.219
7.279
6.299
5.819
6.179
4.679
5.979
5.699
8.500
6.239
6.099
6.619
6.539
4.899
6.059
6.079
6.059
6.639
6.099
6.379
6.379
5.679
5.699
5.779
6.299
6.299
5.699
6.099
5.299
333
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
13
13
13
13
13
13
13
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
82.299
82.000
81.799
82.000
82.199
82.500
82.699
82.790
82.899
82.699
83.199
83.599
83.699
83.699
83.630
83.560
83.500
83.520
83.550
83.570
83.599
83.699
83.699
84.000
84.090
84.199
84.199
84.000
84.299
84.199
84.350
84.500
84.899
84.890
84.899
84.890
84.890
84.899
85.199
84.899
6.000
6.199
5.439
5.239
5.639
5.299
5.959
5.730
5.519
5.959
5.059
5.899
6.000
6.579
6.320
6.060
5.819
5.590
5.370
5.150
4.939
5.899
5.979
6.479
6.130
5.799
5.699
5.439
6.199
6.459
6.170
5.899
6.299
6.230
6.179
6.140
6.120
6.099
6.119
6.019
334
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
84.899
85.000
84.899
84.699
84,699
84.740
84.799
84.899
84.699
84.899
84.899
84.699
84.899
84.920
84.950
84.970
85.000
84.899
84.890
84.890
84,899
84.899
85.099
85.099
84.899
84.740
84.599
84.000
83.899
83.899
83.699
83.500
83.299
82.899
83.000
82.799
83.000
82.899
82.799
82.699
6.039
6.059
5.799
5.859
5.279
5.480
5.699
5.679
5.639
5.779
5.939
5.599
5.699
5.460
5.230
5.000
4.779
4.879
4.960
5.040
5.139
5,079
5.379
5.479
5.439
5.380
5.339
5.199
5.139
5.219
6.899
6.779
6.479
6.299
6.639
6.179
4.899
6.119
5.939
5.899
335
-------
ta.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Mo.
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
Day
13
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
Time
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
Temp,
82.500
82.299
82.399
82.299
81.899
81.890
81.899
81.899
82.000
81.899
81.890
81,899
81.699
81.699
81.699
81.699
81.899
81.699
81.690
81.699
81.699
81.699
81.699
81.699
81.500
81.500
81.500
81.600
81.699
81.500
81.599
81.599
81.500
81.599
81.500
81.500
81.500
81.500
81.199
81.500
D.O.
6.279
6.279
4.779
5.839
4.979
4.970
4.979
4.899
4.899
4.859
4.860
4.879
5.039
6.139
5.939
5.039
4.979
5.059
5.040
5.039
5.159
4.859
5.019
5.000
4.979
4.980
5.000
5.050
5.099
5.079
5.179
5.159
4.939
5.039
5.000
5.019
5.010
5.019
5.059
5.919
336
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
14
14
14
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
81.500
81.600
81.699
81.799
81.699
81.699
81.500
81.699
81.500
81.599
81.500
81.399
81.399
81.000
80.899
80.799
80.500
80.500
80.399
80.340
80.299
80.199
80.199
80.000
79.899
80.000
79.500
79.500
79.500
79.560
79.630
79.699
79.500
79.799
79.699
79.699
79.699
79.699
79.740
79.799
4.959
4.960
4.979
5.019
5.000
5.059
4.919
6.099
6.479
4.979
6.079
4.839
6.579
5.000
5.259
4.899
4.979
4.979
5.239
5.130
5.039
5.039
7.199
5.059
6.079
5.899
5.899
4.899
5.859
5.840
5.820
5.819
5.759
5.779
5.699
5.719
5.679
5.699
5.780
5.879
337
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
I
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
80.000
80.199
79.899
79.699
80.000
80.000
80.000
80.000
79.799
79.599
79.699
79.699
79.699
79.699
79.699
79.799
79.699
79.699
79.699
79.399
79.500
79.500
79.500
79.399
79.399
79.699
79.500
79.500
79.899
79.799
79.699
79.599
79.699
79.699
79.699
79.500
79.699
79.699
79.699
79.500
5.879
6.439
5.879
5.819
5.919
5.839
5.850
5.879
5.779
5.839
5.859
5.839
5.879
5.839
5.839
5.779
5.779
5.839
5.759
5.639
5.699
5.679
5.699
5.739
5.699
5.759
5.759
5.599
5.759
5.719
5.739
5.619
5.699
5.719
5.619
6.019
5.719
5.799
5.719
5.639
338
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
79.299
79.500
79.500
79.699
79.500
79.500
79.699
79.500
79.500
79.699
79.699
79.599
79.799
80.000
80.000
79.799
79.799
79.599
79.299
79.399
79.099
78.799
79.099
78.990
78.899
78.799
78.899
78.899
78.799
78.799
78.699
78.799
78.500
78.500
78.699
78.699
78.799
78.990
79.199
79.399
5.659
5.659
5.619
5.619
5.599
5.579
5.659
5.639
7.179
5.699
5.779
5.779
5.939
6.000
6.179
5.979
6.519
5.979
6.779
5.819
5.799
5.679
5.759
5.690
5.639
5.759
5.739
6.399
5.559
5.559
5.539
5.479
5.639
5.459
5.459
5.500
5.539
5.570
5.619
5.539
339
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
18
18
18
18
18
18
18
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
79.099
79.500
79.340
79.199
79.199
79.399
79.500
79.500
78.699
78.890
79.100
79.300
79.500
79.399
79.500
79.699
79.500
79.500
79.699
79.720
79.760
79.799
79.599
79.500
79.399
79.699
79.699
79.699
79.699
79.599
79.599
79.599
79.199
79.000
79.099
79.000
78.899
78.899
78.899
78.899
5.519
5.519
5.500
5.500
5.479
5.439
5.500
5.539
5.399
5.390
5.390
5.390
5.399
5.359
5.439
5.479
5.459
5.539
5.479
5.550
5.630
5.719
5.599
5.699
5.579
5.739
5.759
5.779
5.839
5.779
5.739
5.619
5.479
5.259
5.439
5.939
5.399
5.279
5.319
5.299
340
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
1930
2000
2030
2100
2130
2200
2230
2300
78.899
79.299
78.899
79.000
79.199
79.290
79.399
79.500
79.699
79.699
79.899
80.000
80.000
80.099
80.000
80.000
80.100
80.199
80.140
80.099
80.099
80.299
80.199
80.000
80.000
80.000
80.000
80.199
80.199
80.199
79.899
79.799
79.799
80.000
79.899
79.899
80.099
80.299
80.500
80.199
5.279
5.299
5.339
5.279
5.359
5.330
5.319
5.239
5.439
5.279
5.319
5.899
7.000
6.879
6.959
6.879
6.870
6.879
6.820
6.779
6.779
6.759
6.659
6.599
6.590
6.599
6.639
6.779
6.819
6.799
6.679
6.659
6.979
6.699
6.739
6.779
6.939
7.059
7.039
6.899
341
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
18
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
1530
1600
1630
1700
1730
1800
1830
1900
80.299
80.199
80.099
80.000
80.000
80.000
79.699
79.699
79.799
79.699
79.699
79.699
79.690
79.699
79.899
79.899
80.000
80.099
80.199
80.299
80.399
80.490
80.599
80.500
80.799
80.500
81.000
80.899
80.899
80.899
80.500
80.699
80.899
80.899
80.899
81.000
80.500
80.899
81.000
81.500
6.879
6.839
6.739
6.679
6.659
6.579
6.579
6.419
6.459
6.379
6.279
6.339
6.350
6.379
6.339
6.339
6.259
6.319
6.379
6.339
6.299
6.300
6.319
6.419
6.379
6.259
6.500
6.379
6.379
6.339
6.259
6.179
6.339
6.179
6.259
6.259
6.259
6.179
6.299
7.599
342
-------
Sta. Mo. Day Time Temp. D.O.
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
19
19
19
19
19
19
19
19
19
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
1930
2000
2030
2100
2130
2200
2230
2300
2330
30
100
130
200
230
300
330
400
430
500
530
600
630
700
730
800
830
900
930
1000
1030
1100
1130
1200
1230
1300
1330
1400
1430
1500
81.699
81.099
80.899
81.099
80.699
80.899
81.099
81.099
81.199
80.899
80.899
81.000
81.199
81.199
80.699
80.699
80.699
80.500
80.500
80.500
80.540
80.599
80.699
80.799
80.899
80.840
80.799
81.000
81.299
81.399
81.500
81.500
81.500
81.699
81.699
81.899
81.950
82.000
81.950
81.899
6.539
6.439
6.379
6.419
6.279
6.459
6.579
6.519
6.579
6.500
6.519
6.479
6.439
6.379
6.179
6.059
6.000
5.919
5.959
5.959
5.890
5.839
5.819
5.879
5.839
5.760
5.699
5.699
5.659
5.679
5.659
5.599
5.579
8.439
5.500
4.299
4.900
5.500
5.470
5.459
343
-------
Sta.
Mo.
Dav
Time
Temp.
D.O.
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
V
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
20
20
20
20
20
20
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
7
7
7
1530
1600
1630
1700
1730
1800
1302
1332
1402
1432
1502
1532
1602
1632
1702
1732
1802
1832
1902
1932
2002
2032
2102
2132
2202
2232
2302
2332
2
32
102
132
202
232
302
332
402
432
502
532
81.899
81.890
81.899
81.890
81.899
81.899
79.000
78.899
78.899
79.000
78.699
78.899
79.000
78.899
78.899
79.099
78.899
78.899
78.899
78.899
78.890
78.899
78.899
79.000
78.899
78.899
78.799
78.899
78.899
78.899
79.000
79.000
79.000
79.000
79.000
79.000
79.099
79.199
79.199
79.099
5.339
5.370
5.419
5.320
5.239
5.299
.659
.639
.759
.939
.939
1.119
1.099
.879
1.000
1.079
.959
1.039
.899
1.099
1.220
1.359
1.279
1.339
1.039
1.419
1.139
1.339
1.139
1.279
1.319
1.419
1.470
1.539
1.619
1.639
.299
.299
.299
.279
344
-------
Sta. Mo. Day Time Temp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
T.-
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
1402
1432
1502
1532
1602
1632
1702
1732
1802
1832
1902
1932
2002
2032
2102
2132
2202
2232
2302
2332
2
32
102
132
79.000
79.000
79.099
78.899
78.899
78.899
79,000
78.899
78.899
78.899
78.899
78.899
78.899
78.899
78.899
78.899
78.899
78.899
78.899
78.899
78.899
78.899
78.899
78.899
79.000
79.199
79.199
79.199
79.199
79.199
79.199
79.299
79.099
79.000
79.099
79.199
79.199
79.299
79.299
79.399
.299
.279
.379
.379
.439
.439
.399
.500
.459
.439
.459
.579
.719
.639
.719
.879
.939
.959
.899
1.079
1.219
1.179
1.359
1.139
1.379
1.500
1.519
1.639
1.479
1.500
1.599
1.719
1.359
1.559
.719
1.279
.739
1.019
.839
1.099
345
-------
Sta. Mo. Day Time Tenp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
202
232
302
332
402
432
502
532
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
1402
1432
1502
1532
1602
1632
1702
1732
1802
1832
1902
1932
2002
2032
2102
2132
79.199
79.299
79.500
79.399
79.399
79.199
79.340
79.500
79.500
79.500
79.500
79.500
79.500
79.500
79.500
79.450
79.399
79.299
79.399
79.299
79.199
79.299
79.399
79.399
79.199
79.299
79.299
79.199
79.299
79.399
79.199
79.199
79.199
79.199
79.299
79.500
79.399
79.500
79.500
79.500
.899
1.219
1.339
1.299
1.379
1.479
1.540
1.619
1.379
1.599
1.500
1.500
1.639
1.719
1.719
1.690
1.679
1.759
1.799
1.779
1.879
1.939
2.019
2.059
.739
.959
.979
1.059
1.439
1.359
1.619
1.539
1.559
1.719
1.759
1.879
1.839
1.899
2.000
1.939
346
-------
Sta. Mo. Day Time Temp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
2202
2232
2302
2332
2
32
102
132
202
232
302
332
402
432
502
532
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
1402
1432
1502
1532
1602
1632
1702
1732
79.500
79.500
79.500
79.500
79.699
79.699
79.699
79.699
79.699
79.699
79.599
79.500
79.500
79.500
79.500
79.699
79.599
79.599
79.500
79.500
79.299
79.399
79.500
79.500
79.399
79.199
79.399
79.399
79.099
79.399
79.399
79.450
79.500
79.500
79.500
79.500
79.500
79.500
79.500
79.500
2.059
2.139
2.159
2.179
2.139
2.279
2.279
2.359
2.399
2.359
2.319
2.299
2.299
2.379
2.399
2.379
2.399
2.399
2.459
2.379
2.399
2.399
2.339
2.379
2.379
2.299
2.359
2.379
2.279
2.299
2.239
2.250
2.299
2.219
2.279
2.199
2.179
2.239
2.159
2.259
347
-------
Sta. Mo. Day Time Temp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
9
9
9
9
9
9
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
1802
1832
1902
1932
2002
2032
2102
2132
2202
2232
2302
2332
2
32
102
132
202
232
302
332
402
432
502
532
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
79.500
79.699
79.699
79.899
79.799
79.699
80.000
80.000
79.899
80.000
80.000
80.199
80.199
80.299
80.299
80.299
80.500
80.299
80.500
80.699
80.399
80.699
80.500
80.699
80.599
80.699
80.799
80.899
80.799
80.899
80.799
80.799
80.899
80.799
80.840
80.899
80.899
81.000
80.899
81.000
2.239
2.139
2.199
2.359
2.199
2.399
2.399
.319
.519
.359
.299
.279
.259
.279
.239
.299
.299
.299
.299
.339
.319
.399
.439
.399
.439
.399
.419
.579
.559
.819
.959
1.139
.759
.799
1.070
1.359
.879
1.159
1.099
1.059
348
-------
Sta. Mo. Day Time Temp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
1402
1432
1502
1532
1602
1632
1702
1732
1802
1832
1902
1932
2002
2032
2102
2132
2202
2232
2302
2332
2
32
102
132
202
232
302
332
402
432
502
532
602
632
702
732
802
832
902
932
80.899
80.990
81.099
81.299
81.099
81.230
81.370
81.500
81.599
81.599
81.699
81.699
81.790
81.899
81.699
81.899
82.000
82.000
82.000
82.099
82.199
82.199
82.299
82.199
82.099
82.299
82.399
82.500
82.599
82.699
82.699
82.799
82.899
82.699
82.899
82.799
82.810
82.830
82.850
82.870
1.099
1.120
1.159
1.379
1.139
1.180
1.230
1.299
1.919
1.779
1.779
1.739
1.620
1.519
1.500
1.819
1.479
1.799
1.959
1.639
1.699
1.939
2.039
1.879
2.059
1.839
1.739
1.959
1.919
1.939
2.039
2.000
2.079
2.279
2.319
2.299
2.310
2.330
2.350
2.370
349
-------
Sta. Mo. Day Time Temp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
12
12
12
12
12
12
12
12
12
12
12
12
1002
1032
1102
1132
1202
1232
1302
1332
1402
1432
1502
1532
1602
1632
1702
1732
1802
1832
1902
1932
2002
2032
2102
2132
2202
2232
2302
2332
2
32
102
132
202
232
302
332
402
432
502
532
82.899
83.000
83.090
83.199
83.099
83.199
83.199
83.399
83.299
83.299
83.299
83.500
83.199
83.299
83.199
83.500
83.500
83.699
83.699
83.699
83.799
83.699
83.699
83.799
83.799
83.799
83.699
83.799
83.599
83.599
83.899
83.899
83.599
83.799
83.699
83.699
83.500
83.399
83.500
83.699
2.399
.679
.940
1.219
1.319
1.500
1.219
1.379
1.259
1.419
1.339
1.000
1.339
1.099
1.179
1.539
1.319
1.539
1.399
1.539
1.719
1.539
1.599
1.839
1.759
1.879
1.979
2.000
2.119
2.259
2.239
2.299
2.279
2.279
2.279
2.339
2.359
2.359
2.459
2.500
350
-------
Sta. Mo. Day Time Temp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
13
13
13
13
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
1402
1432
1502
1532
1602
1632
1702
1732
1802
1832
1902
1932
2002
2032
2102
2132
2202
2232
2302
2332
2
32
102
132
83.699
83.500
83.399
83.500
83.399
83.299
83.299
83.199
83.199
83.099
82.990
82.899
83.099
83.099
83.000
83.099
83.299
83.260
83.220
83.199
83.270
83.350
83.430
83.500
83.599
83.500
83.500
83.550
83.599
83.199
83.500
83.500
83.500
83.500
83.500
83.500
83.600
83.699
83.660
83.620
2.439
2.479
2.459
2.479
2.500
2.459
2.539
2.579
2.519
2.679
2.690
2.719
2.639
2.819
2.839
2.959
2.959
2.910
2.870
2.839
2.860
2.880
2.900
2.939
2.859
2.919
3.019
3.020
3.039
2.959
3.039
3.059
3.059
3.070
3.099
3.139
2.110
1.099
1.290
1.490
351
-------
Sta. Mo. Day Time Temp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
202
232
302
332
402
432
502
532
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
1402
1432
1502
1532
1602
1632
1702
1732
1802
1832
1902
1932
2002
2032
2102
2132
83.599
83.699
83.599
83.699
83.699
83.799
83.699
83.799
83.740
83.699
83.799
83.899
84.000
83.899
83.890
83.899
83.840
83.790
83.740
83.699
83.699
83.690
83.690
83.699
83.699
83.590
83.500
83.500
83.400
83.399
83.599
83.299
83.599
83.500
83.399
83.399
83.500
83.399
83.390
83.399
1.699
1.719
1.879
1.939
1.779
1.779
1.879
1.819
1.850
1.899
1.859
2.019
2.099
2.239
2.250
2.279
2.300
2.340
2.380
2.419
2.539
2.570
2.610
2.659
2.639
2.690
2.759
2.759
2.810
2.879
2.979
3.039
3.139
3.039
3.139
3.179
3.019
3.179
3.260
3.359
352
-------
Sta.
Mo.
Day
Time
Temp,
D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
13
13
13
13
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
2202
2232
2302
2332
2
32
102
132
202
232
302
332
402
432
502
532
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
1402
1432
1502
1532
1602
1632
1702
1732
83.500
83.599
83.500
83.699
83.500
83.399
83.599
83.599
83.440
83.299
83.299
83.399
83.399
83.290
83.199
83.000
83.299
83.000
83.299
83.000
83.000
82.950
82.899
82.699
82.799
82.699
82.799
82.760
82.720
82.699
83.640
82.599
82.500
82.500
82.500
82.500
82.450
82.399
82.390
82.390
3.379
3.359
3.379
3.379
3.559
3.539
3.500
3.500
3.460
3.419
3.479
3.500
3.479
3.490
3.500
3.459
3.539
3.500
4.519
3.699
3.699
3.710
3.739
3.819
3.819
3.819
3.799
3.820
3.840
3.879
3.870
3.879
3.899
3.920
3.959
4.039
4.060
4.099
4.070
4.050
353
-------
Sta. Mo. Day Time Temp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
14
14
14
14
14
14
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
1802
1832
1902
1932
2002
2032
2102
2132
2202
2232
2302
2332
2
32
102
132
202
232
302
332
402
432
502
532
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
82.390
82.399
82.199
82.199
82.190
82.199
82.199
82.299
82.199
82.099
82.099
82.199
81.799
82.099
82.199
82.199
82.199
82.099
82.000
82.040
82.099
82.199
82.000
82.000
82.000
82.000
81.799
81.599
81.500
81.599
81.500
81.599
81.510
81.440
81.370
81.299
80.899
80.899
80.890
80.899
4.020
4.000
3.979
4.079
4.030
4.000
4.000
4.079
4.179
4.099
4.039
4.039
3.679
2.239
2.879
2.899
2.779
3.039
2.979
2.960
2.959
3.079
3.199
3.379
3.379
3.459
3.479
3.359
3.439
3.319
3.379
3.339
3.330
3.330
3.330
3.339
3.399
3.500
3.550
3.619
354
-------
Sta,
Mo.
Day
Time
Temp.
D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
1402
1432
1502
1532
1602
1632
1702
1732
1802
1832
1902
1932
2002
2032
2102
2132
2202
2232
2302
2332
2
32
102
132
202
232
302
332
402
432
502
532
602
632
702
732
802
832
902
932
80.820
80.760
80.699
80.500
80.399
80.299
80.199
80.199
80.000
80.060
80.130
80.199
80.199
80.099
80.000
80.199
80.000
80.199
80.000
80.000
80.099
80.140
80.199
80.299
80.000
80.199
80.299
80.199
80.000
80.199
80.299
80.099
80.199
80.199
80.199
80.199
80.099
80.099
80.099
79.899
3.600
3.600
3.599
3.579
3.599
3.679
3.639
3.679
3.639
3.760
3.900
4.039
4.159
4.119
4.279
4.379
4.459
4.579
4.599
4.599
4.639
4.580
4.539
4.679
4.599
4.639
4.739
4.779
4.839
4.859
4.939
4.939
4.919
4.879
4.859
4.919
4.979
4.939
4.899
3.219
355
-------
Sta. Mo. Day Time Temp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
17
17
17
17
17
17
17
17
17
17
17
1002
1032
1102
1132
1202
1232
1302
1332
1402
1432
1502
1532
1602
1632
1702
1732
1802
1832
1902
1932
2002
2032
2102
2132
2202
2232
2302
2332
2
32
102
132
202
232
302
332
402
432
502
532
79.899
79.699
79.699
79.799
79.699
79.699
79.699
79.699
79.799
79.500
79.500
79.599
79.599
79.599
79.699
79.500
79.500
79.500
79.500
79.500
79.399
79.500
79.399
79.500
79.599
79.500
79.600
79.699
79.599
79.599
79.399
79.599
79.500
79.699
79.799
79.699
79.699
79.699
79.699
79.500
4.399
4.079
4.000
4.179
4.159
4.259
4.299
4.319
4.399
4.519
4.599
4.699
4.719
4.939
4.919
4.939
5.019
5.059
5.179
5.139
5.179
5.239
5.139
5.239
5.239
5.179
5.260
5.359
5.299
5.359
5.399
5.339
5.339
5.279
5.339
5.299
5.279
5.279
5.359
5.339
356
-------
Sta. Mo. Day Time Temp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
18
18
18
18
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
1402
1432
1502
1532
1602
1632
1702
1732
1802
1832
1902
1932
2002
2032
2102
2132
2202
2232
2302
2332
2
32
102
132
79.600
79.699
79.599
79.399
79.500
79.500
79.500
79.399
79.299
79.399
79.399
79.299
79.390
79.490
79.590
79.699
79.500
79.699
79.399
79.500
79.500
79.500
79.560
79.630
79.699
79.699
79.699
79.799
79.699
79.899
79.699
79.699
79.699
79.699
79.599
79.699
79.699
79.699
80.000
79.799
3.360
5.399
5.439
5.359
5.379
5.330
5.299
5.399
5.359
5.359
5.299
5.279
5.290
5.320
5.350
5.379
5.339
5.500
5.439
5.419
5.439
5.439
5.410
5.390
5.379
5.399
5.339
5.339
5.239
5.279
5.339
5.379
5.379
5.399
5.419
5.379
5.439
5.379
5.459
5.479
357
-------
Sta. Mo. Day Time Temp. D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
»
*
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
202
232
302
332
402
432
502
532
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
1402
1432
1502
1539
1602
1632
1702
1732
1802
1832
1902
1932
2002
2032
2102
2132
79.799
79.799
79.799
79.699
79.799
79.699
79.899
79.799
79.740
79.699
79.799
79.799
79.799
79.699
79.500
79.699
79.699
79.799
79.699
79.690
79.699
79.640
79.599
79.699
79.599
79.699
79.699
79.699
79.699
79.699
79.699
79.599
79.599
79.699
79.699
79.500
79.500
79.899
79.799
79.899
5.399
5.359
5.339
5.339
5.279
5.259
5.299
5.339
5.330
5.339
5.359
5.299
5.279
5.839
3.199
3.399
3.779
3.679
3.639
3.660
3.699
3.740
3.799
3.939
4.019
4.079
4.199
4.159
4.159
4.199
4.179
4.199
4.279
4.339
4.379
4.419
4.459
4.599
4.579
5.779
358
-------
Sta.
Mo.
Day
Time
Temp.
D.O.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
18
18
18
18
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
2202
2232
2302
2332
2
32
102
132
202
232
302
332
402
432
502
532
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
1402
1432
1502
1532
1602
1632
1702
1732
79.699
79.699
79.799
79.799
79.899
80.000
79.799
80.000
79.799
80.000
80.000
79.799
79.899
80.000
79.899
79.950
80.000
79.899
79.699
80.000
80.000
80.000
80.199
80.099
80.050
80.000
80.199
80.199
80.099
80.000
80.199
80.299
80.199
80.299
80.199
80.299
80.199
80.299
80.099
80.299
4.939
4.939
4.839
4.679
4.719
4.599
4.679
4.639
4.599
4.619
4.559
4.579
4.599
4.539
4.439
4.410
4.399
4.399
4.339
4.279
4.279
4.239
4.219
4.179
4.130
4.099
4.039
4.039
4.000
3.939
3.939
3.939
3.899
3.879
3.879
3.819
3.799
3.759
3.739
3.699
359
-------
Sta. Mo. Day Time Temp. D.o.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
19
19
19
19
19
19
19
19
19
19
19
19
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
1802
1832
1902
1932
2002
2032
2102
2132
2202
2232
2302
2332
2
32
102
132
202
232
302
332
402
432
502
532
602
632
702
732
802
832
902
932
1002
1032
1102
1132
1202
1232
1302
1332
80.399
80.399
80.500
80.399
80.500
80.299
80.299
80.599
80.599
80.699
80.699
80.500
80.699
80.699
80.599
80.599
80.699
80.500
80.699
80.699
80.799
80.799
80.899
80.890
80.899
80.899
80.899
80.799
80.840
80.899
80.899
80.799
80.899
80.699
80.799
80.899
80.899
80.799
81.000
80.950
3.639
3.659
3.579
3.619
3.559
3.519
3.500
3.500
3.459
3.399
3.399
3.359
3.339
3.299
3.279
3.279
3.279
3.239
3.179
3.139
3.139
3.139
3.119
3.100
3.099
3.079
3.039
3.759
3.410
3.079
2.979
2.939
2.879
2.859
2.500
2.719
2.639
2.679
2.659
2.660
36O
-------
Sta. Mo. Day Time Temp. D,0.
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
20
20
20
20
20
20
20
20
20
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
1402
1432
1502
1532
1602
1632
1702
1732
1802
1304
1334
1404
1434
1504
1534
1604
1634
1704
1734
1804
1834
1904
1934
2004
2034
2104
2134
2204
2234
2304
2334
4
34
104
134
204
234
304
334
404
80.099
80.890
80.899
80.899
80.890
80.899
80.950
81.000
81.199
79,299
79.500
79.399
79.199
79.000
79.500
79.500
79.799
79.799
79.799
79.699
79.799
79.699
79.699
79.500
79.399
79.599
79.299
79.299
79.299
79.199
79.199
79.199
79.199
79.000
78.899
78.799
79.000
78.799
78.899
78.899
2.679
2.650
2.639
2.639
2.590
2.559
2.550
2.559
2.559
1.159
1.059
1.199
1.039
.759
1.139
1.500
2.379
1.639
1.500
1.019
.899
.959
.859
.959
.819
1.000
1.159
1.159
1.099
1.000
.879
1.139
.779
.739
.739
.699
.639
.659
.659
.639
361
-------
Sta.
Mo.
Day
Time
Temp.
D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
1234
1304
1334
1404
1434
1504
1534
1604
1634
1704
1734
1804
1834
1904
1934
2004
2034
2104
2134
2204
2234
2304
2334
4
78.899
78.899
79.000
78.899
79.199
79.199
79.099
79.199
78.899
79.000
79.099
79.199
79.299
79.399
79.199
79.099
79.199
79.199
79.399
79.500
79.500
79.199
79.500
79.599
79.699
79.699
79.799
79.599
79.500
79.500
79.599
79.500
79.699
79.699
79.500
79.500
79.500
79.199
79.199
79.000
.559
.459
.439
.419
.399
.379
.439
.379
.439
.399
.319
.519
.859
.699
.759
.719
.839
.699
1.279
1.159
1.579
1.139
1.319
1.459
1.739
1.519
1.079
.759
.799
.639
.579
.579
.599
.699
.619
.879
.879
.659
.819
.739
362
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
34
104
134
204
234
304
334
404
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
1234
1304
1334
1404
1434
1504
1534
1604
1634
1704
1734
1804
1834
1904
1934
2004
79.199
78.899
79.000
79.099
78.899
78.699
78.899
78.899
78.699
78.799
78.899
78.899
78.899
78.799
78.799
78.799
78.899
78.899
78.699
78.899
78.899
78.699
78.699
78.799
78.899
78.699
78.799
78.899
78.899
78.799
78.899
78.699
78.899
78.699
78.799
79.099
79.000
79.000
78.899
78.899
.819
.699
.819
.659
.679
.599
.579
.579
.519
.479
.359
.359
.299
.299
.299
.299
.259
.259
.359
.259
.379
.539
.559
.419
.539
.539
.519
.539
.500
.459
.699
.559
.419
.439
.579
.739
.679
.819
.419
.339
363
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
2034
2104
2134
2204
2234
2304
2334
4
34
104
134
204
234
304
334
404
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
1234
1304
1334
1404
1434
1504
1534
1604
78.899
78.899
78.899
78.899
78.799
78.799
78.799
78.699
78.899
78.799
78.799
78.699
78.799
78.899
78.699
78.799
78.699
78.699
78.799
78.699
78.699
78.599
78.699
78.599
78.699
78.699
78.699
78.699
78.799
78.899
79.000
79.099
79.399
79.599
79.690
79.799
80.000
80.199
80.500
80.399
.439
.539
.439
.419
.359
.299
.379
.359
.359
.339
.319
.359
.299
.319
.419
.339
.339
.299
.239
.279
.199
.179
.199
.159
.179
.179
.179
.199
.179
.259
.379
.379
.459
.679
.670
.679
.559
.559
1.059
.979
364
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
1634
1704
1734
1804
1834
1904
1934
2004
2034
2104
2134
2204
2234
2304
2334
4
34
104
134
204
234
304
334
404
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
80.899
80.399
80.500
80.299
80.399
79.899
79.799
79.500
79.500
79.599
79.599
80.000
79.899
79.699
79.899
79.599
79.599
79.699
79.599
79.699
79.899
79.699
79.899
80.099
79.500
79.799
79.799
79.699
79.599
79.500
79.699
79.699
79.500
79.699
79.899
80.000
80.399
80.199
80.500
80.799
5.639
2.879
1.799
1.099
2.019
.739
.579
.359
.279
.279
.259
.979
.439
.399
.559
.359
.359
.359
.339
.299
.299
.299
.379
1.159
.379
.279
.439
.239
.259
.259
.259
.239
.219
.179
.279
.199
.599
.319
.459
.799
365
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
1234
1304
1334
1404
1434
1504
1534
1604
1634
1704
1734
1804
1834
1904
1934
2004
2034
2104
2134
2204
2234
2304
2334
4
34
104
134
204
234
304
334
404
434
504
534
604
634
704
734
804
80.599
81.899
80.699
81.699
81.699
83.299
82.799
82.399
82.399
82.699
82.000
82.399
82.000
81.799
81.599
81.199
81.299
81.000
80.899
81.000
80.899
81.599
81.000
80.899
81.000
80.899
81.199
81.199
81.199
81.199
81.199
80.899
81.299
81.199
81.199
81.199
81.099
81.099
80.899
80.899
.439
1.779
.639
1.139
1.079
2.919
5.539
3.000
4.039
3.299
.979
2.839
1.719
1.659
.979
.479
.619
.619
.779
.579
.399
1.739
.739
.399
.319
.379
.359
.299
.279
.259
.259
.279
1.759
.659
.299
.279
.259
.199
.179
.199
366
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
12
12
12
12
12
12
12
12
12
834
904
934
1004
1034
1104
1134
1204
1234
1304
1334
1404
1434
1504
1534
1604
1634
1704
1734
1804
1834
1904
1934
2004
2034
2104
2134
2204
2234
2304
2334
4
34
104
134
204
234
304
334
404
80.890
80.899
80.899
81.299
81.299
81.099
81.299
81.500
81.699
82.199
82.199
82.099
81.799
82.000
82.099
82.399
82.500
82.500
82.399
81.899
82.399
82.399
82.299
82.099
82.000
81.699
81.899
81.500
81.599
81.699
81.500
81.899
81.699
81.699
81.899
81.699
81.799
81.699
81.699
81.899
.180
.179
.199
.299
.339
.759
.579
.639
.399
1.019
1.519
1.439
.359
.359
.619
.579
.679
.799
.439
.299
1.819
1.299
.779
.639
.379
.299
.459
.439
.399
.319
.279
.759
.259
.299
.279
.239
.259
.239
.259
.219
367
-------
Sta.
Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
13
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
1234
1304
1334
1404
1434
1504
1534
1604
1634
1704
1734
1804
1834
1904
1934
2004
2034
2104
2134
2204
2234
2304
2334
4
81.799
81.799
81.699
81.899
81.799
81.899
81.890
81.899
81.890
81.899
81.699
82.000
82.199
82.000
81.500
82.500
82.399
82.799
83.500
83.500
83.299
83.500
82.799
83.199
83.199
83.199
84.899
83.699
83.590
83.500
83.299
83.199
82.799
82.740
82.699
82.599
82.500
82.500
82.599
82.299
.159
.179
.199
.239
.259
.239
.240
.259
.240
.239
.239
.439
.619
.239
1.419
3.759
3.539
3.739
4.839
4.000
3.959
3.859
3.039
3.039
3.179
3.099
9.699
4.919
4.810
4.719
2.879
3.099
2.759
2.570
2.399
2.379
2.500
2.239
2.259
1.879
368
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
34
104
134
204
234
304
334
404
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
1234
1304
1334
1404
1434
1504
1534
1604
1634
1704
1734
1804
1834
1904
1934
2004
82.500
82.500
82.399
82.500
82.500
82.599
82.599
82.399
82.500
82.399
82.500
82.599
82.599
82.500
82.399
82.299
82.400
82.500
82.699
82.620
82.540
82.470
82.399
82.699
82.599
82.640
82.699
82.699
82.890
83.000
82.899
83.000
83.000
82.899
82.899
82.899
83.500
83.500
82.899
83.199
1.899
2.339
2.019
2.000
2.379
2.000
1.839
1.799
1.839
1.579
1.699
1.539
1.559
1.500
1.639
1.439
1.510
1.599
1.599
1.570
1.560
1.550
1.539
1.419
1.619
1.740
1.359
1.839
2.120
2.419
2.559
2.739
2.359
1.979
1.899
1.839
4.399
5.899
4.239
2.119
369
-------
Sta.
Mo.
Day
Time
Temp,
D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
13
13
13
13
13
13
13
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
2034
2104
2134
2204
2234
2304
2334
4
34
104
134
204
234
304
334
404
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
1234
1304
1334
1404
1434
1504
1534
1604
82.899
82.760
82.630
82.500
82.699
82.699
82.399
82.299
82.500
82.500
82.500
82.299
82.399
82.500
82.500
82.000
82.299
82.199
82.000
82.099
81.899
82.000
82.199
82.140
82.099
82.000
82.099
82.299
82.399
82.399
82.699
82.599
82.699
82.500
82.500
82.199
82.290
82.399
82.290
82.199
1.859
1.790
1.720
1.659
1.500
1.919
1.379
1.279
1.159
1.179
1.119
1.219
1.539
' 1.139
1.199
1.279
1.199
1.299
1.279
1.339
1.319
1.339
1.279
1.290
1.319
1.179
1.559
1.179
1.459
1.339
1.879
1.379
1.479
1.099
.919
1.000
1.120
1.259
1.290
1.339
37O
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
1634
1704
1734
1804
1834
1904
1934
2004
2034
2104
2134
2204
2234
2304
2334
4
34
104
134
204
234
304
334
404
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
82.199
82.150
82.120
82.099
82.199
82.099
82.000
82.099
82.299
82.000
82.000
81.899
81.899
82.000
82.000
82.000
81.899
81.799
81.899
81.799
81.699
81.699
81.799
81.599
81.399
81.699
81.500
81.500
81.599
81.399
81.299
81.299
81.399
81.000
81.299
81.299
81.299
81.199
81.500
81.500
1.419
1.430
1.450
1.479
1.599
1.559
1.619
1.919
2.059
1.599
1.379
1.439
1.179
1.139
.979
.879
.739
.699
.839
.799
.799
.779
.839
.839
1.139
1.099
1.139
1.179
1.179
1.199
1.199
1.159
1.179
1.219
1.199
1.119
1.039
1*079
1.099
1.199
371
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
1234
1304
1334
1404
1434
1504
1534
1604
1634
1704
1734
1804
1834
1904
1934
2004
2034
2104
2134
2204
2234
2304
2334
4
34
104
134
204
234
304
334
404
434
504
534
604
634
704
734
804
81.500
81.590
81.699
81.500
81.299
81.699
81.500
81.899
81.699
81.500
81.599
81.500
81.299
81.400
81.500
81.500
81.599
81.599
81.699
81.500
81.500
81.500
81.500
81.399
81.640
80.899
81.199
81.000
81.199
81.099
80.899
80.899
81.000
80.899
81.099
80.799
80.699
80.699
80.699
80.699
1.219
1.340
1.479
1.179
1.319
1.979
1.500
2.139
2.059
1.799
1.839
1.739
1.819
1.830
1.859
2.019
1.959
2.479
2.279
2.199
1.939
1.779
1.779
1.679
1.460
1.259
1.079
.979
1.179
1.179
1.059
1.179
1.179
1.319
1.459
1.439
1.479
1.439
1.439
1.539
372
-------
Sta. Mo. Day Time Temp . D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
17
17
17
17
17
17
17
17
834
904
934
1004
1034
1104
1134
1204
1234
1304
1334
1404
1434
1504
1534
1604
1634
1704
1734
1804
1834
1904
1934
2004
2034,
2104
2134
2204
2234
2304
2334
4
34
104
134
204
234
304
334
404
80.699
80.699
80.699
80.699
80.899
80.799
80.899
80.899
81.299
81.500
81.500
81.699
81.899
81.299
81.899
81.699
81.500
81.399
82.099
81.699
82.099
82.299
81.799
81.699
81.699
81.799
81.699
81.399
81.500
81.599
81.399
81.399
81.299
81.399
81.199
81.099
81.199
81.199
80.899
80.899
1.559
1.579
1.539
1.519
1.839
1.599
2.039
1.639
2.059
2.279
1.839
2.259
2.539
1.539
2.239
1.939
1.779
1.899
2.239
2.519
3.000
3.559
2.939
2.559
2.699
3.899
2.899
2.459
3.539
2.679
2.339
2.139
1.839
1.799
1.699
1.779
1.559
1.479
1.519
1.339
373
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
18
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
1234
1304
1334
1404
1434
1504
1534
1604
1634
1704
1734
1804
1834
1904
1934
2004
2034
2104
2134
2204
2234
2304
2334
4
80.899
80.899
80.899
81.099
81.000
80.799
80.899
80.899
80.899
80.799
80.699
80.699
80.899
80.899
80.699
80.530
80.360
81.199
81.500
81.699
81.699
81.399
81.500
81.399
81.399
81.799
80.799
81.799
81.599
81.799
81.599
81.699
81.500
81.199
81.199
81.199
81.399
81.399
81.199
81.199
1.459
1.699
1.379
1.439
1.539
1.559
1.519
1.539
1.599
1.679
1.659
1.699
1.759
1.799
1.859
2.120
2.390
2.659
2.559
2.099
2.379
1.839
1.779
1.899
1.559
3.299
2.099
2.099
1.939
2.359
2.079
2.239
2.099
2.000
2.059
1.919
6.079
3.279
2.239
1.859
374
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
«/
3
J
3
3
J
3
3
3
3
^
3
J
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
34
104
134
204
234
304
334
404
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
1234
1304
1334
1404
1434
1504
1541
1604
1634
1704
1734
1804
1834
1904
1934
2004
81.199
81.399
81.099
81.099
81.199
81.000
81.199
81.199
81.000
80.899
80.799
81.000
80.899
81.199
80.699
80.799
80.799
80.899
80.899
80.899
80.699
81.099
81.199
81.500
81.099
81.000
81.500
81.799
81.799
82.199
81.899
82.099
81.799
82.000
82.000
81.500
81.599
81.599
81.699
81.699
1.839
1.659
1.659
1.519
1.399
1.339
1.319
1.239
1.259
1.199
1.199
1.159
1.299
1.279
1.419
1.459
1.459
1.500
1.539
1.559
1.559
1.739
1.599
2.579
1.639
2.059
2.219
2.259
2.299
3.299
2.279
2.399
2.199
2.000
2.039
1.759
1.639
1.939
1.899
2.239
375
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
18
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
2034
2104
2134
2204
2234
2304
2334
4
34
104
134
204
234
304
334
404
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
1234
1304
1334
1404
1434
1504
1534
1604
81.500
81.500
81.399
81.500
81.399
81.299
81.599
81.699
81.299
81.199
80.899
81.199
80.899
81.199
81.199
81.000
80.899
81.099
80.990
80.899
81.000
81.000
81.099
81.099
80.899
81.000
81.199
81.199
81.399
81.299
81.199
80.699
81.299
81.500
80.699
81.399
80.699
81.000
81.899
80.899
2.099
2.179
1.979
1.879
1.819
1.819
4.759
4.379
2.079
1.719
1.719
1.759
1.639
1.639
1.579
1.559
1.399
1.299
1.280
1.279
1.339
1.339
1.439
1.459
1.599
1.559
1.619
1.639
1.839
1.739
2.059
1.879
2.599
5.179
2.039
2.579
1.939
2.599
4.199
2.579
376
-------
Sta. Mo. Day Tine Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
1634
1704
1734
1804
1834
1904
1934
2004
2034
2104
2134
2204
2234
2304
2334
4
34
104
134
204
234
304
334
404
434
504
534
604
634
704
734
804
834
904
934
1004
1034
1104
1134
1204
81.199
80.899
81.199
81.500
80.899
81.599
81.099
81.000
80.899
81.099
80.799
81.099
80.799
80.799
80.899
80.699
81.000
81.000
80.899
80.699
80.799
80.699
80.599
80.500
80.399
80.399
80.399
80.699
80.500
80.699
80.399
80.699
80.699
80.500
81.199
80.799
80.799
80.799
81.399
81.399
2.539
2.139
2.339
2.599
2.439
3.199
2.299
2.379
2.199
2.759
2.359
2.659
2.399
2.339
2.259
2.179
4.399
3.099
2.859
2.000
2.979
2.019
1.979
1.919
1.859
1.759
1.719
1.739
1.699
1.699
1.739
1.679
2.099
2.239
2.659
2.119
1.979
,2.019
2.639
2.739
377
-------
Sta. Mo. Day Time Temp. D.O.
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
20
20
20
20
20
20
20
20
20
20
20
20
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
1234
1304
1334
1404
1434
1504
1534
1604
1634
1704
1734
1804
1306
1336
1406
1436
1506
1536
1606
1636
1706
1736
1806
1836
1906
1936
2006
2036
2106
2136
2206
2236
2306
2336
6
36
106
136
206
236
81.799
82.099
82.099
81.899
82.000
82.500
82.199
82.699
82.500
82.299
81.799
81.899
79.699
79.799
79.500
79.699
79.599
79.799
79.799
79.699
79.799
79.899
79.899
79.799
79.799
79.899
79.699
79.599
79.599
79.500
79.399
79.500
79.500
79.399
79.299
79.000
79.099
79.199
79.299
79.299
2.739
3.359
3.879
6.419
4.059
4.959
3.759
4.839
5.139
4.659
3.179
3.000
1.899
2.039
1.899
1.899
1.819
1.779
1.919
1.919
2.059
2.059
2.079
2.019
2.079
2.219
2.039
1.939
2.059
2.039
2.000
2.099
2.119
2.039
2.039
1.899
1.779
1.779
1.859
1.939
378
-------
Sta. Mo. Day Time Temp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
^
4
*T
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
306
336
406
436
506
536
606
636
706
736
806
836
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
1506
1536
1606
1636
1706
1736
1806
1836
1906
1936
2006
2036
2106
2136
2206
2236
79.299
79.199
79.000
79.199
79.299
79.199
78.899
78.899
79.199
79.199
79.199
79.099
79.399
79.500
79.500
79.699
79.699
79.500
79.199
79.299
79.199
79.299
79.399
79.799
79.299
79.500
79.599
79.699
79.799
79.799
79.799
79.699
79.799
79.799
79.599
79.500
79.500
79.399
79.500
79.500
1.859
1.799
1.839
1.779
1.839
1.799
1.779
1.799
1.779
1.839
1.899
1.839
2.219
1.959
2.079
2.139
2.079
2.159
2.139
2.299
2.279
2.339
2.239
2.639
2.039
2.000
2.079
1.939
2.000
2.079
2.099
2.119
2.099
2.139
2.259
2.299
2.339
2.299
2.339
2.299
379
-------
Sta. Ho. Day Tine Temp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
2306
2336
6
36
106
136
206
236
306
336
406
436
506
536
606
636
706
736
806
836
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
1506
1536
1606
1636
1706
1736
1806
1836
79.500
79.099
79.199
78.899
79.099
78.899
78.899
78.899
78.699
78.699
78.899
78.899
78.899
78.899
78.899
78.799
78.799
78.899
78.899
79.099
78.899
78.899
79.199
78.899
78.899
78.899
78.899
78.699
78.799
78.699
78.699
78.699
78.899
78.799
78.799
78.899
78.799
78.899
78.899
78.899
2.339
2.379
2.279
2.279
2.379
2.399
2.359
2.299
2.199
2.179
2.079
2.099
2.079
2.079
2.059
1.959
2.000
2.059
2.099
2.139
2.199
2.559
2.599
2.439
2.239
2.219
2.319
2.399
2.500
2.579
2.659
2.619
2.619
2.739
2.519
2.399
2.379
2.179
2.279
2.279
38O
-------
Sta. Mo. Day Time femp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
1906
1936
2006
2036
2106
2136
2206
2236
2306
2336
6
36
106
136
206
236
306
336
406
436
506
536
606
636
706,
736
806
836
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
78.899
79.000
79.000
78.899
78.899
78.899
78.899
78.799
78.899
78.899
78.699
78.699
78.699
78.799
78.699
78.699
78.799
78.599
78.500
78.500
78.699
78.699
78.599
78.500
78.299
78.399
78.399
78.599
78.699
78.699
78.699
78.899
78.899
79.000
79.199
79.299
79.399
79.500
79.500
79.899
2.319
2.259
2.239
2.219
2.239
2.219
2.179
2.219
2.339
2.379
2.399
2.379
2.439
2.359
2.299
2.239
2.199
2.079
2.079
2.099
2.019
1.939
1.879
1.839
1.859
1.879
1.899
1.899
1.899
1.899
1.839
2.019
2.079
2.219
2.379
2.579
2.699
2.839
2.839
2.839
381
-------
Sta,
Mo.
Day
Time
Temp.
D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
1506
1536
1606
1636
1706
1736
1806
1836
1906
1936
2006
2036
2106
2136
2206
2236
2306
2336
6
36
106
136
206
236
306
336
406
436
506
536
606
636
706
736
806
836
906
936
1006
1036
80.000
80.299
80.899
79.899
79.399
79.699
79.299
79.399
79.500
79.500
79.399
79.199
79.299
79.299
79.299
79.399
79.599
79.500
79.500
79.500
79.500
79.500
79.500
79.299
79.399
79.500
79.199
79.299
79.099
79.000
78.899
79.000
79.099
79.199
79.199
79.199
79.299
79.599
79.699
79.699
2.939
3.339
3.639
2.739
2.199
2.239
2.059
2.139
2.139
2.159
2.039
1.959
2.000
2.179
2.219
2.279
2.500
2.379
2.479
2.479
2.399
2.299
2.439
2.539
2.579
2.539
2.500
2.399
2.099
2.039
2.059
1.919
2.059
2.119
2.099
2.099
2.000
2.259
2.279
2.439
382
-------
Sta. Mo. Day Time 'amp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
11
11
11
11
11
11
11
11
11
11
11
11
11
11
1106
1136
1206
1236
1306
1336
1406
1436
1506
1536
1606
1636
1706
1736
1806
1836
1906
1936
2006
2036
2106
2136
2206
2236
2306
2336
6
36
106
136
206
236
306
336
406
436
506
536
606
636
80.399
81.199
81.099
80.899
81.000
81.399
80.699
81.500
81.599
81.699
81.099
81.000
80.899
80.599
80.599
80.799
80.500
80.299
80.699
80.399
80.399
80.399
80.399
80.299
80.399
80.099
80.399
80.199
80.199
80.199
80.199
80.199
80.399
80,299
80.399
80.399
80.399
80.299
80.399
79.899
2.899
3.879
3.979
3.919
4.000
3.859
3.179
3.879
4.159
4.199
3.459
3.439
3.199
2.939
3.159
3.319
3.079
3.179
3.199
3.079
3.039
3.039
2.959
2.899
2.899
3.119
3.159
3.079
2.979
3.000
2.979
3.039
3.239
3.199
3.139
3.119
3.079
3.000
3.039
2.739
383
-------
Sta. Mo. Day Time Temp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4 .
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
12
12
12
12
12
12
706
736
806
836
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
1506
1536
1606
1636
1706
1736
1806
1836
1906
1936
2006
2036
2106
2136
2206
2236
2306
2336
6
36
106
136
206
236
80.099
80.000
80.000
80.000
80.000
80.199
80.099
80.299
80.699
80.899
81.500
81.500
81.699
82.199
81.399
82.299
82.699
82.799
82.699
82.099
82.500
82.000
82.000
81.299
80.699
80.599
80.399
80.399
80.399
80.399
80.500
80.500
80.500
80.599
80.399
80.500
80.500
80.500
80.799
80.799
2.719
2.739
2.779
2.780
2.799
3.059
2.839
3.000
3.099
3.139
4.219
4.299
4.159
4.219
3.599
4.479
4.759
4.719
4.839
4.659
4.539
4.359
4.259
3.879
3.259
3.279
3.299
3.279
3.279
3.179
3.139
3.099
3.119
3.179
3.119
3.179
3.179
3.259
3.339
3.359
384
-------
Sta. Mo. Day Time Temp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
306
336
406
436
506
536
606
636
706
736
806
836
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
1506
1536
1606
1636
1706
1736
1806
1836
1906
1936
2006
2036
2106
2136
2206
2236
81.000
80.899
81.000
80.899
80.899
81.299
80.899
81.099
80.899
80.899
80.399
80.299
80.399
80.500
80.599
77.899
77.899
78.000
78.199
79.199
79.299
79.699
79.890
80.099
80.099
80.000
80.199
80.000
79.500
79.000
78.700
78.300
78.000
77.800
77.599
78.099
78.199
78.199
78.199
78.299
3.339
3.379
3.379
3.339
3.339
3.339
3.299
3.319
3.339
3.279
3.059
2.979
3.039
3.000
3.439
3.279
5.059
5.000
5.379
6.159
6.699
6.899
6.990
7.099
7.179
6.659
6.619
6.800
7.100
7.400
7.700
8.000
8.250
8.500
8.739
8.379
8.299
8.000
7.879
7.779
385
-------
Sta. Mo. Day Time Temp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
12
12
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
13
2306
2336
6
36
106
136
206
236
306
336
406
436
506
536
606
636
706
736
806
836
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
1506
1536
1606
1636
1706
1736
1806
1836
78.199
78.399
78.299
78.500
78.399
78.500
78.399
78.399
78.399
78.399
78.699
78.699
78.599
78.799
78.699
78.899
78.899
78.799
78.699
78.490
78.299
78.199
78.240
78.290
78.340
78.399
78.399
78.500
78.650
78.799
79.299
79.500
79.399
79.699
79.699
79.500
79.699
79.599
79.699
79.599
7.659
7.879
7.619
7.500
7.379
7.359
7.319
7.199
6.899
6.739
6.699
6.759
6.659
6.619
6.339
6.259
6.179
6.379
6.399
6.450
6.539
6.599
6.790
7.050
7.300
7.479
7.399
7.359
7.370
7.399
8.959
8.559
8.339
8.879
8.439
8.079
7.679
7.859
8.079
8.099
386
-------
Sta. Mo. Day Time Temp. B.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
13
13
13
13
13
13
13
13
13
13
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
1906
1936
2006
2036
2106
2136
2206
2236
2306
2336
6
36
106
136
206
236
306
336
406
436
506
536
606
636
706
736
806
836
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
79.599
79.299
79.000
78.699
78.500
78.500
78.500
78.299
78.500
78.399
78.399
78.399
78.199
78.199
78.399
78.399
78.199
78.199
78.399
78.299
78.399
78.399
78.500
78.699
78.500
78.699
78.599
78.599
78.599
78.799
78.899
78.799
78.699
78.599
78.500
78.699
78.699
78.599
78.500
78.399
7.879
6.739
7.279
6.059
7.079
7.110
7.159
6.899
7.179
7.000
6.579
6.500
6.539
6.319
6.199
6.000
5.839
5.699
5.699
5.559
5.479
5.299
5.259
5.139
5.899
4.959
4.979
5.419
5.439
5.759
6.979
7.099
7.159
6.859
6.839
6.919
6.759
6.359
5.719
5.739
387
-------
Sta. Mo. Day Time Temp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
1506
1536
1606
1636
1706
1736
1806
1836
1906
1936
2006
2036
2106
2136
2206
2236
2306
2336
6
36
106
136
206
236
306
336
406
136
206
236
306
336
406
436
506
536
606
636
706
736
78.500
78.670
78.699
78.699
78.899
78.899
78.799
78.799
78.899
78.899
78.699
78.699
78.500
78.399
78.199
78.099
78.000
77.899
77.899
77.699
77.699
77.699
77.500
77.899
77.899
77.799
77.899
77.699
77.500
77.899
77.899
77.799
77.899
78.099
78.000
78.000
78.000
78.199
78.000
77.899
6.159
5.950
5.759
5.679
5.939
8.439
5.699
5.779
5.599
5.000
5.079
5.459
5.159
5.000
5.219
4.979
6.979
4.939
4.919
4.919
4.899
4.819
4.739
4.799
4.779
4.779
4.559
4.819
4.739
4.799
4.779
4.779
4.559
4.559
4.339
4.259
4.119
4.179
4.179
4.179
388
-------
Sta.
Mo.
Day
Time
Temp.
D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
16
16
16
16
806
836
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
1506
1536
1606
1636
1706
1736
1806
1836
1906
1936
2006
2036
2106
2136
2206
1936
2006
2036
2106
2136
2206
2236
706
736
806
836
78.099
78.000
77.500
77.899
77.899
78.000
77.899
78.099
78.000
78.000
78.099
78.299
89.199
78.299
78.399
78.299
78.399
78.299
78.299
78.500
78.399
78.399
78.199
78.199
78.199
78.000
77.899
78.000
77.899
78.199
78.199
78.000
77.899
78.000
77.899
77.899
77.199
77.099
77.199
77.000
4,079
4.000
4.219
4.339
4.419
4.419
4.699
5.219
5.719
5.719
5.679
5.939
6.639
6.939
6.919
6.039
6.179
5.899
5.939
6.039
5.739
5.879
6.199
5.959
5.959
5.979
6.099
5.579
5.899
5.959
5.959
5.979
6.099
5.579
5.899
5.239
4.619
4.779
4.619
4.479
389
-------
Sta. Mo. Day Time Temp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
17
17
17
17
17
17
17
17
17
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
1506
1536
1606
1636
1706
1736
1806
1836
1906
1936
2006
2036
2106
2136
2206
2236
2306
2336
6
36
106
136
206
236
306
336
406
436
77.099
77.399
77.599
77.599
77.299
77.599
78.099
77.699
77.799
77.699
77.699
77.799
77.699
77.799
77.899
78.899
78.199
79.699
79.500
79.000
78.199
78.199
78.299
78.399
78.399
78.099
78.199
77.500
77.000
77.299
77.099
77.299
77.199
77.599
77.599
77.199
77.500
77.399
77.500
77.399
4.179
3.659
3.500
4.339
5.159
5.739
6.519
5.399
5.259
5.139
4.699
4.699
4.279
4.179
4.839
7.659
5.359
8.399
8.059
6.579
5.779
5.179
5.579
6.119
6.019
5.500
4.979
4.299
3.799
3.879
4.359
4.539
4.859
4.939
5.059
5.159
5.000
4.359
4.239
4.099
390
-------
Sta. Mo. Day Time Temp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
17
18
18
506
536
606
636
706
736
806
836
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
1506
1536
1606
1636
1706,
1736
1806
1836
1906
1936
2006
2036
2106
2136
2206
2236
2306
2336
6
36
77.299
77.399
77.399
77.199
77.199
77.199
77.299
77.199
77.399
77.399
77.500
77.899
77.799
77.699
77.790
77.899
77.899
77.699
77.799
77.799
77.799
77.899
77.799
77.899
77.699
77.699
77.799
78.099
78.099
78.299
78.199
78.199
78.399
78.399
78.299
78.299
78.099
78.199
77.799
77.399
4.179
4.159
4.179
4.339
4.359
4.059
3.979
4.039
4.019
4.179
4.359
4.419
4.539
4.759
5.250
5.719
5.359
4.859
5.159
4.879
4.479
4.259
4.099
4.000
3.679
3.839
4.279
5.279
5.119
5.639
5.219
5.279
5.439
5.379
5.319
5.199
5.179
4.739
4.119
3.699
391
-------
Sta. Mo. Day Time Temp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
18
106
136
206
236
306
336
406
436
506
536
606
636
706
736
806
836
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
1506
1543
1606
1636
1706
1736
1806
1836
1906
1936
2006
2036
77.299
77.299
77.299
77.299
77.299
77.199
77.299
77.299
77.399
77.399
77.199
77.299
77.399
77.399
77.699
77.799
77.799
78.000
77.899
77.899
77.899
78.199
78.199
78.500
78.199
78.000
79.500
78.399
78.199
77.899
78.099
78.000
78.099
78.099
78.000
77.799
77.699
78.399
78.199
78.299
3.639
3.500
3.539
3.699
3.659
3.819
3.639
3.699
3.599
3.699
3.679
3.539
3.599
3.679
3.839
4.000
4.139
4.159
4.219
4.179
4.179
4.039
4.719
5.019
4.039
5.079
6.659
5.199
4.859
4.599
4.619
4.459
4.419
4.179
3.419
3.539
4.159
5.979
5.359
5.199
392
-------
Sta» Mo. Day Time Temp. D.O.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
18
18
18
18
18
18
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
2106
2136
2206
2236
2306
2336
6
36
106
136
206
236
306
336
406
436
506
536
606
636
706
736
806
836
906
936
1006
1036
1106
1136
1206
1236
1306
1336
1406
1436
1506
1536
1606
1636
78.199
78.399
78.199
78.399
78.399
78.299
78.299
78.299
78.099
77.699
77.699
77.599
77.399
77.099
77.500
77.199
77.299
77.399
77.500
77.299
77.500
77.599
77.699
77.799
77.899
78.099
78.099
78.399
78.199
78.399
78.099
78.399
78.500
78.699
78.399
78.299
78.500
78.399
78.299
78.399
5.079
5.219
5.079
5.179
5.179
5.159
5.199
5.139
4.500
4.000
3.959
3.839
3.639
3.679
4.000
3.459
3.819
3.899
3.979
4.000
4.000
4.339
4.079
4.199
4.439
4.739
4.739
5.139
4.979
5.039
5.039
5.179
5.239
5.859
4.719
5.099
5.199
4.939
5.000
4.979
393
-------
Sta. Mo. Day Time Temp. 1).0.
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
19
19
19
19
19
19
19
19
19
19
19
19
19
19
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
1706
1736
1806
1836
1906
1936
2006
2036
2106
2136
2206
2236
2306
2336
6
36
106
136
206
236
306
336
406
436
506
536
606
636
706
736
806
836
906
936
1006
1036
1106
1136
1206
1236
78.699
78.699
78.500
78.399
78.299
78.299
78.299
78.899
78.699
78.500
78.699
78.500
78.599
78.500
78.500
78.399
78.500
78.399
78.099
78.000
77.699
77.599
77.599
77.699
77.799
77.699
77.699
77.799
77.699
77.899
77.699
77.899
78.199
78.299
78.699
78.899
79.099
79.199
79.500
79.799
5.500
6.199
4.599
4.279
4.179
3.939
4.619
5.839
5.439
4.859
5.699
5.539
5.639
5.699
5.639
5.639
5.579
5.179
4.619
3.739
4.459
3.719
3.500
3.639
3.739
3.779
3.779
3.839
3.819
4.079
4.079
4.179
4.719
4.779
5.139
5.479
5.779
5.939
6.299
6.699
394
-------
Sta. Mo. Day Time Temp. D.O.
4
4
4
4
4
4
4
4
4
4
4
7
7
7
7
7
7
7
7
7
7
7
20
20
20
20
20
20
20
20
20
20
20
1306
1336
1406
1436
1506
1536
1606
1636
1706
1736
1806
79.799
79.899
79.799
78.899
79.399
79.099
78.799
78.899
78.699
78.500
78.399
7.039
7.139
6.939
5.619
6.279
6.459
5.359
5.539
5.279
5.159
4.959
395
-------
396
-------
1
Accession .Vumber
5
o I Subject
' Field i Group
05A
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization
Stochastics Incorporated, Blacksburg, Virginia
_____
STOCHASTIC MODELING FOR WATER QUALITY MANAGEMENT
10
Au f ho if s)
Krutchkoff , Richard G.
11
16
Date
1971
]2 | Pages
395
Project Number
16090DUH
c ' Contract Number
14-12-849
2j Note
22
i Citation
23
Descriptors (Starred First)
*Stochastic processes, *water pollution, *estuaries
Biochemical oxygen demand, Dissolved Oxygen, streams,
Mathematical models
25 ! Identifiers (Starred First)
' *Stochastic models, Segmented model, Random inputs, Potomac, Ohio
07! Abstract
' The purpose of this work was to extend previous stochastic
models and to verify this extension In particular there were
four tasks undertaken, a) to adapt the model to accept variable
or random input loads, b) to adapt the estuary model to treat
segmented estuaries, c) to verify the adapted model with data
supplied by WQO, d) to find a method for using data to estimate
and predict the stochastic parameter A. The four tasks were
successfully completed. Verification was done with data from
the Ohio River and the Potomac Estuary. This report was sub-
mitted in fulfillment of project number 16090DUH, contract
number 14-12-849 under the sponsorship of the Water Quality
Office of the Environmental Protection Agency. (Krutchkoff,
VPI&SU)
Abstractor
Rinhard G. Krutchkoff
l"^gtto"Poly tech . Inst. & State. Univ
OB; 102 IREV. OCT. !««>
MM1IC
WASHINGTON. DC. 20240
397
------- |