Title: Offstream Reservoir Yield Analysis: Peace River / Ft. Ogden Reservoir
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Permanent Link: http://ufdc.ufl.edu/UF00052665/00001
 Material Information
Title: Offstream Reservoir Yield Analysis: Peace River / Ft. Ogden Reservoir
Alternate Title: SWFWMD. Offstream Reservoir Yield Analysis: Peace River / Ft. Ogden Reservoir, by Hung T. Nguyen and Richard V. McLean
Physical Description: 50p.
Language: English
Creator: Nguyen, Hung T. ( Author )
McLean, Richard V. ( Author )
Publication Date: September 1982.
 Subjects
Spatial Coverage: North America -- United States of America -- Florida
 Notes
General Note: Box 5, Folder 12 ( SF MINIMUM FLOWS AND LEVELS, Volumes 1 and 2 ), Item 12
Funding: Digitized by the Legal Technology Institute in the Levin College of Law at the University of Florida.
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Bibliographic ID: UF00052665
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: Levin College of Law, University of Florida
Rights Management: All rights reserved by the source institution and holding location.

Full Text










OFFSTREAM RESERVOIR YIELD ANALYSIS:

PEACE RIVER/FT. OGDEN SITE





PEACE RIVER BASIN BOARD

SOUTHWEST FLORIDA WATER MANAGEMENT DISTRICT


Ronald Lambert Co-Chairman Ex Officio
Archibald Updike, Jr. Co-Chairman Ex Officio
Carl Simmons Vice Chairman
George Mason Secretary
Vasco Peeples Member
James Lloyd Ryals Member
C. Lamar Daniels Member

RESOURCE MANAGEMENT DEPARTMENT

PROJECT DEVELOPMENT AND MANAGEMENT SECTION



Hung T. Nguyen
Richard V. McLean


September 1982

















The authors wish to thank the following people for their review and comments:







ft




















































\












TABLE OF CONTENTS

PAGE

I. Introduction 1

II. Yield Analysis Discussion 4

III. Results 7

IV. Conclusions 15

V. Appendicies

A. General Methodology for Estimating Offstream 16
Reservoir Yield

B. Peace River/Ft. Ogden Offstream Reservoir 95% 20
Dependable Yield Analysis

C. Transfer of Surface Water Records from One 36
Stream to Another

VI. References 46























ii









LIST OF FIGURES


TITLE PAGE

1. Location Map 1

2. Offstream Reservoir System 5

3. Dependable Yield of a 2,500 Acre-Foot Reservoir 10

4. Dependable Yield of a 5,000 Acre-Foot Reservoir 11

5. Dependable Yield of a 16,000 Acre-Foot Reservoir 12

6. Dependable Yield Using a 50 CFS Diversion Pump 13

7. Dependable Yield Using a 100 CFS Diversion Pump 14




LIST OF TABLES

TITLE PAGE

1. Dependable Yield Summary Sheet 9



















"iii









I. INTRODUCTION

River water has long been a source of public water supply. However, seasonal
flow fluctuation in streams with little ground water base flow necessitates
the development of the capacity to store water when it is available for use
when it normally would not be available. Traditionally, this has been done
by constructing a dam and creating an instream reservoir. The development
of instream reservoirs such as Lake Manatee in Manatee County and Shell Creek
Reservoir in Charlotte County have some drawbacks.

Florida, especially the coastal areas, is flat. The creation of such reservoirs
flood many acres and thus require the acquisition of large amounts of land at
an ever increasing cost. In many cases, much of the flooded lands are riverine
forests which are both environmentally and recreationally beneficial and are
destroyed by a permanently raised water level. This fact, plus water quantity
and quality impacts to valuable riverine and estuarine habitats potentially
caused by such a system were at least part of the basis for the increase of
environmental regulations to protect the natural systems. The acquisition of
the necessary environmental permits made development of instream systems less
feasible. Instream reservoirs are also subject to contamination by pollutants
that may reach the river flowing into the reservoir. A pollutant load reaching
the reservoir during the dry season could have disastrous results for the
people depending on the system. All of these factors have combined to make
development of instream reservoirs a costly and time consuming process, and
thus have reduced the feasibility of such systems.

Partially as a result of the above limitations, offstream reservoirs have
become more widely used as a method of making maximum reasonable and benefi-
cial use of stream flow for public supply. The water storage facility for
this type of system is usually built in the uplands, not in the riverine
forest, and thus avoids many of the environmental impacts of the instream
system. The potential for pollution of the reservoir is greatly decreased
since it is not instream, but receives its supply through a withdrawal pump
facility. If potential pollutants are detected, the withdrawal operation
can be stopped until the danger has passed. There is also a great deal more
flexibility for maintain higher quality minimum stream flow using the
offstream system.

The purpose of this report is to determine the potential yield of the Peace
River at Fort Ogden (Figure 1) using an offstream reservoir under certain
selected conditions. Data collection and early work done on the project
started in 1981 and was used to support the District's Regulatory effort
and the efforts to form a regional water supply system in the Charlotte
Harbor area.

The report predicts the yield of an offstream storage system which is limited
by such factors as river flow, withdrawal pump capacity and storage capacity.
Potential constraints on withdrawal from the river by regulatory agencies to
maintain and environmentally healthy downstream flow are included in the yield
analysis in the report. However, the constraints used here do not duplicate
the current consumptive Use Permit (CUP) constraints placed on the General
Development Corporation (GDC) by the Southwest Florida Water Management District.
This report is not an analysis of the existing facility, but does help deter-
mine the facility requirements to obtain larger safe yields.

-1-







Figure 1: Reservoir Location





-I









S.Manatee Conty Arcdi
S, -!ee.. .





0 Venice



aMaota .CCount 4_ GM _W __ D Soto .lCun___


Port Churotu











.-Ch dotted 1 II Jl I







Rew1roi System
A U.S.G.S. Gages




0 10 20 30
scale in mtes










An important aspect of this work is the use of a model, developed by staff,
which simulates the function of an offstream system. The simulation allows
the manipulation of all constraints which affect the potential yield so a
better understanding of the systems potential usefulness in regional water
supply can be determined. Input data to the model can also be changed to
reflect modified or new constraints which affect the system's yield.













































-3-










II. YIELD ANALYSIS DISCUSSION

Figure 2 is used to illustrate the general operation of an offstream system.,
Source water availability is the key limiting factor in this and all other
water supply systems. This factor is beyond the control of the supplier and
is dependent on rainfall and regulation. Other surface water users located
upstream from the system's withdrawal point can reduce the amount of water
available for withdrawal and thus limit the system's yield. The amount and
timing of water withdrawal by the system is subject to limitation by regu-
latory constraint. This is done to better manage the water resource and to
assure adequate downstream flow to maintain healthy riverine and estuarine
habitat.

In this report, historical river flow is obtained from three U. S. Geological
Survey gage stations show in Figure 1. This omits about 70 square miles of
drainage basin and is thus somewhat conservative. The historical flow data
was manipulated as discussed in the appendices to produce very long-term flow
data for use in the analysis. No upstream diversions are included in the
analysis since if they exist, they are small. Yield of the offstream system
is analyzed using a series of constant percentage withdrawal rates as limiting
factors. A constant downstream flow was maintained in this manner (for example,
if 5% was the allowable diversion rate, the offstream system could take up to
5% at all times, depending on its pump and storage capacity, and at least 95%
would remain as downstream flow.)

The offstream facility itself consists of a withdrawal facility located on the
source stream, a reservoir, a reservoir withdrawal facility and a treatment
plant. During high stream flow periods, the stream withdrawal facility pumps
water to the storage reservoir and to the water treatment plant. This allows
an increase in the amount of stored water both by directly adding water to
storage and eliminating withdrawal from storage since the water demand is being
met from the river. As river flow decreases and regulation becomes more con-
straining, the water demand is met by a combination of river and reservoir
pumping facilities sending water to treatment. As river flow decreases, the
percentage of the demand being met from the reservoir increases. Under the
existing CUP, there are times when the total demand is met from the reservoir.

Facility size is under control of the supplier and determines the yield of the
system given the stream flow and regulation constraints. Large withdrawal and
storage facilities allow the supplier to obtain vast quantities of water
during high flow periods. This greatly increases the system's sustained
yield since more water is available during the low flow months.

A computer simulation was developed to analyze the potential 95% dependable
yield of the system. It accounts for all variables shown on Figure 2 including
reservoir gains and losses. Any variable or combinations of variables can be
changed in order to determine their impact on yield. Yield analyses were run






-4-













Figure 2. SKETCH OF AN OFFSTREAM RESERVOIR SYSTEM







a1

IUpstrem WithdmsP
Offstream Reservoirn fdor Othr Uses


Pumping Station "'A"



Pumping Station ,B",



















RESER YOIR GAINS OR LOSSES
Downstream flow to
SEvaporaon Loss Protect the Natural System
jj Ramnfall Gain
3 Loss or Gain from Bank Storge
4nW Upwad Leakance
[5] DoawvnwdLetkance

Demand, cors aId nornontroiable constraints dictate the size of the facility.
15-










using three potential reservoir sizes, five potential stream withdrawal pump
capacities and five potential diversion percentages. This amounts to 75
possible combinations for which yield projections were developed. A descrip-
tion of the model and how it was developed is found in the appendices.














































-6-







III. RESULTS

Each of the offstream facility options was run through the simulation model
to determine its dependable yield. Three reservoir sizes were used in the
analysis, and each has 25 feet of usable depth. The smallest holds 2,500
acre-feet, or 815 million gallons of water, and has a 100 acre surface area.
The intermediate sized reservoir has a 200 acre surface area and contains
5,000 acre-feet (1.63 billion gallons) of water. The largest reservoir
analyzed in this report has an area of 640 acres and holds 16,000 acre-feet
(5.21 billion gallons) of water. Five stream withdrawal pump capacities--
20, 50, 100, 200 and 500 cubic feet per second (cfs)--and five allowable
diversion rates as a flat percentage of flow--5, 10, 15, 25 and 50 percent--
are used in the yield analysis for each of the three reservoir options. The
model uses these limiting criteria as well as very long term river flow data
based on actual historical flows to predict the 95% dependable yield for
each option. The results of each analysis are shown in Table 1 and are
illustrated in Figures 3 through 7.

Once river flow and allowable diversion rates are established, then the facili-
ties become the factor that determines yield. This report does not attempt to
give the absolute dependable yield of the Peace River because that answer does
not lie in an engineering analysis. It is determined by total river flow and
regulatory constraints placed on the amount and timing of withdrawal. Once the
legal limits of withdrawal are determined, a facility can be designed and, if
economically feasible, built to obtain whatever yield is allowed. If there
is good coordination between the supplier and the regulator during development
of the facility, it can be designed with the constraints taken into account
and thus function efficiently. This efficiency can drop considerably if such
coordination is not developed.

The analysis resulted in yields that ranged from 6 mgd for the smallest reservoir
at the 5% allowable diversion rate, to 41.2 mgd for the largest reservoir at
50% allowable diversion. This raises an interesting point that needs clarifi-
cation; that is the difference between allowable diversion rate and actual
diversion rate as used in this report.

The average annual flow of the Peace River at Ft. Ogden is approximately one
billion gallons per day (1,000 mgd). An allowable diversion rate of 5% equates
to 50 mgd, but a review of the predicted yield for all options using the 5%
diversions shows results ranging from 6 to 16.5 mgd. So depending on the
option selected, the actual diversion rate as a percentage of annual river flow
ranges from .6 to 1.65 percent. Only with much larger facilities could the
actual diversion percentage approach the allowable diversion percentage on an
annual basis.

The reader is cautioned that existing regulatory constraints on withdrawal do
not use the constant percent diversion approach. For enviornmental and water
management reasons, the current permit allows no diversion from the river at
the Ft. Ogden site when flow drops below established levels, which vary by
month. If these or any other constraints are run through the simulation, the
yield projection would probably change. The model is flexible, so this can
be done and revised yield figures can be generated. Again, if these con-
straints are known early enough, they can be incorporated into a new
facilities design, and improve efficiency.

"-7-









While this is an analysis of a surface water system, the report would be
incomplete without mention of ground water. A large surface water supply
can be expanded by blending ground water into the system. In the Ft. Ogden
area, ground water could probably be used to increase the system's yield
by 33 to 50 percent without significantly altering the water treatment
facilities. The addition of a ground water source would also give added
reliability to the overall system. In order to protect the resource and
other users, a ground water withdrawal is also subject to permitting
constraints, but the option should be pursued.










































-8-









TABLE 1 : 95 PERCENT DEPENDABLE YIELDS IN MGD OF A PEACE RIVER/
FORT OGDEN OFFSTREAM RESERVOIR SYSTEM OF DIFFERENT
STORAGE CAPACITIES AND UNDER VARIOUS DIVERSION RATES
& PUMPING CAPACITIES.

1.- RESERVOIR STORAGE CAPACITY : 2,500 ACRE-FEET *

PUMP : DIVERSION RATES FROM RIVER FLOW
(CFS) 5.00% 10.00% 15.00% 25.00% 50.00%

20 6.00 8.20 10.10 10.90 11.10
50 6.00 8.30 10.30 13.40 17.10
100 : 6.00 8.30 10.30 13.40 17.10
200 6.00 8.30 10.30 13.40 17.10
500 6.00 8.30 10.30 13.40 17.10


2.- RESERVOIR STORAGE CAPACITY : 5,000 ACRE-FEET *

PUMP DIVERSION RATES FROM RIVER FLOW
(CFS) 5.00% 10.00% 15.00% 25.00% 50.00%


20 8.40 10.70 11.90 12.20 13.40
50 : 9.10 12.40 14.70 18.90 26.50
100 : 9.10 12.50 14.90 19.20 26.90
200 9.10 12.50 14.90 19.20 26.90
500 9.10 12.50 14.90 19.20 26.90


3.- RESERVOIR STORAGE CAPACITY : 16,000 ACRE-FEET *

PUMP : DIVERSION RATES FROM RIVER FLOW
(CFS) : 5.00% 10.00% 15.00% 25.00% 50.00%

20 : 11.00 13.00 14.00 15.20 16.30
50 : 15.70 22.00 25.20 26.60 27.10
100 : 16.50 23.70 28.20 32.70 35.80
200 : 16.50 23.70 28.90 35.50 41.20
.500 : 16.50 23.70 28.90 35.50 41.20



THE YIELD VALUES ARE GRAPHICALLY PORTRAYED IN FIGURES 3, 4, 5, 6 & 7






-9-







FIGURE 3 : j5 PERCENT DEPENDABLE YIELDS IN MGD OF A PEACE RIVER/
FORT OGDEN OFFSTREAM RESERVOIR SYSTEM : 2,500 ACRE-FEET
CAPACITY ( 100 ACRES OF SURFACE AREA ) AND UNDER VARIOUS
DIVERSION RATES & PUMPING CAPACITIES.


I I l I i I l i l l ll l l l i.1 1 l l 1 *

RESERVOIR STORAGE CAPACITY : 2,500 ACRE-FEET




1 8 lIlli I I I II mIII I1 8









S 14..
M N +! *.u


=E 12
N ... ...... .





a. a -













16 :.6
1 1 Jill, I f 1,1








N O
1 .. .1111111 1 1 M, MON H.i I I 1 11E11. 111111 MO i ........ 1
*2 5I 1 200
UNION ,Jll 1 1 2 Jill 1 11 .1-.. 1

w- J i ll --




PUMPING C
L I0 I fill I- I


20 50 100 2I 500
PUMPING CAPACITIES IN CFS
0-
1 I I i i i i iI iI ~1t 1 11 1 llt Ill ilflll i I i llllll llln lH I I i I 1 t1 ~1 II Ii 1 1I1H1 tll il{ll
rcc:I I 1 I I.1--1 r7- --1I -I- rrfrl T~illl n 1 II rrnrrrrrr I-- r~ --Ir~ rrr--Ir r~ r,,,, f i
13 ~ ~~ .... 0.6 1ifIII1I1 IIIiftlllll 1~iII~~~II 111 II11i11ri
QI I .r r ~ i r 1 ~ I ..11 i1 i1 I III tt 11I1II1 11. I I. 1. I f II 11 11.1111111 ~ I t tI Ict I 1 i 11~ ii t 1111II111 II1I 1i














-lO-









FIGURE 4 : 95 PERCENT DEPENDABLE YIELDS IN MGD OF A PEACE RIVER/
FORT OGDEN OFFSTREAM RESERVOIR SYSTEM : 5,000 ACRE-FEET
CAPACITY ( 200 ACRES OF SURFACE AREA ) AND UNDER VARIOUS
DIVERSION RATES & PUMPING CAPACITIES.

I ii I i jj I [ 1 iii [i1I[I~ii I~i1i1iiiiiti i itiiii~iiii~uiii ii l ii Ft n I1 i ii [1. III

RESERVOIR STORAGE CAPACITY : 5,000 ACRE-FEET I



20 2.0






18 1.8






16 l6
ION











14 1.1






H 12 11 11
I I I I- H .-11.11 M -1^0.--^ -. 11. 1 W 111 1 ..11 1 .. .. I





































20 50 100 200 500
-11-,
14 1 P-.-. l.111,11;;. Hill4 1 1 H





tW ::::
CL ^ ^ ^ . ^ .. . ..
3Sl 5 Z
Cj7^ - ^ . . . . .
I Q C
O S: 1C.- -^ . ., . .-.- , .
LU 1P r-r.1r ^ UJ 0 T7 rI1IT nllnTP- lP-Tlmrnrrr r~ ~ I- 1Irrrrr rmrlrlrn l ir-rt! t
Q -. f- . .. .. ,., . I. .. . .... I. i ^11 111111111 1 1It l~l~lll I i I I I I tI1IIIIiII
^L - - ,. . ., ,, . .
tj 1 I I I .. ... .. ,.. -33 11 I 1I I i .. ... 1 I .t .. .i t
-- .,.... ...., c

--- ___ -. ,| ^ ,. -- - . ,Q
u, I r I -......... ....rr tr irrrrrr 11rrlrrrrnrir~ .. ...rr - ..... ...rnr r.rr~r m .-... ^ .
3- -- -......... .... ,"" '"""" -- -....,..... ,. ......."L'LLLLL~ .0.8 ~cc




20 50100 20 50
PUMPIG CAACITES. N CF
-11-L






FIGURE 5 -oQ5 PERCENT DEPENDABLE YIELDS I"MGD OF A PEACE RIVER/
.ORT OGDEN OFFSTREAM RESERVOIR ,oSTEM : 16,000 ACRE-FEET
CAPACITY ( 640 ACRES OF SURFACE AREA ) AND UNDER VARIOUS
DIVERSION RATES & PUMPING CAPACITIES.


S I Il I l l iH1 1 llllll illll illlM llllll li l I 1 1 1 1 1 1 Ill 1 1 ;:
RESERVOIR STORAGE CAPACITY 16,000 ACRE-FEET



36 3.6

Lz


32





o 28 3
28







LrJ

S16 I I I I I I I I I I I I I I
8 IL







PUMPING CAPACITIES IN CFS

















-12-.
20~~Ot 50F020 0
t ~ I.fI Ir tI1.v~ Lt 1111 PUMPING1111 1~ .LAPAI liTlll~IES IN CF t has lm ~ sna. iut aniI .
QI f t ItII 4 1 1 1I1t1 IIIli llif tII1 IIti 11Ill~lt f I f t ?~3 r l'fl~-tf ii nl12 111 t








FIGURE 6 : 95 PERCENT DEPENDABLE YIELDS IN MGD OF A PEACE RIVER/
FORT OGDEN OFFSTREAM RESERVOIR SYSTEM : 50 CFS DIVERSION
PUMPING CAPACITY AND UNDER VARIOUS DIVERSION RATES &
RESERVOIR CAPACITIES.






DIVERSION PUMPING CAPACITY : 50 CFS

50 1 LIIi I I I I 5.10- 1 1 11 1 15


4 0 4.0 g
0

LL.
3 0 1 1 1 a I I I I I I 1 1 1 13 1 1 1
LL



- 20 2.0


0 1 1 r I II I I I. I i IIi
W..
o
IrJ


11 0

Lu
.. ..-.--..--...- - ------------ ---- <: '







,. 5 |||m|| |||ALLOWABLE DIVERSION RATES -0.5 '

;=:==== === =:= =:==:=====: -( "" ---* ,--
.-. -.- -25% -. ---- --. --- ---,,:












2,500 5,000 10,000 15,000 ACRE-FEET
100 200 400 600 ACRES
RESERVOIR CAPACITIES IN ACRE-FEET
SURFACE AREA IN ACRES
c~ t,- 3-







FIGURE 7 : PERCENT DEPENDABLE YIELDS IN .JD OF A PEACE RIVER/
FORT OGDEN OFFSTREAM RESERVOIR SYSTEM : 100 CFS DIVERSION
PUMPING CAPACITY AND UNDER VARIOUS DIVERSION RATES &
RESERVOIR CAPACITIES.






DIVERSION PUMPING CAPACITY : 100 CFS
50 5.0
50 H1/1.;1; n 1 1 1 1 1 1 1 1 m n i 1 1 1 1 1 1 i i i i i i i i i I i-lliiiiiiii '


40 4.0



30 3.0 ot




0 20 2.0 1
n MC3




I AW I, I I I I
I-,

-kv I mom J
-Jr-


I ----- -I


0 0 LL =

-- -S = -- -





S5% .------ .. ... .
15% .












100 200 400 600 ACRES
0%=0
t~ 1- i r -1 -L - - ~1











SURFACE AREA IN ACRES










-14-
ta. Am I I- f f- I I =A1 S m s t 1 h M p













2,500 5,000 1 O, 000 15,000 ACRE-FEET
lO0 100 2 400 600 ACRES

RESERVOIR CAPACITIES IN ACRE-FEET
SURFACE AREA IN ACRES
-14-









IV. CONCLUSIONS
1. Simulation modeling is very useful in understanding the operation and
limitations of an offstream system, and in determining its dependable
yield.

2. The components of the offstream reservoir system should be sized taking
all constraints hydrologicc, legal and economic) into account to achieve
maximum yield at the least cost.

3. The dependable yield values generated in this report ranged from 6 to
41.2 mgd depending upon the option selected. Larger yields could be
obtained with larger facilities, particularly with a larger reservoir.

4. The surface water facility should be augmented with ground water to
increase the yield and reliability.



































-15-










APPENDIX A

GENERAL METHODOLOGY FOR ESTIMATING OFFSTREAM RESERVOIR YIELDS

This appendix describes the general methodology used in the determination of the
95-percent dependable yield of an offstream reservoir system. The end product
of the methodology is an understanding of the operational behavior of the
system, so that an optimization of the water supply under various constraints
(such as diversion rates from the river flow, regulatory downstream minimum flow,
pumping capacity from the river to the reservoir, from the river to the treatment
plant and from the reservoir to the treatment plant, sizes of the reservoir,
upstream withdrawal, water conservation measures during drought etc.) can be
performed.

GENERAL METHODOLOGY

Basic Considerations

The general procedure for the computation of the reservoir yield consists: (1)
compile a statistically valid record of streamflow data at the reservoir site;
(2) fit these data to a synthetic flow generator model capable of projecting a
number of sets (or traces) of data, each with a 50-year record length; (3)
subject each set of synthesized data to a preset set of constraints, as
mentioned above, to produce a set of allowable and pumpable flow values;
(4) route each set of allowable and pumpable flow values through an offstream
reservoir system of known physical characteristics (i.e., surface area and
capacity, adjustment due to evaporation loss and gain from rainfall over the
reservoir, to seepage loss or to gain or loss due to bank storage being made
at that point in time) to determine the yield of the reservoir; and (5) repeat
the same procedure for 100 traces and construct a yield versus probability
relationship to interpret the 95-percent dependable yield of the reservoir.

Compilation Of Streamflow Data

Streamflow records at the location where an offstream reservoir system would be
built, need to be compiled. The records need to be as long as possible, so a
reasonable long-term average can be then obtained, and the extreme ranges from
wet to dry conditions adequately appraised.

Synthetic Flow Generator Model

Synthetic streamflow sequences are increasingly in use in the fields of plan-
ning, design, management and simulation of water resource systems. The synethic
data are of interest to water resources' workers because the historical data
is either not available or available over too short a period to be useful for
forecasting.

-16-










A first order autoregressive model has been extensively used over the past
decade for the synthetic generation of streamflow (Thomas and Fiering, Matalas,
Fiering and Jackson, Beard).
The following equation represents this autoregressive model for unit time
intervals of months.

Qi+1 = j+l + bj(Qi--j) + tiSj+\/(1-rj2) (1)
where

Qi and Qi+1 = Flows during the ith and (i+1)th month respectively,
reckoned from the start of the synthesized sequence.

-Tj and qj+l = Mean monthly flows during jth and (j+1)th month respectively,
within a repetitive annual cycle of 12 months.
bj = Regression coefficient for estimating flow in the
(j+1)th month from the jth month.
ti = Random normal deviate with zero mean and unit variance.
Sj+i = Standard deviation of flows in the (j+1)th month.
rj = Correlation coefficent between the flows of the jth and
(j+l)th month.
Equation (1) characterizes a circular random walk, a model in which the flow in
the (i+1)th month is composed of a component linearly related to that in the ith
month and a random component. The variation in sign and magnitude of the random
additive component makes for a continuous, unbounded, and serially correlated
sequence of data for simulation studies.
The autoregressive model is based on statistical methods which do not pretend to
provide causal models for actual flow. However, the simulated sequence will
have the same statistical characteristics as the observed data and can be synthesized
as long as desired from which the entire sequence may be divided into a large
set of responses to aid decision-making with respect to the design operation and
regulation of a system. The most difficult part of the model application is the
estimation of the distribution of data because this distribution of data may vary
from month to month. Four probability functions, normal distribution (ND), cubic
root normal distribution (CD), square root normal.distribution (SD) and log
normal distribution (LD), are considered in this study, other probability
functions might be added later.
The model consists of three main functions:
1. First, the historical data is analyzed by statistical methods and
the parameters of mean, standard deviation, correlation and regres-
sion for each time period are calculated, based on each of the
four probability functions considered.




-17-









2. Second, the generated sequences of monthly flows for each distri-
bution based on equation (1), are compared to the historical data by
using Chi-Square test for goodness-of-fit, in order to choose the best
fit distribution.

3. Third, still utilizing equation (1) and based on the statistical
parameters of the best fit distribution previously determined,
the model will generate 50 years of monthly synthetic streamflows
for each of the 100 traces. A trace is defined as a 50-year
record of monthly flows from which one value of yield is obtained.
One hundred traces is considered a minimum requirement to achieve
statistical validity.

Operations Routing Simulation Model

This model consists of two components:

1. The first component utilizes each 50-year trace of synthetic
monthly flows to obtain the monthly values of allowable and
pumpable water, defined as:
APW = DVR* (FLO-UPW)

subject to
Max (APW) = PUC
FLO UPW APW => MDR

where

APW = Monthly allowable and pumpable water, in cfs
DVR = Diversion rate in percentage
FLO = Average monthly synthetic flow, in cfs
UPW = Average monthly upstream withdrawals, in cfs
PUC = Maximum pumping capacity, in cfs
MDR = Average monthly minimum downstream release, in cfs

2. The second component of the model is an offstream reservoir
operations routing simulation that computes the yield from
the 50 years of monthly allowable and pumpable flow data
converted to volumes. The iterative technique uses demand,
i.e., yield as the trial value. The algorithmic calculations
start with the reservoir at maximum reservoir operational
level. The trial value of demand is compared to the allowable
and pumpable water. When a deficiency occurs, the difference
is made up from the reservoir storage, and when there is a
surplus, this surplus is pumped to the reservoir to make up
the storage deficit due to previous pumpage, after being
adjusted for evaporation loss and rainfall gain, loss due
to seepage, or gain due to bank storage. This procedure
is continuously applied for each month of the trace, and the

-18-









reservoir storage is continuously monitored. If the storage
stage drops below intake level, the trial value of demand is
adjusted downward and the procedure is repeated. When a
successful run through the entire trace is accomplished
within a preset tolerance, the trial value of demand is
taken as the yield for the trace.


Yield Frequency Analysis

The above procedure is repeated for 100 traces of synthetic data, each with a
length of 50 years. One hundred values of annual yield are obtained and a
frequency analysis of these values gives a yield versus probability curve for
the reservoir. The 95-percent dependable reservoir yield is the annual yield
value equalled or exceeded in 95 of the 100 traces.

































-19-











APPENDIX B

PEACE RIVER/FORT OGDEN OFFSTREAM RESERVOIR
95-PERCENT DEPENDABLE YIELD ANALYSIS

COMPILATION OF STREAMFLOW DATA

The Peace River/Fort Ogden offstream reservoir system is assumed to be located
a few miles southwest of Fort Odgen, and has its intake structure built just
downstream from where Horse Creek enters the Peace River, eleven miles downstream
from the junction of Peace River and Joshua Creek and about fifteen miles downstream
from Arcadia. The information on the data available for the area is from the
following stations operated by the U. S. Geological Survey.

Station No. Name Area (sq.miles) Period of Record

02296750 Peace River at Arcadia 1367 1932 1980
02297310 Horse Creek near Arcadia 218 1951 1980
02297100 Joshua Creek at Nocatee 132 1951 1980
Peace River flow at Fort Ogden is assumed to be the combined flows of Peace
River at Arcadia, Horse Creek near Arcadia and Joshua Creek at Nocatee. The
flow gain from additional drainage basin from these gauges to the intake struc-
ture is not considered and thus makes the flow estimate somewhat conservative.

Peace River at Arcadia has the longest period of record of 49 years from 1932 to
1980, Horse Creek near Arcadia and Joshua Creek at Nocatee have only 30 years of
record from 1951 to 1980. A "transfer of surface water records from one stream
to another" scheme is used to extend the flow data of Horse Creek and Joshua
Creek back to 1932 to fill the gap from 1932 to 1951. This transfer method is
discussed in Appendix C. Forty-nine (49) years of streamflow at Fort Ogden are
compiled and listed on Table B-1.

SYNTHETIC FLOW GENERATOR MODEL

Statistical Parameters Computation

The parameters of mean, standard deviation, correlation and regression are
computed from the forty-nine years of historical streamflow data and for each of
the four probability functions considered, i.e., normal distribution (ND), cubic
root normal distribution (CD), square root normal distribution (SD) and log
normal distribution (LD). These parameters are listed on Tables B-2 and B-3.

Chi-Square Test for Goodness-of-Fit

Based on equation (1), from Appendix A, the generated sequences of monthly flows
of 50, 100, 250 and 400 years length and for each of the considered distribution
functions, are compared to the historical data by using the Chi-Square test for
goodness-of-fit. The Chi-Square values are listed on Tables B-4 and B-5.
-20-






























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-20
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TABLE B-2 VALUES OF MEAN & STANDARD DEVIATION PARAMETERS OF HISTORICAL DATA
BASED ON ND, CD, SD, LD DISTRIBUTION


MEAN STANDARD DEVIATION
MONTH :-------------
: ND CD SD LD : ND CD SD LD


OCT :2156.75 11.85 42.22 3.16 : 2000.51 3.66 19.55 0.40
NOV 642.90 8.09 23.58 2.68 : 536.26 2.13 9.42 0.34
DEC 516.37 7.46 20.90 2.58 :568.02 2.00 9.02 0.31
JAN 714.14 8.14 24.07 2.67 :732.04 2.58 11.73 0.39
FEB 911.69 8.69 26.72 2.75 :1075.22 3.00 14.20 0.43
MAR :1048.39 8.83 27.77 2.74 :1223.95 3.56 16.82 0.51
APR 715.73 7.83 23.13 2.58 :774.95 3.09 13.58 0.51
MAY 418.18 6.72 18.10 2.42 :531.48 2.24 9.62 0.39
JUN 1466.14 10.01 33.28 2.91 :1695.62 3.79 19.13 0.48
JUL :2499.43 12.60 46.07 3.25 :2077.82 3.63 19.63 0.39
AUG :2758.98 13.25 49.31 3.33 :2081.84 3.26 18.29 0.32
SEP :3726.63 14.54 56.83 3.44 :3015.42 3.81 22.53 0.34




TABLE B-3 VALUES OF CORRELATION & REGRESSION PARAMETERS OF HISTORICAL DATA
BASED ON ND, CD, SD, LD DISTRIBUTION

CORRELATION REGRESSION
MONTH :-------------
: ND CD SD LD : ND CD SD LD

OCT 0.50 0.50 0.50 0.48 : 0.76 0.52 0.58 0.40
NOV 0.75 0.74 0.74 0.73 : 0.80 0.56 0.53 0.88
DEC 0.73 0.72 0.72 0.74 0.69 0.77 0.75 0.79
JAN 0.48 0.64 0.61 0.70 : 0.38 0.50 0.47 0.56
FEB 0.52 0.73 0.69 0.78 : 0.35 0.62 0.57 0.70
MAR : 0.53 0.70 0.66 0.78 : 0.47 0.59 0.56 0.66
APR 0.58 0.67 0.64 0.73 : 0.91 0.77 0.80 0.73
MAY 0.51 0.64 0.61 0.68 : 0.75 0.88 0.86 0.89
JUN 0.17 0.24 0.23 0.24 : 0.05 0.14 0.12 0.19
JUL : 0.61 0.65 0.65 0.64 : 0.50 0.68 0.63 0.78
AUG 0.49 0.61 0.58 0.66 : 0.49 0.68 0.62 0.81
SEP 0.60 0.53 0.55 0.48 : 0.41 0.46 0.45 0.45


ND = Normal Distribution
CD = Cubic Root Normal Distribution
SD = Square Root Normal Distribution
LD = Log Normal Distribution


-22-









TABLE B-4 CHI-SQUARE VALUES OF SYNTHESIZED SEQUENCES BASED ON
ND, CD, SD, LD DISTRIBUTION ( 50 & 100 YEARS SEQUENCES )


CHI SQUARE VALUES

MONTH : 50 YEARS 100 YEARS

SND CD SD LD ND CD SD LD


OCT 43.2** 15.8* 6.1 15.4 : 13.6 9.1 9.3 9.9
NOV 97.7** 40.4** 51.8** 9.9 : 98.5** 37.9** 30.0** 2.7
DEC 51.7** 51.9** 60.1** 11.9 61.5** 47.7** 52.9** 13.7
JAN 54.3** 17.9* 25.5** 10.0 42.6** 21.8** 21.6** 15.2
FEB 28.9** 21.3** 23.0** 15.5 38.9** 19.8* 27.3** 5.3
MAR 24.0** 36.8** 21.2** 51.6** 34.4** 23.6** 24.8** 40.0**
APR 61.6** 13.2 16.6* 8.2 27.1** 18.6* 19.6* 21.6**
MAY 71.3** 36.2** 38.7** 9.1 66.9** 26.9** 30.1** 13.0
JUN 53.4** 20.1** 16.8* 19.8* 39.2** 14.2 21.8** 14.9
JUL 14.8 10.0 11.3 13.0 9.2 4.3 3.4 4.9
AUG 30.8** 19.6* 23.2** 14.6 23.1** 20.1** 19.5* 12.4
SEP 22.0** 5.2 7.7 5.9 42.2** 14.3 16.8* 8.0



TABLE B-5 CHI-SQUARE VALUES OF SYNTHESIZED SEQUENCES BASED ON
ND, CD, SD, LD DISTRIBUTION ( 250 & 400 YEARS SEQUENCES )


: CHI SQUARE VALUES

MONTH 250 YEARS 400 YEARS

SND CD SD LD ND CD SD LD
---------------------------..............----------------------------

OCT : 18.8* 9.9 9.9 7.7 : 24.2** 3.2 7.3 4.9
NOV 97.9** 39.1** 44.3** 3.5 : 95.3** 40.6** 39.1** 2.8
DEC :75.4** 48.1** 52.2** 14.8 69.4** 46.6** 53.0** 9.8
JAN : 45.8** 15.5* 22.6** 11.2 : 43.2** 13.8 19.3* 13.0
FEB : 31.2** 11.9 18.6* 11.7 : 30.7** 13.8 14.8 13.4
MAR 27.2** 36.4** 25.7** 40.3** 29.1** 30.1** 25.8** 37.3** "
APR : 34.4** 9.7 13.7 13.9 : 29.9** 10.8 19.6* 10.8
MAY : 57.6** 29.3** 31.6** 13.2 : 57.2** 23.4** 26.6** 10.0
JUN 34.8** 11.2 10.9 13.0 : 32.5** 12.4 16.0* 14.2
JUL 10.7 1.3 3.2 3.6 11.5 2.4 3.9 2.5
AUG : 16.5* 7.0 9.7 7.9 : 23.6** 11.7 15.1 13.7
SEP : 50.5** 12.9 22.1** 6.2 : 37.4** 14.2 18.2* 8.0

*, ** = The Chi-Square tests are significant at 0.05 & 0.01 levels respectively.


-23-








The comparison shows as follows:

No asterisk implies that the Chi-Square test is not significant. In
other words, both synthetic and historical data give a similar type
of frequency distribution.

One or two asterisks indicate the Chi-Square test is significant at
the levels of 0.05 and 0.01, respectively. The statistical meaning
of 0.05 and 0.01 significant level is that the frequency distribution
of synthetic sequence is either slightly or highly different from the
frequency distribution of the historical data.

In the length of 50, 100, 250 and 400 years synthesized frequency, the
general order of better fitting, which is expressed by the symbol "
is log normal distribution square root normal distribution cubic
root normal distribution normal distribution. The log normal distri-
bution is comparatively chosen as the best distribution and used in the
synthetic flow generation.

Synthetic Flow Generation

Table B-6 lists a sample of synthetically generated flow sequency for one trace
(50 years), using equation:
Qi+1 = 7Ij+1 + bj(Qi-Qj) + tiSj+l (1-rj2) (1)

and based on log normal distribution which has been determined previously as the
best of the four considered distribution functions. The same procedure is
repeated for 100 traces.

OPERATIONS ROUTING SIMULATION MODEL

Computation of Monthly Maximum Available Water

The monthly maximum allowable and pumpable water is defined as:
APW = DVR* (FLO UPW)

subject to
Max (APW) = PUC
FLO UPW APW = MDR

where
APW = Monthly maximum allowable and pumpable water, in cfs
DVR = Diversion rate in percentage
FLO = Average monthly synthetic flow, in cfs
UPW = Average monthly upstream withdrawals, in cfs
PUC = Maximum pumping capacity, in cfs
MDR = Average monthly minimum downstream release, in cfs

-24-















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-25-.









In this study, the diversion rates of 5%, 10%, 15%, 25% and 50%, and the pumping
capacity of 20, 50, 100, 200 and 500 cfs are considered. The minimum downstream
release is equal to whatever is left from the river flow after diversion. The
product of the above computation (for one combination of one diversion rate
and one pumping capacity) is a trace of monthly maximum allowable and pumpable
water for that combination. The same procedure is repeated for 100 traces,
based on the same combination.

Offstream Reservoir Operations Routing Simulation

Each -of the 100 traces of monthly maximum allowable and pumpable water form one
combination of diversion rate and pumping capacity, as computed above, is routed
through an offstream reservoir system of known capacity, using an "offstream
reservoir operations routing simulation model," with the demand, i.e., yield, as
a trial value. The algorithmic calculations start with the reservoir at maximum
reservoir operational level and the reservoir storage is continuously adjusted
for evaporation loss and rainfall gain, loss due to seepage and gain from bank
storage being considered minimal. When a successful run through the entire
trace is accomplished within a tolerance of 5%, the trial value of demand is taken
as the yield for the trace and for that size of reservoir and pumping capacity.
Table B-7 lists the rainfall and evaporation rates over the reservoir area.

In this study, the reservoir sizes of 2500, 5000 and 16000 acre/feet are considered,
and the reservoir has an operational depth of 25 feet. As an example, Table B-8
lists the yields from 100 traces from a combination of 15% diversion rate and 100
cfs pumping capacity and for a reservoir of 5000 acre/feet.

COMPUTATION OF 95-PERCENT DEPENDABLE YIELD

For one combination diversion rate/pumping capacity/reservoir size, a frequency
analysis of the 100 yield values of that reservoir system is made based on
Weibull distribution:

Probability = n
N+1

Table B-9 shows yield versus probability for a 15% diversion rate/100 cfs
pumping capacity/5000 acre-feet reservoir system and from that table the 95%
dependable yield of that reservoir system is picked. The same yield versus
probability procedure is repeated for different combinations, and hence the
corresponding 95% dependable yield values are obtained.

Table B-10 and Figures B-1, B-2, B-3, B-4 and B-5 show the 95% dependable yield
values for different combinations of diversion rate/pumping capacity/reservoir
size.






-26-













TABLE B-7 LIST OF AVERAGE MONTHLY EVAPORATION AND RAINFALL
RATES IN INCHES OVER THE RESERVOIR AREA.





MONTH EVAPORATION RAINFALL
(INCHES) (INCHES)


JAN 2.40 2.68

FEB 3.00 2.87

MAR 4.20 3.65

APR 5.20 2.43

MAY 6.00 2.60

JUN 6.00 7.63

JUL 5.70 8.94

AUG 5.00 9.55

SEP 4.70 8.68

OCT 4.20 3.24

NOV 3.00 1.91

DEC 2.50 2.17

51.90 56.35











-27-







TABLE B-8 :LIST OF YIELD VALUES FROM 100 TRACES OF SYNTHESIZED
STREAMFLOW BASED ON LOG NORMAL DISTRIBUTION AND FOR
THE FOLLOWING COMBINATION :
SIZE OF RESERVOIR : 5,000 ACRErFEET
DIVERSION RATE: 15%
MAX PUMPING CAPACITY 100 CFS

TRACE YIELD TRACE YIELD
NUMBER ( MGD ) NUMBER ( MGD )

1 20.00 51 17.20
2 20.80 52 20.60
3 20.20 53 16.90
4 12.50 54 18.70
5 25.50 55 15.30
6 15.80 56 24.60
7 17.10 57 19.40
8 15.30 58 16.50
9 22.70 59 15.20
10 19.00 60 19.50
11 18.30 61 19.40
12 17.30 62 18.40
13 21.40 63 17.60
14 21.20 64 21.90
15 22.50 65 19.00
16 14.70 66 22.30
17 20.20 67 23.20
18 16.70 68 20.90
19 14.00 69 21.90
20 18.60 70 20.90
21 19.50 71 22.30
22 15.00 72 14.90
23 18.40 73 18.20
24 23.80 74 16.40
25 19.00 75 17.50
26 17.20 76 18.50
27 21.30 77 17.00
28 22.10 78 14.50
29 18.60 79 15.50
30 21.40 80 17.50
31 21.30 81 21.90
32 20.80 82 19.50
33 20.10 83 20.20
34 17.10 84 17.60
35 17.90 85 20.60
36 17.30 86 15.30
37 21.20 87 18.40
38 18.40 88 18.10
39 16.10 89 18.80
40 15.40 90 21.00
41 18.30 91 21.10
42 24.70 92 18.30
43 21.50 93 20.10
44 17.90 94 16.90
45 22.50 95 18.20
46 17.50 96 21.30
47 17.20 97 20.00
48 22.10 98 14.90
49 12.50 99 17.50
50 18.00 100 19.30
-28-







TABLE B-9 YIELD FREQUENCY ANALYSIS WEIBULL
BASED ON 100 YIELD VALUES LISTED ON TABLE B-8

EXCEEDANCE YIELD EXCEEDANCE YIELD
PROBABILITY ( MGD ) PROBABILITY ( MGD )

0.0099 25.50 0.5050 18.60
0.0198 24.70 0.5149 18.50
0.0297 24.60 0.5248 18.40
0.0396 23.80 0.5347 18.40
0.0495 23.20 0.5446 18.40
0.0594 22.70 0.5545 18.40
0.0693 22.50 0.5644 18.30
0.0792 22.50 0.5743 18.30
0.0891 22.30 0.5842 18.30
0.0990 22.30 0.5941 18.20
0.1089 22.10 0.6040 18.20
0.1188 22.10 0.6139 18.10
0.1287 21.90 0.6238 18.00
0.1386 21.90 0.6337 17.90
0.1485 21.90 0.6436 17.90
0.1584 21.50 0.6535 17.60
0.1683 21.40 0.6634 17.60
0.1782 21.40 0.6733 17.50
0.1881 21.30 0.6832 17.50
0.1980 21.30 0.6931 17.50
0.2079 21.30 0.7030 17.50
0.2178 21.20 0.7129 17.30
0.2277 21.20 0.7228 17.30
0.2376 21.10 0.7327 17.20
0.2475 21.00 0.7426 17.20
0.2574 20.90 0.7525 17.20
0.2673 20.90 0.7624 17.10
0.2772 20.80 0.7723 17.10
0.2871 20.80 0.7822 17.00
0.2970 20.60 0.7921 16.90
0.3069 20.60 0.8020 16.90
0.3168 20.20 0.8119 16.70
0.3267 20.20 0.8218 16.50
0.3366 20.20 0.8317 16.40
0.3465 20.10 0.8416 16.10
0.3564 20.10 0.8515 15.80
0.3663 20.00 0.8614 15.50
0.3762 20.00 -0.8713 15.40
0.3861 19.50 0.8812 15.30
0.3960 19.50 0.8911 15.30
0.4059 19.50 0.9010 15.30
0.4158 19.40 0.9109 15.20
0.4257 19.40 0.9208 15.00
0.4356 19.30 0.9307 14.90
0.4455 19.00 0.9406 14.90
0.4554 19.00 0.9505 14.70
0.4653 19.00 0.9604 14.50
0.4752 18.80 0.9703 14.00
0.4851 18.70 0.9802 12.50
0.4950 18.60 0.9901 12.50

-29-








TABLE B-10 :95 PERCENT DEPENDABLE YIELDS IN MGD OF A PEACE RIVER/
FORT OGDEN OFFSTREAM RESERVOIR SYSTEM OF DIFFERENT
STORAGE CAPACITIES AND UNDER VARIOUS DIVERSION RATES
& PUMPING CAPACITIES.

1.- RESERVOIR STORAGE CAPACITY : 2,500 ACRE-FEET *

PUMP : DIVERSION RATES FROM RIVER FLOW
(CFS) : 5.00% 10.00% 15.00% 25.00% 50.00%

20 : 6.00 8.20 10.10 10.90 11.10
50 : 6.00 8.30 10.30 13.40 17.10
100 : 6.00 8.30 10.30 13.40 17.10
200 : 6.00 8.30 10.30 13.40 17.10
500 : 6.00 8.30 10.30 13.40 17.10


2.- RESERVOIR STORAGE CAPACITY : 5,000 ACRE-FEET *

PUMP : DIVERSION RATES FROM RIVER FLOW
(CFS) : 5.00% 10.00% 15.00% 25.00% 50.00%

20 : 8.40 10.70 11.90 12.20 13.40
50 : 9.10 12.40 14.70 18.90 26.50
100 : 9.10 12.50 14.90 19.20 26.90
200 : 9.10 12.50 14.90 19.20 26.90
500 : 9.10 12.50 14.90 19.20 26.90


3.- RESERVOIR STORAGE CAPACITY : 16,000 ACRE-FEET *

PUMP : DIVERSION RATES FROM RIVER FLOW
(CFS) : 5.00% 10.00% 15.00% 25.00% 50.00%

20 11.00 13.00 14.00 15.20 16.30
50 15.70 22.00 25.20 26.60 27.10
100 : 16.50 23.70 28.20 32.70 35.80
200 16.50 23.70 28.90 35.50 41.20
500 : 16.50 23.70 28.90 35.50 41.20



THE YIELD VALUES ARE GRAPHICALLY PORTRAYED IN FIGURES B-l, B-2,
B-3, B-4 & B-5.






-30-








FIGURE B-1 : 95 PERCENT DEPENDABLE YIELDS IN MGD OF A PEACE RIVER/
FORT OGDEN OFFSTREAM RESERVOIR SYSTEM : 2,500 ACRE-FEET
CAPACITY ( 100 ACRES OF SURFACE AREA ) AND UNDER VARIOUS
DIVERSION RATES & PUMPING CAPACITIES.


i;ii i-i ii ii i i i ii i iiiil ii iii !iiil i, l;: ii, iii, I, i I '1 .i i '. i i t l i i i*

RESERVOIR STORAGE CAPACITY 2,500 ACRE-FEET



18
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20 50 1 O0 200 500


-31-








FIGURE B-2 : 95 PERCENT DEPENDABLE YIELDS IN MGD OF A PEACE RIVER/
FORT OGDEN OFFSTREAM RESERVOIR SYSTEM : 5,000 ACRE-FEET
CAPACITY ( 200 ACRES OF SURFACE AREA ) AND UNDER VARIOUS
DIVERSION RATES & PUMPING CAPACITIES.
I I I i i i i i Ii 1iiii iijiiiIIIIIIi iiii i iiiiiiiM I i i i iiiill--rir I
RESERVOIR STORAGE CAPACITY 5,000 ACRE-FEET I-

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PUMPING CAPACITIES IN CFS
-32-







FIGURE B-3 : 95 PERCENT DEPENDABLE YIELDS iN MGD OF A PEACE RIVER/
FORT OGDEN OFFSTREAM RESERVOIR SYSTEM : 16,000 ACRE-FEET
CAPACITY ( 640 ACRES OF SURFACE AREA ) AND UNDER VARIOUS
DIVERSION RATES & PUMPING CAPACITIES.

j li 111j1! j1 I jlll iiliiji i llidili i1i j lliiiltii^ l^^ il i i j 1 1 1 n i mlmiip :::::;
E RESERVOIR STORAGE CAPACITY : 16,000 ACRE-FEET
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-33-










FIGURE B-4 : 95 PERCENT DEPENDABLE YIELDS IN MGD OF A PEACE RIVER/
FORT OGDEN OFFSTREAM RESERVOIR SYSTEM : 50 CFS DIVERSION
PUMPING CAPACITY AND UNDER VARIOUS DIVERSION RATES &
RESERVOIR CAPACITIES.






DIVERSION PUMPING CAPACITY : 50 CFS

50 | .. .. 5. 0
i ~ i i i i [ t i i i i r z
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FIGURE B-5 : 95 PERCENT DEPENDABLE YIELDS IN MGD OF A PEACE RIVER/
FORT OGDEN OFFSTREAM RESERVOIR SYSTEM : 100 CFS DIVERSION
PUMPING CAPACITY AND UNDER VARIOUS DIVERSION RATES &
RESERVOIR CAPACITIES.






DIVERSION PUMPING CAPACITY : 100 CFS
50.0



400








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REE V I CAP CI E IN ',.i .....
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APPENDIX C

TRANSFER OF SURFACE WATER RECORDS
FROM ONE STREAM TO ANOTHER

When evaluating two or more streams in a study area, and at least one stream has
long-term data, it is possible to transfer this long-term data to the other
streams when it is needed.

In this study, the Peace River/Fort Ogden offstream reservoir system is assumed
to be located a few miles southwest of Fort Ogden, and has its intake structure
built just downstream from where Horse Creek enters the Peace River, 11 miles
downstream from the junction of Peace River and Joshua Creek, and about 15 miles
downstream from Arcadia.

The streamflow data available for the study is from the following stations
operated by the U.S.G.S.:

STATION NAME AREA PERIOD OF
NUMBER (SQ. MILES) RECORD

02296750 Peace River at Arcadia 1367 1932-1980 (1)
02297310 Horse Creek near Arcadia 218 1951-1980 (2)
02297100 Joshua Creek at Nocatee 132 1951-1980 (3)

(1) Listed on Table C-1
(2) Listed on Table C-2
(3) Listed on Table C-3

No flow data are available from Arcadia to Fort Ogden. It is conservative to
assume that the flow of Peace River at Fort Ogden to be the combined flows of
Peace River at Arcadia, Horse Creek near Arcadia and Joshua Creek at Nocatee,
the flow gain from additional drainage basin from these gages down to Fort Ogden
being considered minimal.

Tables C-1, C-2 and C-3 show that Peace River at Arcadia has the longest records
of 49 years from 1932 to 1980, both Horse Creek near Arcadia and Joshua Creek at
Nocatee have equally 30 years of records from 1951 to 1980.

Forty-nine year length is considered adequate. From this data a reasonable
long-term average can be obtained and the extreme ranges from wet to dry
conditions adequately appraised. Horse Creek near Arcadia and Joshua Creek
at Nocatee records need to be extended back to 1932 by transferring streamflow
data from Peace River at Arcadia, using a "transfer of surface water records
from one stream to another" scheme as described below.






-36-




























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'-39- ;c r ; I b~p h ;h j ;rn ~ odr~rra;6ac









Horse Creek near Arcadia Transfer

Average monthly discharges from 1951 to 1980 at "Horse Creek near Arcadia" are
plotted on log paper against concurrent average monthly discharges at "Peace
River at Arcadia," (i.e. discharges at "Peace River at Arcadia" are plotted along
the x-axis while discharges at "Horse Creek near Arcadia" along the y-axis).
This is done because we wish to estimate the discharge at Horse Creek for
a given discharge at "Peace River at Arcadia"; discharge at "Peace River at
Arcadia" is therefore the independent variable and discharge at "Horse Creek
near Arcadia" the dependent variable.

From Figure C-1 it is seen that there is a general relationship between the two
variables as separated from individual excursions of the data points. These
individual digressions away from the relationship occurred when one basin
received rainfall at a time when the other did not. By separating these side
excursions from the general relationship, a curve is drawn passing through the
generalized data.

The estimating or transfer equation is of the type log Y = log A + B log X,
and the constants log A and B are obtained by solving simultaneously the normal
equations:

I log Y = N log A + B. log X

II S(log X. log Y) = log A. E log X + B. o (log X)2

Table C-4 lists the equations used to transfer streamflow from "Peace River at
Arcadia" to "Horse Creek near Arcadia."

Joshua Creek at Nocatee Transfer

The same procedure, as described above and applied to "Horse Creek near Arcadia,"
is repeated for "Joshua Creek at Nocatee."

Figure C-2 shows the relation of average monthly discharge at "Joshua Creek at
Nocatee" over "Peace River at Arcadia."

Table C-5 lists the equations used to transfer streamflow from "Peace River at
Arcadia" to "Joshua Creek at Nocatee."

Peace River at Fort Ogden

Based on the above data transfer scheme, monthly discharges at "Peace River at
Fort Ogden" are compiled and listed on Table C-6. These monthly discharges will
be manipulated and used in the Peace River/Fort Ogden offstream reservoir Yield
Analysis.







-40-










FIGURE C- : RELATION OF AVERAGE MONTHLY FLOW IN CFS
"HORSE CREEK NEAR ARCADIA"/"PEACE RIVER AT ARCADIA"
( FROM 1951 TO 1980 )











+










+
S++.++


++
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-42-.










FIGURE C-2 : RELATION OF AVERAGE MONTHLY FLOW IN CFS
"JOSHUA CREEK AT NOCATEE"/"PEACE RIVER AT ARCADIA"
( FROM 1951 TO 1980 )








+ + + ++




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-43-

























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I-45-







VI. REFERENCES


Beard, L. R. "Monthly Streamflow Simulation," in Hydrologic Engineering
Methods for Water Resources Development, Vol. 2, Hydrologist Data Manage-
ment, U. S. Army Corps of Engineers, Hydrologic Engineering Center, 1972.

Croxton, F. E. and D. J. Cowden, "Applied General Statistics," Second Edition,
Prentice-Hall, Inc., 1960.

Fiering, M. B., "Streamflow Synthesis," Harvard University Press, Cambridge,
Mass., 1967.

Fiering, M. B. and B. B, Jackson, "Synthetic'Streamflows," American Geophysical
Union, Water Resources Monograph 1, 1971, pp. 1-38.

Hamming, R. W,, "Numerical Methods for Scientists and Engineers," McGraw Hill
Book Company, Inc., New York, 1962, pp. 34-389.

Kendall, M, G. and A. Stuart, "The Advanced Theory of Statistics," Harper
Publishing Company, New York, 1968.

Maass, A,, M. M. Hufschmidt, R. Dorfman, H. A, Thomas, Jr., S, A. Marglin
and G. M. Fair, "Design of Water Resource Systems," Harvard University
Press, Cambridge, Mass., 1970.

Matalas, N. C., "Mathematical Assessment of Synthetic Hydrology," Water
Resources Research, 1967, Vol. 3(4); 937-945.

Shih, S. F., "Synthetic Data Generator--A Joint Distribution Technique
(Technical Supplement)," Resource Planning Department, Central and
Southern Florida Flood Control District, Technical Publication No. 76-1,
February 1976.

Thomas, H. A., J. T. and M. B. Fiering, "Mathematical Synthesis of Streamflow
Sequence for the Analysis of River Basins by Simulation," Chapter 12 of
Design of Water Resources System, Harvard University Press, Cambridge,
Mass., 1962, pp. 459-493





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