Title: Instream Reservoir Yield Analysis: Lake Manatee Reservoir
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 Material Information
Title: Instream Reservoir Yield Analysis: Lake Manatee Reservoir
Alternate Title: SWFWMD. Instream Reservoir Yield Analysis: Lake Manatee Reservoir, by Hung T. Nguyen and Richard V. McLean
Physical Description: 60p.
Language: English
Creator: Nguyen, Hung T. ( Author )
McLean, Richard V. ( Author )
Publication Date: July `982
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Spatial Coverage: North America -- United States of America -- Florida
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General Note: Box 5, Folder 12 ( SF MINIMUM FLOWS AND LEVELS, Volumes 1 and 2 ), Item 13
Funding: Digitized by the Legal Technology Institute in the Levin College of Law at the University of Florida.
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Full Text










INSTREAM RESERVOIR YIELD ANALYSIS:

LAKE MANATEE RESERVOIR










Manasota Basin Board
Southwest Florida Water Management District



Mary Kumpe Chairman Ex-Officio
Gordon D. Hartman Vice Chairman
Michael Stuart Secretary
Berryman T. Longino Member
Randolph Snell Member
J. Lynn Harrison Member
John J. Whelan Member







Resource Management Department
Project Development and Management Section
Hung T. Nguyen
Richard V. -McLean


July 1982











INSTREAM RESERVOIR YIELD ANALYSIS:
LAKE MANATEE RESERVOIR


TABLE OF CONTENTS


Page


I. Executive Summary 1

II. Introduction 2

III. Method of Developing Yield Analysis 5

IV. Results 21

V. Conclusions and Recommendations 22

VI. Appendices 23

A. Analysis of Lake Manatee During Drought of 1981 23
B. Yield Analysis by Mathematical Simulation Model 29
C. Yield Analysis by Mass Curve 45


VII. References 56























i













ACKNOWLEDGEMENTS

The authors wish to thank the following for their review and comment on this
report:

Charlie Miller, Director, Resource Management
John Heuer, Hydrologist
Bruce Wirth, Hydrologist
Alison Adams, Environmental Engineer
Gary Comp, Biologist
Tricia Dooris, Supervisor, Environmental Section
Ken Jones, Project Hydrologist
Larry Lee, Sr. Project Hydrologist

































ii









LIST OF FIGURES

Page


1. Project Location Map 4

2. Factors Affecting Lake Yield 6

3. Reservoir Area and Capacity 7

4. Reservoir Stage versus Surface Area 8

5. Reservoir Stage versus Volume 9

6. Geologic Cross-Section at Dam 12

7. Relationship Between Lake and Surficial Aquifer 13

8. Stream Gage Stations 15




LIST OF TABLES


1. Past Yield Estimates 3

2. Data Sets Used in Simulation 18

3. Example Simulation 19

4. Yield in MGD 21
















iii










I. EXECUTIVE SUMMARY

Rapid urban development in coastal Manatee and Sarasota Counties caused those
counties to request water supply investigation assistance from the Southwest
Florida Water Management District (District). In response, the Manasota Basin
Board investigated numerous potential water supply sites in both Counties, and
initiated an analysis of a regional water supply system which directly lead to
the formation of the Peace River/Manasota Regional Water Supply Authority
(PR/MRWSA). Part of the regional system analysis involved determining the yield
of existing water supply sources. This report is an analysis of the yield of
the Lake Manatee Reservoir in Manatee County and it has two purposes: (1) To
develop a yield analysis of the lake based on the best available data, and
(2) To demonstrate the management and regulation use of simulation models in
evaluating the yield of instream reservoirs.

The model uses reservoir gains and losses plus any other constraints placed on
the system to determine a 95 percent dependable yield. Long-term synthetic flow
data were developed using actual flow data as a base and run through the simu-
lation model in 100, fifty-year traces. A yield estimate was obtained for each
trace. This was followed by a statistical analysis of the 100 yield simulations
to determine the 95 percent dependable yield. The mass curve method was also
used to verify the yield estimate. Other factors such as reservoir gains or
losses to the ground water system, and gains from agricultural discharge runoff
were also analyzed and used in the yield simulation. Factors such as the
potential requirement for water releases to maintain minimum flow are not
currently known, but should be added once they are determined.

It is emphasized that the yield estimate developed in this report is based on
hydrologic parameters, and that the actual yield also depends on the environmental
and other regulatory constraints which may be placed on the system. An analysis
of the potential environmental constraints is currently being performed by
Manatee County as required by the District's Consumptive Use Permits' stipulations.

Based on the analysis and with the reservoir intake structure set at 21 feet
above mean sea level (msl), the 95 percent dependable hydrologic yield was
estimated to be 37.8 million gallons per day (mgd). Major steps that could be
taken to improve the accuracy of the model include determination of: (1) accurate
reservoir bottom contours, (2) accurate flow at the dam, (3) the timing and
quantity of agricultural runoff into the reservoir, and (4) the downstream
release requirements. The report demonstrates the usefulness of the simulation
model in determining the safe yield and the impact of various existing or proposed
constraints on that yield.











-1-









II. INTRODUCTION

Lake Manatee (Figure 1) was constructed in the mid-60's by Manatee County, and
although other water sources are currently being investigated it is presently
the County's only operational source of potable water. The lake is used to meet
the water needs of approximately one quarter million people in Manatee and
Sarasota Counties, and as a result it is the source for the largest water
supply system in the Manasota area. -Since so many depend upon the lake for
their sole source of supply, it is imperative to understand how the lake functions
and to know its limits.

The Manasota Basin Board has been working with both Manatee and Sarasota Counties
on the investigation of new potable water sources. It has also been involved
with the establishment of the Peace River/Manasota Regional Water Supply Authority.
The Board and the local governments need to know the capacity of existing Manasota
supply facilities so they can properly evaluate the water situation and identify
possible future water supply actions.

The purpose of the report is not only to project the potential safe yield of the
lake, but also, and perhaps in the long run more importantly, to identify those
factors which should be analyzed in greater detail in order to obtain a more
reliable yield projection. The paper also demonstrates a simulation model that
can be very useful in the yield analysis. As can be seen on Table 1, past works
have produced yield estimates that vary from 16 to 50.5 million gallons per day
(mgd). The demand on the lake is increasing too rapidly for the decision makers
responsible for supplying water to feel comfortable with such a wide range of
yield figures. For this reason Manatee County is currently studying the reservoir
and its drainage basin to determine the safe yield of the system. It is hoped
that this report and its recommendations may be of some benefit in that endeavor
as well as in showing how the Lake Manatee system functions.





















-2-









TABLE 1: PAST LAKE MANATEE YIELD ANALYSIS.
Prepared by Southwest Florida Water Management District
Regulatory Staff.


Potential Reasoning Used in Calculating
Consultant Reservoir Yield the Yield

A. Russell & Axon 30 MGD *Continue with existing intake
(for Manatee Co.-1964) at 28' MSL
SNo apparent consideration for
environmental impacts

B. Geraghty & Miller 16 MGD &Maintains a "minimum flow" in
(for Corps of Engineers- the Manatee River
1977) Continue with existing intake
at 28' MSL

C. Ardaman & Associates 34.2 MGD oLower intake evaluation to
(for Estech (Swift)-1978) 21' MSL
'No apparent consideration for
environmental impacts
*Assumes existing conditions;
that is no phosphate mining
in the drainage basin and no
other reservoir system in
operation on the Manatee River

D. Ardaman & Associates 29 MGD *Considerations same as Item C
(for Estech (Swift)-1978) except continue with existing
intake at 28' MSL

E. Bromwell Engineering 50.5 MGD *Lower intake to 20' MSL
(for Manatee Co.-1980) oNo apparent consideration for
environmental impacts

F. Pullara, Bowen and Watson, 50 MGD *Set flow level at 60' MSL
Malcolm Pirnie (for Manatee
Co.-1958)

G. Southwest Florida Water 28.2 MGD *Consideration same as Item A
Management District-1981 except five-day incremental
average was used instead of
monthly averages

H. Southwest Florida Water 34 MGD *Considerations same as Item C
Management District-1981 except five-day incremental
average was used instead of
monthly averages

I. CH2M Hill (for SWFWMD-1981) 28 MGD *Consideration same as Item A

J. CH2M Hill (for SWFWMD-1981) 34 MGD .Consideration same as Item C


-3-















Figure 1: Location of Lake Manatee Reservoir




HILLSBOROUGH CO. i






S301

S PAIME^ ^ MANATEE CO.

\L r^^^ ^' r' LaLe Manatee 1
Ir Reservoir
SADENTON /








SARASOTA CO.
70
I












Manatee County




\0 5 N
scale in miles
'Q .f '
-4-








III. METHOD OF DEVELOPING YIELD ANALYSIS

As mentioned earlier, many reports have already been done to determine the
"safe" yield of Lake Manatee. As far as could be determined from a review of
those reports, this is the first to use a routing simulation model to predict
the yield. The simulation used in this report was developed by District staff
and allows the user to account for and balance all of the inflow and outflow
variables that affect the lake's yield through time and thus determine the yield
itself. It also allows the user to change variables singly or in groups in
order to determine what impact a new set of conditions may have on the yield.
This is very important and useful when studying the impacts of withdrawals,
augmentation and possible management requirements that may be placed on the
system.

The model is based-on the fact that all water that-flows into.the reservoir is
exactly balanced by water leaving the reservoir, (water is neither created nor
destroyed in the reservoir). Figure 2 depicts all major ways water moves into
or out of the reservoir and is the bais for the data sets which were developed
to run the routing simulation. Before further discussing the data and how it
was manipulated, the reader should be aware that thebaccuracyf_ much of.. the
existing- data .is questionable and data sets for new items such as possible
mandatory riverine and estuarine maintenance, releases -donot exist. However, it
is believed that the method used here gives as good a yield estimate as is
possible under existing conditions. It also allows thb determination ofthose
fators-which are the most crucial to improving the yield estimate so they can
be given priority in future data collection efforts. The data sets are sum-
imarized in the four following categories.

A. Facility Affects on Reservoir Yield

To say that reservoir storage capacity has a significant impact on the yield of
the system is somewhat of a understatement. Yet, there have been no recent
surveys to determine the storage capacity of the Lake Manatee Reservoir. The
original documents prepared in 1963 by Russel and Axon, Inc., pertaining to the
then proposed Rutland Reservoir, contained an evaluation of the stages and
related volumes and surface areas for that reservoir. The Rutland Reservoir was
constructed and is the present Lake Manatee. The information prepared by
Russel and Axon is used in this report and is shown in Figures 3, 4 and 5. The
routing simulation uses all three factors in the yield determinations. Storage
capacity has undoubtedly changed in the years since the reservoir Was constructed
through siltation and accumulations of organic particulate. This evaluation
does not adjust for the potential storage capacity reduction so the actual
storage capacity is possibly less than used here. If the sediment tends to move
toward the deeper parts of the lake, its impact on storage capacity would be
minimized because the intake structure is approximately 15 feet higher than the
reservoir's lowest point.

The second factor in the facility affects category deals with the operation of
the lake's control structures. Lake Manatee has an earthen dam with a clay
core. The current spillway capacity of the facility is not large enough to




-5-
























"Rainfall
Riverine and Estuarme Evaoration
Maintenance Release E rao

Wet Season
Spilway Release





-- charge Inflow

Industrial Water Supply Withdrawal
Agricultural Water Supply Withdrawal


Surfi and Artesian
Aquifer Contribution to or.
Recharge from the Reservoir




Public Water Supply Safe Yield

River Inflow




Figure 2: Factors which affect the public water supply yield of Lake Manatee














-6-










60

Reservoir Volume in Millions of Gallons

55

eservoir Area In Acres

50



45 -----



40



35



30



25


20 Figure 3.
20
LAKE MANATEE
Reservoir Area and Capacity
from: Ruwar & Axon, Inc.
15 Water Work* Proect-
1 Mantee Comuty, Florida
Project No. 6353-3

10



5




Reservoir Area in Acres: 500 1000 1500 2000 2500 3000 3500 4000
Reservoir Volume in
Millions of Gallons: 5000 10000 15000 20000 25000 30000 35000 40000


"-7-


























Figure 4: Lake Manatee stage/surface area curve expanded from Figure 3.


42


40





S36


J 34


32


30


28 ---
1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000

Surface Area in Acres














-8-





















Figure 5: Lake Manatee stage/volume curve expanded from Figure 3.


40


38


- 36


34


32


30


28
2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500
Volume in MUllions of Gallons















*g









release all of the water that flows into the reservoir during a major rainfall
event in its drainage basin. For this reason it is possible that during such an
event, even with the structure's existing gates fully opened, the water level in
the reservoir can still rise. If this were to happen and the water level in the
reservoir were too high, water could flow over the top of the dam. This water
would quickly erode and destroy the dam and thus release all the water in the
reservoir causing considerable downstream flooding and loss of a major public
water source.

Manatee County officials have long realized this potential problem and, at the
time of this report, use a wet season spillway release to protect the dam. At
the beginning of the wet season (usually in June), the operating level of the
reservoir is lowered to allow additional.storage in anticipation of any potential
major rainfall events. The County also has a sophisticated stream flow and
rainfall measuring system in the upper watershed which allows them to monitor
incoming water with sufficient lead time to allow emergency water releases to
further protect the dam. An additional spillway is being designed by the County
which will have a large emergency release capacity which will eliminate possible
loss of the dam in all but the most severe situations. While the protection of
the dam is necessary, lowering the operating level does pose a problem. What
happens if the "wet season" turns out not to be so wet? The answer is that the
reservoir level would be low at the beginning of the dry season, and the avail-
able water supply may not be enough to meet the demand. Thus, the safe yield of
the system is reduced by the necessity to protect the dam.

In this first run of the routing simulation, it was assumed the dam had a
permanent 40-foot operating level and could safely release any water in excess
of its storage capacity at that level. This was done with the thought that once
the emergency spillway is in place, 40 feet could possibly be the permanent
operating level. The model is designed so that this variable can be changed in
later runs, and be made to simulate actual management conditions and thus
better reflect the system's true yield. The water intake was run at three
different levels; 21, 24 and 28 feet. This was done to give a range of possible
yields.

A third facility factor is leakage around the gates of the existing spillway.
It is known that a small amount of water does leak around the gates, but the
amount of leakage is insignificant when compared-to the volumes of other factors
in the model. In running the simulation model there was assumed to be no
leakage. If data on leakage is collected in the future, it can be added to the
model to refine the yield estimate.












-10-









B. Ground Water Affects on Reservoir Yield

Theoretically, the amount of stored water in Lake Manatee can be positively or
negatively affected by both the surficial and artesian aquifer systems. Figure 6
is a general illustration of a cross-section of Lake Manatee at the dam. Thick
sands of the surficial aquifer overlay the secondary artesian aquifer which
starts at about 25 feet mean sea level (msl). Although the secondary system
does produce some water, it contains thick layers of clay so it is usually
considered a confining unit between the surficial and the Floridan aquifer
below. The actual amount of water the surficial or secondary aquifers either
contribute to or receive from the lake can be muted if a layer of low permea-
bility material has formed on the lake's bottom. Such a layer can act as a
semi-confining bed between the ground and surface water systems.
The artesian system will accept water from both the surficial aquifers and
surface water systems if its head pressure is lower than the head pressures of
those systems. It will contribute water to those systems if its pressure is
higher than theirs. However, the thick confining layer between the upper water
producing zone of the artesian system and the surficial and surface water water
systems would restrict the vertical movement of water in either direction. The
potentiometric surface of the secondary artesian aquifer in the Lake Manatee
area has been estimated to be about 50 feet msl (Seaburn & Robertson, 1979)
which is higher than the reservoir water level. But, this value may have
little significance because of the confining layer's influence. It has been
observed that even during heavy ground water withdrawal periods, the surficial
aquifer water level in the area does not drop. This supports the assumption
that the surficial aquifer/surface water system is effectively separated from
the artesian system in the Lake Manatee area. Confirmation of this awaits
testing of a recently constructed monitor well in the area.

The major ground water impact to reservoir storage thus appears to come from the
surficial aquifer. In theory, this aquifer should provide additional storage
capacity for the reservoir. Figure 7 illustrates the likely seasonal relation-
ship between the lake and the surficial aquifer. Since it is assumed that the
artesian aquifer has no significant impact on either the surficial aquifer or
the surface water body, they are analyzed in isolation. If no water was gained
or lost by surficial or the lake, ideally their water levels would become equal,
but since there are constant gains and losses of water, the relationship of the
two also constantly change.

During periods of little or no rainfall, decreasing stream flow and high water
usage from the lake, the reservoir is constantly dropping in relation to the
surficial aquifer. This causes the surficial to discharge water into the lake
since the water level in the lake is lower. The amount of discharge depends on
the aquifers transmissivity and the difference in water levels between the two.
The lake drops very slowly at current use rates, and thus one would expect a
fairly low but even discharge from the surficial.









-11-
















Figure 6: Generalized cross section at the dam on Lake Manatee




Feet MSL
65
65~ ..







WATER PRODUCING (sand and clay) D





25could act as semi-co g

5' Reservoir Bottom








CONFINING (sandy clay)
'.























SATER PRODUCING (sandy limestone)
S . .
I .
":'" "" ""Potential sediment laRDC- (d m
,".5 "- " -,-o,,-- act -- se-,-co------




































~-1 2-


















Figure 7: General relationship between Lake Manatee and the surficial aquifer











DRY SEASON: Reservoir dropping, FOLLOWING RAINFALL: Reservoir
surficial contributing water to rises quickly and contributes water to
reservoir the surficial aquifer which is rising
more slowly

SUr fFICIA
AQUFR Dam

WATER LEVEL

CoaCibutioor t tr'











SECONDAR Y ARTESIAN'(upper confining layer)














-13










During periods of moderate to heavy rainfall, increasing stream flow and low
water use, the reservoir rises in relation to the surficial. The rate of rise
can be substantially faster than the rate of fall as discussed above because of
the amount of water coming from the large drainage basin. When this occurs,
water flows from the lake into the surficial but at a higher rate than previ-
ously discussed since the transmissivity of the aquifer is unchanged and the
water level difference between the lake and the surficial is greater.

This discussion illustrates the complex relationship between the surficial
aquifer and the lake. They are constantly in flux depending on inflow and water
usage. The water available for use is not confined to the reservoir, but is a
combination of the lake. and surficial aquifer water. The amount of water which
flows neither direction is evaluated later under Agricultural Discharge
Inflow and in Appendix A.

C. Surface Water Affects

Flow of the Manatee River upstream of the dam has been monitored since 1939 by
the United States Geological Survey (USGS). As shown in Figure 8, the original
gage was established in April 1939, and was in operation until May 1966, and
monitored a drainage area of about 87 square miles or 71 percent of the 123
square mile Lake Manatee basin. This gage site was flooded by the creation of
Lake Manatee in 1966. A second gage, the one currently in operation, was
activated in May 1966, several miles upstream from the old gage site. It
monitors a drainage area of 65 square miles or 53 percent of the Lake Manatee
basin. There was essentially no overlap in data collection between the two
gages so no valid statistical relationship between the two could be developed.

In this report, surface water inflow to the lake was determined for all years
except 1966 by a drainage area method. The flow records for the old gage were
multiplied by a factor of 1.41 which represents a 41 percent increase in drainage
area from the old gage to the dam. The new gage values were multiplied by 1.89
to yield the flow at the dam. While this method allows the creation of a
continuous record of flow at the dam assumes that each square mile of drainage
basfn has the same runoff values as every other square mile, and that all
rainfall is equally distributed over the basin. In addition the age and
location of the two gages may fail to adequately account for land use changes
which affect surface water flow in the vicinity of the lake. Such changes as
increased intensive agricultural practices and the resulting increase in irri-
gation runoff around the lake are unaccounted using only stream flow data.

As mentioned above, USGS flow information for the year 1966 is split between the
two gage sites. In order to develop a complete flow record from 1939 to present,
transfer equations were developed which statistically compared 1939 through 1965
flow records from the Little Manatee River USGS gage (Figure 8) to the 1939 to
1965 old gage site on the Manatee River. Once the relationship of flow of the
Little Manatee to that in the Manatee was established, the 1966 Manatee flow at
the old gage was transferred from the Little Manatee flow of the same year and
then multiplied by 1.41 to give flow at the dam.


-14-











Figure 8: USGS stream gage stations


Little Manatee I
No 02300500
(19 present

SHILLSBOROUGH CO.
-! I





41 301 MANATEE CO.
AMETTO -Lake Ma ntee Dam Du


*L RADENTON

'1 Manatee old gage) 64
No. 02300000 Ma



Yi._j3 __
SARASOTA CO.

70






a






0 5 10






J15-









Once a total flow record had been produced, it was analyzed using the procedure
discussed in Appendix B to develop a synthetic flow record. This statistical
analysis of the actual flow allows the development of long-term synthetic flow
records which accurately simulated flows. This is a fairly new method, but is
widely used to project "safe yields" since it gives more reliable values than
the short-term actual flow data. The simulation uses 100 fifty-year traces as a
flow record for the lake. Once a gage has been installed at the dam and run for
a number of years, this same system can be used to expand that record.

Direct reservoir gain from or loss to the atmosphere is a second surface water
affect. The Manatee River gages represent only the relatively small surface
areas of a stream, and do not adequately address the massive evaporative loss
from or rainfall directly into the lake. The impact of these two factors was
accounted for in the simulation by applying monthly average rainfall and evapo-
ration factors to the surface area of the reservoir and then changing the
volume and surface area accordingly. The long-term average values for rainfall
and evaporation were used for this first run, but if better data is developed in
the future it can be applied to the simulation. The model could be further
improved if evapotranspiration (ET) were used in place of straight evaporatative
loss. This would include evaporation from the open water areas, and transpi-
ration losses in areas covered by hyacinths.

Agricultural discharge inflow to Lake Manatee is a third factor, and occurs
during heavy irrigation periods. The actual amount of water contributed to the
lake is unknown, but flows in the millions of gallons per day have been reported.
Such inflows could have a significant impact on the yield of the lake if they
are sustained for long enough periods of time. In fact, there has been serious
discussion in the past of using the agricultural wells around the lake as an
emergency back-up water supply during drought periods.

While few irrigation inflow values exist, the drought of 1981 offered the
opportunity to perform a short-term water balance analysis on the lake with
fairly good data. Changes in the balance that could not be accounted for by
known factors were attributed to unknown factors such as irrigation inflow, gain
from or loss to the ground water system, some unknown withdrawal, or to inaccu-
racies in the collection of available data. One of the most important of the
findings was that the reservoir gained approximately 4.5 mgd during the 1981
drought period (See Appendix A). Detailed analysis could not specifically
identify the source of the gain, however it is probably attributable to a
combination of inflow from the surficial aquifer and agricultural discharge.
This data, although not used in the simulation, was added to the projected safe
yield derived from the model. When better data are obtained they will be added
to the simulation to improve the accuracy of the yield projection.

D. Other Water Demands' Affect on Reservoir Yield

Lake Manatee and its watershed are often viewed as being used exclusively for
public water supply, however, there are other legitimate users. There are many
agricultural water users in the area, but most of them use deep ground water and
thus probably have little negative impact on the public water supply yield of



-16-








the lake. In fact, they do have a positive impact during the dry season since
agricultural discharge does flow into the lake and augments public supply to
some extent. There is one permitted agricultural withdrawal from Lake Manatee,
but it is not very large and peaks at .47 mgd and averages .02 mgd.

Manatee River water is also used for industrial purposes. At present only the
phosphate industry uses the Manatee directly. The County sells about 1.4 mgd of
raw water to the AMAX Piney Point Chemical Plant, but a large part of the Lake
Manatee drainage basin is owned by phosphate companies. Currently, only one has
a Consumptive Use Permit (CUP) for a surface water withdrawal. Estech's permit
allows an average withdrawal of 6.5 mgd and a peak of 9.4 mgd. Other phosphate
companies in the area may someday also apply to use surface water. There is
another aspect of mining activities which impacts the lake. As the phosphate
companies mine the watershed they severely disrupt the surficial aquifer. The
base flow of the river appears to be maintained by surficial aquifer discharge.
Large slime settling ponds would reduce surficial storage, and the mine's
water recirculation system's would increase storage. Manatee County is currently
evaluating this impact, and when data is available it can be entered into the
model.

The final user discussed here is the natural system. At present, there is no
minimum downstream release required of Lake Manatee, but the current CUP may
requires an evaluation of the need for and potential timing of riverine and
estuarine maintenance release from the reservoir to maintain the vitality of
those systems in the Manatee River downstream from the dam. Once this info-r-
mation is developed, the results will be considered during CUP renewal.

This run of the routing simulation does not include values for known additions
or withdrawals, but they were subtracted from or added to the simulated yield
estimate to produce a final yield estimate. The value for any required down-
stream release should be added to the simulation when it is developed. Table 1
summarizes all of the potential data sets and shows what action was taken on
each for this run of the model. The data sets discussed in Table 2 are used in
the model in the following manner.





















-17-














TABLE 2: DATA SETS USED IN THE ROUTING SIMULATION







O
-J 3
0


CD -- --


"" O* M 0 "- a E
a) U ao (0 0 2
i-- 0 M ."= S w .-

(0 ) S. 3 +S
)- O; rd P 0 t'-- rw S "
Da D lopd ad Ud C a a
2. Sepa e Q y Va S ue




Added to Simulated Yield 0
03. Separate Quantity Value0 C S S
*- 0 a) 4.) 0 > 0( S. .. -o +4
4. F ctors C Whii (.: L: ACTION

1. Data Developed and Used x

"E .... .... ........
as Part of the Simulation

2. Separate Quantity Value
Developed Which can bet t
Added to Simulated Yield |

3. Separate Quantity Value
Developed Which can be Subfor this report, but their combined impact was
traced from Simulated


4. Factors Which will Affect18


















-18-









TABLE 3: EXAMPLE OF HOW THE YIELD SIMULATION WORKS


F DO Fl El R1 Dl V1 D2 T2 Sl Al
(CFS) (CFS) (CFS) (AFT) (AFT) (AFT) (AFT) (AFT) (CFS) (FT) (AC)

Partial Model Run As An Example

17.51 45.00 9.30 896.88 1139.04 -2510.93 20507.07 0.00 0.00 38.36 1685.92

30.09 45.00 9.30 800.81 1256.01 -3496.34 19521.66 0.00 0.00 37.72 1631.34

138.30 45.00 9.30 677.01 1296.92 0.00 23018.00 2121.68 35.66 40.00 1825.00

201.31 45.00 9.30 711.75 1323.13 0.00 23018.00 9359.12 157.28 40.00 1825.00

Where:

F (CFS) = River Inflow in Cubic Feet Per Second (CFS).

DO (CFS) = Demand (Yield) in CFS.

Fl (CFS) = Upstream Withdrawals in CFS.

El (AFT) = Evaporation in Acre Feet (AFT).

R1 (AFT) = Rainfall in AFT.

D1 (AFT) = Reservoir Volume Deficit in AFT.

Vl (AFT) = Reservoir Volume at the End of the Period in AFT.

D2 (AFT) = Discharge at the Dam in AFT.

T2 (CFS) = Discharge at the Dam in CFS. -

S1 (FT) = Reservoir Stage at the End of the Period in Feet (FT).

Al (AC) = Reservoir Surface Area at the End of the Period in Acres (AC).









-19-











The model run starts with the reservoir set at whatever stage the user desires.
In this case it was assumed the reservoir was full (40 feet msl). The run
started with October, which is the beginning of the water year. The demand
variable (DO) is then set at a level chosen by the user, and the run is started.
First, reservoir storage losses (DO, Fl, El) are compared to gains in storage
(F, R1). If losses exceed gains, the losses, which represent a deficit in
storage, are tallied and recorded under D1, and the amount of water stored in
the reservoir is adjusted appropriately in Vl. If gaines exceed losses, the
additional water is added to the amount in storage in VI. If the gain in
storage exceeds reservoir storage capacity, or if the reservoir is already full,
the excess water is recorded as discharge in both D2 and T2. After adjusting
for either a gain or a loss, the volume of water in storage is additionally
represented as stage height (Sl) and surface area (Al). This entire computation
is done for each monthly flow period. The resulting storage volume, stage and
surface area for each monthly period is used in the calculation of yield for the
next month. Evaporation out of and rainfall into the reservoir are calculated
using the surface area as a result of the previous month's changes.

During the yield analysis the computer automatically raises or lowers the demand
variable (DO) until a yield for each of the synthetic flow traces is obtained.
Each trace was run independently so 100 yield estimates were developed. The 100
yield values are then arranged numerically from the highest to the lowest and a
statistical frequency analysis is performed to determine yield probabilities.
For comparative purposes a yield analysis using the standard mass curve tech-
nique is also done. Detailed discussions of both methods are included in
Appendices B and C.
























-20-








IV. RESULTS

Table 4 shows the results of both the simulation model and the mass curve yield
analyses for Lake Manatee with the water intake set at three different levels.
Three levels are shown because at the time this report was being written,
Manatee County was modifying its facilities including lowering the water intake
level. The new structure is complete and is at approximately 21 feet msl.



TABLE 4: YIELD IN MGD WITH A 95 PERCENT EXCEEDANCE PROBABILITY
28' MSL 24' MSL 21' MSL

Simulation Model 27.4 31.6 33.3
Mass Curve 27.6 31.6 33.5


As discussed in the previous section, there are many factors which affect
reservoir yield for which values are either unknown or are.only estimated at
this time. Factors such as the operation schedule, leakage around the gates and
natural system water needs are not included in this run of the model, but
definitely affect the ultimate yield. Once values for these factors are known
they can be incorporated into the simulation to improve the yield projection.

Combined agricultural discharge inflow and ground water affect were calculated
to add approximately a 4.5 mgd to the reservoir during the 1981 spring drought.
Currently planned industrial water demands other than those supplied by the
County would have little impact on the yield of the reservoir since the planned
diversion is to be regulated by a fixed crest weir which allows water to be
diverted only during high flow periods. Thus, if the Lake Manatee intake
structure is assumed to be at 21 feet msl, and 4T5 mgd is added, the projected
yield is 37T8 mgd witFTa"h 5 percent exceedance probabilTty. The reader is
reminded that this projection does not include values for riverine and estuarine
maintenance release. When such values are developed and implemented they could
lower the projected yield.












-21-








V. CONCLUSIONS AND RECOMMENDATIONS

Conclusions

1. Presently, Lake Manatee is the only source of supply for about one-quarter
million people in the Manasota Basin and thus an accurate determination of its
dependable yield is essential.

2. The existing data base for use in determining the lake's safe yield is
sufficient for a general analysis only. Better data collection is required to
improve the yield analysis.

3. The 1981 spring drought allowed a reasonable determination of the combined
affect of several unknown variables on the yield of Lake Manatee during drought
periods.

4. The computer simulation model and synthetic flow data offer a valuable and
flexible tool for analyzing potential yields of instream surface water supply
systems.

5. Based on the analysis and assumptions stated in this report with the 95
percent dependable yield of the reservoir is 37.8 mgd.

6. Regulatory constraints, when determined, should be added to the simulation
to refine the yield projection.

Recommendations

1. Conduct a morphometric survey to determine the present storage capacity of
the reservoir. Develop a new and accurate stage-volume-surface area graph from
this information.

2. Incorporate the reservoir operating schedule into the simulation model
including any required natural system maintenance releases.

3. Determine the leakage around the water control gates of the dam under
varying reservoir stages and incorporate into the simulation.

4. Develop an accurate set of synthetic river flow data using the following
procedure:

A. Record daily reservoir releases and the amounts of water withdrawn
at the dam.
B. Develop a monthly factor for use in transferring flow records from
the existing Manatee River USGS gage to the dam. This factor would account
for all unknown variables in inflow and diversion.
C. Establish the statistical relationship between the downstream gage
on the Little Manatee River (1939-Present) and the old gage on the
Manatee River in order to use transfer data to create a long-term flow
record at the dam.
D. Use synthetic flow data to develop a long-term flow record at the dam.

5. Develop an emergency spillway so that more water can be stored during the
wet season.
r22-









VI. APPENDICES

APPENDIX A

ANALYSIS OF LAKE MANATEE DURING THE DROUGHT OF 1981

The drought of 1981 presented an excellent opportunity to evaluate the combined
impact of certain unaccountable factors which affect the yield of the Lake
Manatee Reservoir. The following equation was used in this determation:

VC VP EVAP + RAIN + INFL + UV = 0
Where:

VC = Change in the volume of water stored in the reservoir.

VP = Amount of water pumped from the reservoir.

EVAP = Evaporative loss from the reservoir.

RAIN = Rainfall directly into the reservoir.

INFL = Surface water inflow to the reservoir via the Manatee River.

UV = Unaccounted volume affect which includes any unknown gains
to or losses from the reservoir.

The equation can be rewritten as:
UV = VP VC + EVAP RAIN INFL

and solved for UV. Table A-1 shows the calculations of UV for 12 time intervals
from April 1 through June 21, 1981. Figure A-1 is a graphical depiction of the
average daily values of the same information and is useful in analyzing the
interrelationship of the various factors.

The average volume pumped (VP) ranged from 37.5 mgd to 29.1 mgd, but remained at
about 35 mgd until rainfall and inflow increased in late May at which time it
dropped to around 30 mgd. However, it appears that as the rain slowed in mid-
June, the volume pumped began to increase again. The records for VP are of
excellent quality and represent the quantity of water withdrawn from Lake
Manatee by the county for public supply and for a nearby phosphate processing
plant.

The values for the average evaporative loss (EVAP) are of fair quality and were
obtained by comparing the evaporation measured at the Bradenton Agricultural
Research and Education Center to the surface area of Lake Manatee. The Bradenton
values were used because at the time of the analysis there was no evaporation
pan at Lake Manatee. Surface areas acres were obtained from Figure 4. EVAP
ranged from about 8.5 mgd to 6.3 mgd and totaled 600 million gallons during the
study period.







-23-








TABLE A-i: CALCULATIONS OF THE UNACCOUNTED VOLUME AFFECT (UV)
IN MILLION GALLONS


NO.
INTERVAL DAYS VP1 VC2 + EVAP3 RAIN4 INFLOW5 = UV

4/01-4/07 7 235.1 212.5 52.7 1.4 35.2 38.7

4/08-4/14 7 264.5 275.0 53.1 0 24.8 17.8

4/15-4/21 7 243.6 240.0 55.9 0 17.8 41.7

4/22-4/28 7 242.7 300.0 47.1 0 16.8 -27.0

4/29-5/05 7 246.8 240.0 59.2 0 13.2 52.8

5/06-5/12 7 242.7 195.0 49.5 16.2 11.2 69.8

5/13-5/19 7 259.3 325.0 52.7 0 7.0 -20.0

5/20-5/26 7 238.8 375.0 57.7 4.6 6.8 -89.9

5/27-5/31 5 149.6 100.0 31.9 53.7 113.8 -86.0

6/01-6/07 7 203.8 0.0 45.9 136.7 154.8 -41.8

6/08-6/14 7 214.7 145.0 43.7 1.8 172.0 -60.4

6/15-6/21 7 229.8 195.0 51.2 24.7 46.9 14.4

Total 82 2771.4 2602.5 600.6 239.1 620.3 -89.9

Per Day Total 33.8 31.7 7.3 2.9 7.6 -1.1



1Furnished by MCUD.

2Reservoir level furnished by MCUD, volume obtained from stage-volume curve.

3Evaporation pan readings at the Bradenton Agricultural Research Station
times lake surface.

4Rainfall reading by MCUD times lake surface.

5USGS Manatee gauge time 1.89 drainage area factor.



-24-















Figure A-1: Plot of average daily values of information shown on Table A-1.


60












(Ee \ Volsme Defir20

Miion Gallons Per 4Day ---j
(Excpt Reserwoir Stay 20 -A
which is in Feet MSL)


10


^\---- / \ // --T7\-- -If




-10 / %
%I





4/7 4/14 4/21 4/28 5/5 5/12 5/19 5/26 5/31 6/7 6/14 6/21
Inremments Analyzed During 1981 Drought (April 1- June 21)










-25--
0/ ..... "-2 _.,: 51 ---'=. , 5/ 5/t Voh nw14
,,/mmt ..cid D~n 8 rog~(pi ]n 2





".. "....... _"









Rainfall directly into the lake (RAIN) was essentially zero during the first
half of the study period, but substantially increased during the final weeks.
Stream inflow (INFLOW) showed a slow but continuous decline during the period of
no rainfall, but increased rapidly as the rains began. The rain records are
fair. They were obtained by comparing the excellent rainfall records collected
at the dam by Manatee County Utility Department (MCUD) personnel to the lake's
surface area obtained from Figure 4. INFLOW records were developed by multi-
plying the stream flow at the USGS gauge by a 1.89 area increase factor. The
inflow data seems to be fair relative to rainfall, but the actual quantity is
unknown because it is obtained by using actual upstream flow measurements multi-
plied by an area factor. Since a single factor is used, it has a constant
affect on the analysis. For example, if a higher factor had been used, the
variations in the unaccounted volume affect would not change, but that entire
line on the graph would be moved upward. It is felt that the 1.89 factor is a
good general factor to use. In an earlier yield analysis (Bromwell, 1980), a
higher factor than those produced using the area method was used. However, that
factor accounted for many variables which are considered separately here.
Including more variables within the factor necessitates the use of a higher
factor. Since variables such as rainfall and evaporation are considered sepa-
rately in this report, it is felt the 1.89 factor is usable.

The volume change (VC) was obtained by comparing the lake stage as recorded by
MCUD personnel with Figure 5, the reservoir stage/volume curve. This is a very
sensitive factor in the analysis because the change in volume reflects the
impacts of all the known variables plus the unknown variables. Without the
change in volume, the value of the unknown variables could not be determined.
The stage/volume curve is generally accurate since the river basin in the area
of the reservoir in deeply incised (for Florida) and probably had a fairly
easily contoured slope. However, the original graph (Figure 3) was general, and
the best accuracy one can expect is probably plus or minus 10 million gallons.
Reading of the lake stage is critical. For example, a tenth of an inch between
38' msl and 37.9' msl equals approximately 60 million gallons of water in the
lake. For at least part of the study period, lake level readings were taken
from an exposed staff gauge. Wave action can make readings from such an instru-
ment within an accuracy of an inch difficult and impossible to the tenth of an
inch. VC is the most important of the "known" values, and is probably the least
accurate in this analysis. Large changes in the VC curve without a similar
change in any other "known" variable curves can be attributed to two factors:
(1) inaccuracies in the known data and (2) an unaccounted volume factor (UV)
such as flows to or from the surficial aquifer and agricultural discharge
inflows.

A point by point analysis of the major jumps in the VC curve is useful in the
overall analysis. There appears to be nothing unusual in the May 7 through
May 21 curves, but on May 28 something has happened. During that period, the
reservoir lost 8 mgd (56 million gallons), but pumpage, evaporation, inflow and
rainfall all remained relatively unchanged from before. The UV curve shows that




-26-










the reservoir lost the water to an unknown source. Similar reservoir losses
were recorded during the May 19 and 26 periods. An unaccounted reservoir gain
took place during the May 21 period with similar unchanged conditions in the
other known variables.

It is unlikely that a withdrawal by some unknown user of the magnitude required
to produce the indicated deficits would have escaped detection. It is also
unlikely that water from the reservoir would recharge the surficial aquifer when
the lake stage is steadily dropping, in fact the reverse should be true. There
were no releases through the dam, and any possible leakage through the dam would
be constant and small. For these and the reasons discussed above, it is probable
that the readings could not be taken accurately enough to reflect actual reservoir
conditions.

For this reason, all but the most general conclusions are inappropriate, but
conclusions can be drawn. Although the VC and UV curves fluctuate, there is a
point at which a definite change takes place. During the time when there is no
rainfall and decreasing inflow, the unaccounted volume is almost always positive,
and the time it is negative (April 28) is questionable. When the rains start,
the UV curve becomes negative, and as the rains decrease it moves back toward
the positive.

This demonstrates that during drought periods, when there is heavy demand on the
reservoir and its level is dropping, it receives an unaccounted contribution.
This is probably from either the surficial aquifer or agricultural runoff. If
the values from Table A-1 are used to calculate this contribution when these
circumstances existed (April 7 through May 12), the total is 193 million gallons
over 42 days, or a 4.6 mgd gain. Using this longer period, the variations in
the VC curve tend to cancel one another, so the value is probably close to
correct. It is also possible to check this figure.

River flow at the USGS gauge during this time period amounted to 96.6 million
gallons over 42 days, or 2.3 mgd. This is probably base flow since it had not
rained for about two months and there is little agriculture in the upper Manatee
basin. If an area ratio is used, this equates to 4.3 mgd at the dam, which is
close to the 4.6 mgd gained calculated above.

If a similar analysis is done for the time when the reservoir was gaining water
and demand had decreased, the total is 9.0 mgd. This is logical since a reser-
voir will lose water to the surficial aquifer faster than it gained it because
the head gradients are larger following a substantial rainfall than they are as
the reservoir slowly drops during a drought.







-27-










Conclusions


1. There is a need for accurate reservoir stage-volume and stage-surface area
curves.

2. There is a need for an accurate reservoir stage determination method.

3. The 1.89 area factor used to obtain flows is generally useful, but more
accurate factors (by month) can be developed when flow at the dam and
storage changes are accurately known.

4. The analysis indicates that during drought periods similar to the one
experienced in 1981, the reservoir will probably gain about 4.5 mgd from
bank storage.

5. Following substantial rainfall in the basin, the lake will recharge the
surficial aquifer for a short period.

6. If this analysis were computerized and run continuously with improved
data, the function of the reservoir and its relationship to the drainage
basin could become well understood.




























-28-









APPENDIX B


SAFE YIELD ANALYSIS
BY MATHEMATICAL SIMULATION MODEL

PART I: GENERAL METHODOLOGY FOR ESTIMATING INSTREAM RESERVOIR YIELD

This appendix describes the general methodology used in the determination of the
95 percent dependable yield of Manatee River instream reservoir. The end
product of the methodology is an understanding of the operational behavior of
the reservoir, so that an optimization of the water supply system under various
constraints such as regulatory downstream minimum flow release, operational
maximum reservoir storage level, operational intake level, upstream withdrawal,
water conservation measures during drought, etc., to meet water requirements in
the area, 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 dam 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) route
each set of synthetic data through the reservoir to determine the average yield
of the reservoir; and (4) construct a yield versus probability relationship to
interpret the 95 percent dependable yield.

Compilation of Streamflow Data

Streamflow records at the location where an instream reservoir system would be
built, need to be compiled. The records need to be as long as possible, so a
reasonable long-term average could then be 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 planning,
design, management and simulation of water resource systems. The synthetic 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.

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).






-29-










The following equation represents this autoregressive model for unit time
intervals of months.

i+1 = Qj+l + bj(Qi-Qj) + tij+1 (l-r2) (1)

Where:

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

Qj and Qi+l Mean monthly flows during jth and (j+l)th month
respectively within a repetitive annual cycle of
12 months.

bj Regression coefficient for estimating flow in the
(j+i)th month from the jth month.

i = Random normal deviate with zero mean and unit
variance.

Sj+l = Standard deviation of flows in the (j+l)th month.
rj Correlation coefficient 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+l)th month is composed of a component linearly related to that in the ith
month and a random additive 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
and operation 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 portions:
1. First, the historical data is analyzed by statistical methods and the
parameters of mean, standards deviation, correlation and regression for
each time period are calculated, based on each of the four probability
functions considered.
2. Second, the generated sequences of monthly flows for each distribution and
based on equation (1), are compared to the historical data by using the
Chi-Square test for goodness-of-fit, in order to choose the best fit
Distribution.
-30-









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 require-
ment 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 monthly values of available water, defined as:

AW = (IN LE + LR.- UW DR SE + BS), in cfs

Where:

AW = Monthly available water, in cfs
IN = Monthly synthetic inflow, in cfs
LE = Average monthly lake evaporation, in cfs
LR = Average monthly rainfall over lake, in cfs
UW = Average monthly upstream withdrawal, in cfs
DR = Average monthly minimum downstream release, in cfs
SE = Average monthly seepage to groundwater system, in cfs
BS = Average monthly bank storage, in cfs

2. The second component of the model is an instream reservoir operations
routing simulation that computes the yield from the 50 years of monthly
available 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 available water. When a deficiency occurs,
the difference is made up from the active reservoir storage, i.e. the
storage accounted for between the maximum operational reservoir level and
the intake level. This procedure is continuously applied to each month of
the trace and the reservoir storage (or the reservoir stage) is continu-
ously monitored. If the storage stage drops below the intake level the
trial value of demand is high and is therefore 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 determined 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.



-31-









PART II: APPLICATION

COMPILATION OF STREAMFLOW DATA

Forty (40) years of streamflow records (from 1940 to 1979) are compiled and
listed on Table BI. The compilation of these records is discussed in detail in
Section 2.

SYNTHETIC FLOW GENERATOR MODEL

Statistical Parameters Computation

The parameters of mean, standard deviation, correlation and regression are
computed from the forty 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 B2 and B3.

Chi-Square Test for Goodness-of-Fit

The generated sequences of monthly flows of 50, 100, 250 and 400 years length
and for each of the considered distributions are compared to the historical data
by using the Chi-square test for goodness-of-fit. The Chi-square values are
listed on Tables B4 and B5.

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 frequency distribution.
One or two asterisks indicate the 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 as a symbol
">", is log normal distribution> square root normal distribution
>cubic root normal distribution> normal distribution.

Synthetic Flow Generation

Table B6 lists a sample of synthetically generated flow sequence for one trace,
using equation:

Qi+l = Qj+1 + bj(Qi-Qj) + tiSj+l (1-rj2)
and based on log normal distribution.

The same procedure is repeated for 100 traces.


-32-








OPERATIONS ROUTING SIMULATION MODEL

Computation of Monthly Average Available Water

The monthly average available water is defined as:

AW = (IN LE + LR UW DR SE + BS) in cfs

Where:

AW = monthly available water, in cfs
IN = monthly synthetic inflow, in cfs
LE = average monthly lake evaporation, in cfs
LR = average monthly rainfall over lake, in cfs
UW = average monthly upstream withdrawal, in cfs
DR = average monthly minimum downstream release, in cfs
SE = average monthly seepage to groundwater system, in cfs
BS = average monthly bank storage, in cfs

Table B7 lists monthly average lake evaporation and monthly average rainfall at
Lake Manatee. Monthly average upstream withdrawal, monthly average minimum
downstream release, monthly average seepage to groundwater system and monthly
average bank storage recharge or discharge are taken equal to zero (see discussion
in Section ).

The product of the above computation is a trace of monthly average available
water. The same procedure is repeated for 100 traces.

Instream Reservoir Operations Routing Simulation

Each of the 100 traces of monthly average available water, as computed above, is
routed through the lake, using an instream reservoir operations routing simulation
model, with the demand, i.e. yield, as a trial value. When a successful run
through the entire trace is accomplished within a tolerance of 5 percent, the
trial value of demand is taken as the yield for the trace.

In this study, the simulation was run for three different intake levels: 28
feet, 24 feet and 21 feet above MSL. The maximum operational reservoir level
was 40 feet above MSL.

- Table B8 lists the yield values of the reservoir with intake level
at 28 feet above MSL.
- Table B9 lists the yield values of the reservoir with intake level
at 24 feet above MSL.
- Table B10 lists the yield values of the reservoir with intake level
at 21 feet above MSL.

COMPUTATION OF 95 PERCENT DEPENDABLE YIELD

A frequency analysis of these 100 yield values of the reservoir at each intake
level is made based on Weiball distribution (probability= n/N+1).

Tables Bll, B12 and B13 show yield versus probability of the reservoir at
intake levels 28 feet, 24 feet, and 21 feet above MSL respectively.

-33-

























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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 134.97 4.55 10.20 1.89 152.37 1.69 5.64 0.49
NOV 45.91 3.19 5.96 1.44 56.24 1.13 3.26 0.45
DEC 46.26 3.29 6.15 1.50 49.64 1.00 2.93 0.36
JAN 77.24 3.72 7.57 1.62 94.49 1.46 4.52 0.48
FEB 85.61 3.92 8.13 1.70 89.47 1.44 4.47 0.48
MAR 96.62 3.85 8.11 1.63 129.86 1.77 5.62 0.58
APR 35.89 2.85 5.10 1.26 43.79 1.19 3.18 0.55
MAY 27.62 2.57 4.37 1.13 41.62 1.10 2.96 0.49
JUN 134.00 4.52 10.14 1.86 142.14 1.75 5.66 0.55
JUL 282.96 5.96 15.14 2.25 261.66 1.99 7.43 0.45
AUG 370.50 6.81 18.18 2.46 236.74 1.68 6.41 0.36
SEP 381.38 6.69 17.89 2.41 319.99 2.03 7.94 0.42




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

CORRELATION REGRESSION
MONTH :...............M---------------------------------ao:
SND CD SD LD ND CD SD LD


OCT 0.25 0.50 0.45 0.58 0.53 0.61 0.63 0.49
NOV 0.33 0.46 0.43 0.51 0.89 0.69 0.75 0.56
DEC 0.57 0.59 0.59 0.58 0.65 0.67 0.66 0.71
JAN 0.48 0.65 0.62 0.70 0.25 0.45 0.40 0.53
FEB 0.39 0.56 0.52 0.62 0.42 0.57 0.53 0.63
MAR 0.21 0.45 0.39 0.56 : 0.15 0.37 0.31 0.46
APR 0.53 0.56 0.54 0.62 : 0.57 0.83 0.95 0.65 :
MAY 0.27 0.41 0.37 0.50 : 0.28 0.45 0.40 0.56 :
JUN 0.19 0.11 0.14 0.04 0.05 0.07 0.07 0.03 :
JUL 0.47 0.48 0.49 0.41 : 0.26 0.42 0.38 0.50 :
AUG 0.30 0.32 0.32 0.30 : 0.33 0.38 0.37 0.38 :
SEP 0.45 0.46 0.46 0.44 : 0.33 0.38 0.37 0.38 :


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

-35-









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

ND CD SD LD ND CD SD LD

OCT 38.3** 15.0* 24.0** 6.6 31.0** 10.4 11.0 4.8
NOV 75.2** 24.8** 24.0** 5.6 83.3** 17.7* 22.9** 6.8
DEC 40.6** 26.3** 31.2** 3.8 47.8** 15.9* 16.7* 6.6
JAN 20.3** 16.1* 14.5* 16.7* 21.7** 12.8 16.2* 11.8
FEB 34.2** 19.6** 19.9** 27.8** 25.3** 22.1** 25.7** 17.2*
MAR 26.3** 12.2 15.3* 19.9** 27.4** 8.6 11.0 2.5
APR 81.8** 18.4* 10.4 8.4 90.7** 9.6 11.8 2.9
MAY 36.8** 21.4** 13.2 9.6 46.4** 20.5** 17.2* 15.4*
JUN 15.3* 12.5 15.5* 10.4 20.2** 4.9 4.7 16.1*
JUL 11.7 15.8* 17.1* 8.6 8.9 3.1 7.6 2.6
AUG 12.5 4.5 6.1 1.7 4.3 2.3 2.9 7.4
SEP 30.6** 19.6** 21.9** 11.7 36.4** 12.9 15.5* 7.6



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

ND CD SD LD ND CD SD LD

OCT : 23.8** 7.6 7.1 9.7 : 28.0** 7.1 11.4 6.7
NOV 75.2** 13.3 29.6** 6.6 : 88.9** 20.9** 28.8** 3.1
DEC 40.5** 11.5 18.4* 2.7 40.9** 16.6* 26.3** 5.5
JAN : 20.6** 21.6** 20.0** 16.8* 24.5** 17.4* 17.1* 17.2*
FEB : 21.8** 10.5 13.2 15.8*" 40.2** 17.3* 20.3** 16.1*
MAR 29.1** 17.8* 19.5** 7.3 29.0** 16.6* 15.4* 15.0*
APR : 79.9** 7.5 9.7 2.6 : 71.6** 9.8 8.4 2.9
MAY : 49.9** 14.7* 17.1* 10.7 : 44.1** 13.8 12.9 9.3
JUN : 20.2** 8.6 12.5 9.6 : 16.3* 10.1 11.9 10.8
JUL : 10.5 5.6 7.6 2.9 : 11.7 4.1 7.2 2.6
AUG 5.6 2.7 3.4 3.0 2.4 1.9 1.2 5.1
SEP : 22.9** 12.2 12.9 12.4 : 33.3** 12.5 15.6* 8.3

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


-36-






















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TABLE B-7 RAINFALL RATE AND EVAPORATION RATE IN INCHES
OVER THE OFFSTREAM-RESERVOIR AREA






MONTH RAINFALL EVAPORATION
(INCHES) (INCHES)


October 3.24 4.20
November 1.91 3.00
December 2.17 2.50
January 2.68 2.40
February 2.87 3.00
March 3.65 4.20
April 2.43 5.20
May 2.60 6.00
June 7.63 6.00
July 8.94 5.70
August 9.55 5.00
September 8.68 4.70
56.35 51.90
























-38-






TABLE B-8 :,-.IST OF YIELD VALUES FROM 100 rACES* OF SYNTHESIZED
STREAMFLOW DATA BASED ON LOG NUb,,AL DISTRIBUTION AND
BY OPERATIONS ROUTING SIMULATION MODEL
( INTAKE LEVEL : 28 FEET ABOVE MSL )

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

1 33.70 51 29.75
2 30.95 52 26.50
3 35.10. 53 31.30
4 27.90 54 31.70
5 33.00 55 33.15
6 32.85 56 27.60
7 30.00 57 35.50
8 34.80 58 31.65
9 30.65 59 32.70
10 31.80 60 33.80
11 33.50 61 31.20
12 36.20 62 30.25
13 33.05 63 29.50
14 33.90 64 34.00
15 29.00 65 33.35
16 31.75 66 30.60
17 29.00 67 30.30
18 27.00 68 32.82
19 33.10 69 35.00
20 32.45 70 30.20
21 28.85 71 33.32
22 35.20 72 31.90
23 32.00 73 31.00
24 30.50 74 27.70
25 33.10 75 33.20
26 33.40 76 34.35
27 33.14 77 32.74
28 33.95 78 29.30
29 29.90 79 30.90
30 32.50 80 30.55
31 35.05 81 32.30
32 34.20 82 33.30
33 32.90 83 29.70
34 28.70 84 28.80
35 28.82 85 32.76
36 34.30 86 33.12
37 26.20 87 36.50
38 34.60 88 33.18
39 29.87 89 33.60
40 31.60 90 29.85
41 27.40 91 30.80
42 25.90 92 32.10
43 34.40 93 33.25
44 31.85 94 27.50
45 28.50 95 34.50
46 29.95 96 32.80
47 32.40 97 36.30
48 28.30 98 27.55
49 35.30 99 29.80
50 30.85 100 28.10

"* A TRACE IS DEFINED AS A 50-YEAR RECORD OF MONTHLY FLOWS

-39- __________






TABLE B-9 2.LIST OF YIELD VALUES FROM 100 rACES* OF SYNTHESIZED
STREAMFLOW DATA BASED ON LOG N,, BY OPERATIONS ROUTING SIMULATION MODEL
( INTAKE LEVEL : 24 FEET ABOVE MSL )

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

1 40.50 51 38.85
2 39.80 52 28.70
3 35.10 53 31.90
4 33.65 54 41.70
5 38.40 55 32.40
6 36.80 56 40.30
7 33.80 57 39.45
8 40.90 58 32.60
9 38.60 59 36.10
10 36.20 60 38.82
11 33.75 61 45.40
12 41.15 62 34.00
13 34.90 63 39.50
14 38.25 64 39.70
15 44.10 65 42.00
16 37.28 66 38.90
17 24.80 67 39.15
18 36.50 68 38.50
19 38.35 69 41.90
20 41.30 70 31.60
21 34.20 71 41.55
22 39.10 72 38.20
23 40.70 73 38.30
24 36.70 74 37.20
25 35.80 75 39.35
26 39.75 76 44.05
27 44.40 77 39.30
28 37.30 78 45.70
29 35.00 79 32.90
30 33.70 80 42.80
31 35.20 81 44.00
32 36.30 82 38.00
33 31.70 83 39.60
34 45.80 84 32.10
35 38.65 85 36.40
36 44.80 86 40.00
37 40.40 87 36.90
38 40.80 88 38.80
39 37.40 89 40.20
40 44.20 90 37.70
41 35.30 91 35.60
42 34.70 92 39.40
43 37.00 93 38.88
44 37.10 94 39.00
45 28.50 95 40.65
46 40.60 96 30.90
47 42.40 97 36.45
48 38.70 98 33.60
49 33.10 99 42.30
50 37.50 100 37.25
* A TRACE IS DEFINED AS A 50-YEAR RECORD OF MONTHLY FLOWS

-40-






TABLE B-10 : kIST OF YIELD VALUES FROM 100 TPACES* OF SYNTHESIZED
,TREAMFLOW DATA BASED ON LOG NO. AL DISTRIBUTION AND
BY OPERATIONS ROUTING SIMULATION MODEL
( INTAKE LEVEL : 21 FEET ABOVE MSL )

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

1 44.60 51 38.80
2 43.45 52 41.60
3 41.70 53 44.40
4 35.10 54 34.80
5 42.90 55 43.20
6 38.50 56 45.90
7 43.15 57 36.50
8 41.15 58 35.40
9 42.55 59 39.70
10 44.20 60 41.20
11 42.60 61 43.05
12 38.70 62 43.60
13 37.60 63 44.95
14 44.90 64 38.00
15 39.80 65 44.30
16 37.40 66 45.50
17 36.30 67 43.02
18 37.80 68 38.20
19 41.45 69 38.10
20 42.50 70 27.80
21 39.00 71 41.30
22 36.20 72 48.40
23 37.30 73 45.85
24 40.70 74 42.00
25 45.30 75 32.40
26 37.90 76 45.10
27 44.10 77 43.40
28 40.50 78 41.40
29 43.10 79 39.90
30 47.60 80 42.10
31 40.55 81 41.25
32 33.60 82 41.50
33 43.85 83 42.70
34 31.90 84 38.75
35 40.60 85 40.40
36 45.20 86 40.00
37 39.50 87 35.80
38 42.20 88 36.40
39 38.05 89 41.10
40 44.00 90 45.80
41 42.65 91 33.30
42 44.50 92 40.30
43 43.00 93 48.80
44 39.85 94 43.50
45 37.10 95 32.70
46 43.10 96 35.90
47 33.40 97 50.00
48 45.60 98 36.10
49 38.60 99 41.80
50 36.90 100 44.70
* A TRACE IS DEFINED AS A 50-YEAR RECORD OF MONTHLY FLOWS
-41-







TABLE B-11 YIELD FREQUENCY ANALYSIS WEIBULL
BASED ON 100 YIELD VALUES LISTED ON TABLE B-8
( INTAKE LEVEL : 28 FEET ABOVE MSL )

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

0.0099 36.50 0.5050 31.85
0.0198 36.30 0.5149 31.80
0.0297 36.20 0.5248 31.75
0.0396 35.50 0.5347 31.70
0.0495 35.30 0.5446 31.65
0.0594 35.20 0.5545 31.60
0.0693 35.10 0.5644 31.30
0.0792 35.05 0.5743 31.20
0.0891 35.00 0.5842 31.10
0.0990 34.80 0.5941 31.00
0.1089 34.60 0.6040 30.95
0.1188 34.50 0.6139 30.90
0.1287 34.40 0.6238 30.85
0.1386 34.35 0.6337 30.80
0.1485 34.30 0.6436 30.65
0.1584 34.20 0.6535 30.60
0.1683 34.00 0.6634 30.55
0.1782 33.95 0.6733 30.50
0.1881 33.90 0.6832 30.30
0.1980 33.80 0.6931 30.25
0.2079 33.70 0.7030 30.20
0.2178 33.60 0.7129 30.00
0.2277 33.50 0.7228 29.95
0.2376 33.40 0.7327 29.90
0.2475 33.35 0.7426 29.87
0.2574 33.32 0.7525 29.85
0.2673 33.30 0.7624 29.80
0.2772 33.25 0.7723 29.75
0.2871 33.20 0.7822 29.70
0.2970 33.18 0.7921 29.50
0.3069 33.15 0.8020 29.30
0.3168 33.14 0.8119 29.00
0.3267 33.12 0.8218 29.00
0.3366 33.10 0.8317 28.85
0.3465 33.05 0.8416 28.82
0.3564 33.00 0.8515 28.80
0.3663 32.90 0.8614 28.70
0.3762 32.85 0.8713 28.50
0.3861 32.82 0.8812 28.30
0.3960 32.80 0.8911 28.10
0.4059 32.76 0.9010 27.90
0.4158 32.74 0.9109 27.70
0.4257 32.70 0.9208 27.60
0.4356 32.50 0.9307 27.55
0.4455 32.45 0.9406 27.50
0.4554 32.40 0.9505 27.40
0.4653 32.30 0.9604 27.00
0.4752 32.10 0.9703 26.50
0.4851 32.00 0.9802 26.20
0.4950 31.90 0.9901 25.90

-42-






TABLE B-12 : YIELD FREQUENCY ANALYSIS WE. LL
BASED ON 100 YIELD VALUES LISTED ON TABLE B-9
( INTAKE LEVEL : 24 FEET ABOVE MSL )


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

0.0099 45.80 0.5050 38.35
0.0198 45.70 0.5149 38.30
0.0297 45.40 0.5248 38.25
0.0396 44.80 0.5347 38.20
0.0495 44.40 0.5446 38.00
0.0594 44.20 0.5545 37.70
0.0693 44.10 0.5644 37.50
0.0792 44.05 0.5743 37.40
0.0891 44.00 0.5842 37.30
0.0990 42,80 0.5941 37.28
0.1089 42.40 0.6040 37.25
0.1188 42.30 0.6139 37.20
0.1287 42.00 0.6238 37.10
0,1386 41.90 0.6337 37.00
0.1485 41.70 0.6436 36.90
0.1584 41.55 0.6535 36.80
0.1683 41.30 0.6634 36.70
0.1782 41.15 0.6733 36.50
0.1881 40.90 0.6832 36.45
0.1980 40.80 0.6931 36.40
0.2079 40.70 0.7030 36.30
0,2178 40.65 0.7129 36.20
0.2277 40.60 0.7228 36.10
0.2376 40.50 0.7327 35.80
0.2475 40.40 0.7426 35.60
0.2574 40.30 0.7525 35.30
0.2673 40.20 0.7624 35.20
0.2772 40.00 0.7723 35.10
0.2871 39.80 0.7822 35.00
0.2970 39.75 0.7921 34.90
0.3069 39.70 0.8020 34.70
0.3168 39.60 0.8119 34.20
0.3267 39.50 0.8218 34.00
0.3366 39.45 0.8317 33.80
0.3465 39.40 0.8416 33.75
0.3564 39.35 0.8515 33.70
0.3663 39.30 0.8614 33.65
0.3762 39.15 0.8713 33.60
0.3861 39.10 0.8812 33.10
0.3960 39.00 0.8911 32.90
0.4059 38.90 0.9010 32.60
0.4158 38.88 0.9109 32.40
0.4257 38.85 0.9208 32.10
0.4356 38.82 0.9307 31.90
0.4455 38.80 0.9406 31.70
0.4554 38.70 0.9505 31.60
0.4653 38.65 0.9604 30.90
0.4752 38.60 0.9703 28.70
0.4851 38.50 0.9802 28.50
0.4950 38.40 0.9901 24.80

-43-







TABLE B-13 YIELD FREQUENCY ANALYSIS WL-_ULL
BASED ON 100 YIELD VALUES LISTED ON TABLE B-10
( INTAKE LEVEL : 21 FEET ABOVE MSL )


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

0.0099 50.00 0.5050 41.20
0.0198 48.40 0.5149 41.15
0.0297 47.60 0.5248 41.10
0.0396 45.90 0.5347 40.70
0.0495 45.85 0.5446 40.65
0.0594 45.80 0.5545 40.60
0.0693 45.60 0.5644 40.55
0.0792 45.50 0.5743 40.50
0.0891 45.30 0.5842 40.40
0.0990 45.20 0.5941 40.30
0.1089 45.10 0.6040 40.00
0.1188 44.95 0.6139 39.90
0.1287 44.90 0.6238 39.85
0.1386 44.70 0.6337 39.80
0.1485 44.60 0.6436 39.70
0.1584 44.50 0.6535 39.50
0.1683 44.40 0.6634 39.00
0.1782 44.30 0.6733 38.80
0.1881 44.20 0.6832 38.75
0.1980 44.10 0.6931 38.70
0.2079 44.00 0.7030 38.60
0.2178 43.85 0.7129 38.50
0.2277 43.60 0.7228 38.20
0.2376 43.50 0.7327 38.10
0.2475 43.45 0.7426 38.05
0.2574 43.40 0.7525 38.00
0.2673 43.20 0.7624 37.90
0.2772 43.15 0.7723 37.80
0.2871 43.10 0.7822 37.60
0.2970 43.09 0.7921 37.40
0.3069 43.05 0.8020 37.30
0.3168 43.02 0.8119 37.10
0.3267 43.00 0.8218 36.90
0.3366 42.90 0.8317 36.50
0.3465 42.80 0.8416 36.40
0.3564 42.70 0.8515 36.30
0.3663 42.60 0.8614 36.20
0.3762 42.55 0.8713 36.10
0.3861 42.50 0.8812 35.90
0.3960 42.20 0.8911 35.80
0.4059 42.10 0.9010 35.40
0.4158 42.00 0.9109 35.10
0.4257 41.80 0.9208 34.80
0.4356 41.70 0.9307 33.60
0,4455 41.60 0.9406 33.40
0.4554 41.50 0.9505 33.30
0.4653 41.45 0.9604 32.70
0.4752 41.40 0.9703 32.40
0.4851 41.30 0.9802 31.90
0.4950 41.25 0.9901 27.80

.44-









APPENDIX C

YIELD ANALYSIS
BY THE MASS CURVE METHOD

Data Compilation

Forty (40) years of streamflow records (from 1940 to 1979) are compiled and
listed on Table Cl. The compilation of these records is discussed in detail in
Section 2.

Computation of the Yearly Yields

The yearly yields of the above 40 years of streamflow records are computed by
the mass curve method and based on the active storage of the reservoir, i.e. the
storage capacity accounted for between the maximum operational reservoir level
at 40 feet above MSL and each of the three intake levels considered at 28 feet,
24 feet and 21 feet above MSL respectively.
- Table C2 lists the yearly yields of the reservoir with intake
level at 28 feet above MSL.
- Table C3 lists the yearly yields of the reservoir with intake
level at 24 feet above MSL.
- Table C4 lists the yearly yields of the reservoir with intake
level at 21 feet above MSL.
Figures Cl, C2 and C3 show sample computation of yearly yield
by the Mass Curve Method.

Yield Frequency Analysis

A frequency analysis of these 40 yearly yields was made, using U. S. Geological
Survey Frequency Analysis Model.

Table C5, C6 and C7, list the annual frequency curve coordinates with yields at
selected exceedance probabilities.




















-45-











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LU 0 0U 0 14 0 0 a 4 0 a a a
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-46-









TABLE C-2 :SUMMARY OF THE YEARLY YIELDS BY THE MASS CURVE METHOD
( INTAKE LEVEL : 28 FEET ABOVE MSL )


YEAR YIELD IN MGD

1940 49.25 *
1941 55.55
1942 73.95
1943 31.50
1944 37.80
1945 32.25
1946 33.05
1947 58.65
1948 49.80
1949 34.00
1950 33.15 *
1951 45.30
1952 40.45
1953 75.60
1954 59.15
1955 40.95
1956 29.15
1957 58.15
1958 76.20
1959 70.00
1960 77.75
1961 52.90
1962 32.85
1963 77.70
1964 60.00
1965 48.05
1966 70.90
1967 32.20
1968 29.85
1969 67.55
1970 90.65
1971 31.25
1972 79.85
1973 63.50
1974 30.70
1975 26.20 *
1976 34.45
1977 36.85
1978 82.30
1979 61.85



see sample computation on Figures C-I, C-2 & C-3




-47-






FIGURE C-1 Si LE COMPUTATION OF 1940 YIELD 5 THE MASS CURVE METHOD
( INTAKE LEVEL : 28 FEET ABOVE MSL )





CUMULATIVE FLOW IN CFS



1400


1300 ACTIVE RESERVOIR STORAGE : STORAGE CAPACITY ACCOUNTED FOR BETWEEN
THE MAX. OPERATIONAL RESERVOIR LEVEL AT
40 FEET ABOVE MSL AND THE INTAKE LEVEL
1200


1100


1000-
/
/
900


800
/ I
700-
7 !

600 /

/ b, ACTIVE RESERVOIR STORAGE*
500 / ( I E LEVEL AT 28 FEET
-/ |ABOVE MSL )
400- / 1


300

200

100- ---



OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP


-48-







FIGURE C-2- SAMPLE COMPUTATION OF 1950 YIELD BY THE MASS CURVE METHOD
( INTAKE LEVEL : 28 FEET ABOVE MSL )





CUMULATIVE FLOW IN CFS


1400

1300

1200 ACTIVE RESERVOIR STORAGE = STORAGE CAPACITY ACCOUNTED FOR BETWEEN
THE MAX. OPERATIONAL RESERVOIR LEVEL AT
40 FEET ABOVE MSL AND THE INTAKE LEVEL
1100

1000 -

900- /-


SI
800

700- J


600 C ,
S^ ACT VE RESERVOIR STORAGE*
"500 ( NTAKE LEVEL AT 28 FEET
500- ABOVE MSL )

400 -

300 '

200

100



OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP

-49-






FIGURE C-3 S .'LE COMPUTATION OF 1975 YIELD L THE MASS CURVE METHOD
( INTAKE LEVEL : 28 FEET ABOVE MSL )





CUMULATIVE FLOW IN CFS


1400
/
1300 ACTIVE RESERVOIR STORAGE = STORAGE CAPACITY ACCOUNTED/FOR BETWEEN
THE MAX. OPERATIONAL RESERVOI LEVEL AT
40 FEET ABOVE MSL AND TlE INTAKE LEVEL
1200


1100- /
/ /

1000 /
/

900
/ I
800 / 1
/ I
/ I
700 /
/I
/ I
600 I
/ I

500 / /


400 / I
/ I
/I
300 /

200 / 0,
20/ TIVE RESERVOIR STORAGE*
/ INTAKE LEVEL AT 28 FEET
100 ABOVE MSL )


0 I iI I I I I I
OCT NOV DEC JAN FEB MAR APR MAY JUN JUL AUG SEP

-50-









TABLE C-3 SUMMARY OF THE YEARLY YIELDS BY THE MASS CURVE METHOD
( INTAKE LEVEL : 24 FEET ABOVE MSL )





YEAR YIELD IN MGD

1940 53.20
1941 59.50
1942 77.20
1943 35.95
1944 42.85
1945 37.30
1946 37.45
1947 65.80
1948 56.90
1949 38.45
1950 38.20
1951 49.75
1952 44.40
1953 83.65
1954 66.25
1955 44.80
1956 32.65
1957 67.00
1958 83.30
1959 77.10
1960 82.15
1961 56.85
1962 37.25
1963 85.95
1964 68.70
1965 52.50
1966 75.30
1967 37.25
1968 34.25
1969 76.45
1970 96.50
1971 35.25
1972 84.25
1973 67.45
1974 35.10
1975 30.60
1976 39.50
1977 40.80
1978 91.20
1979 65.80





-51-








TABLE C-4 :SUMMARY OF THE YEARLY YIELDS BY THE MASS CURVE METHOD
( INTAKE LEVEL : 21 FEET ABOVE MSL )





YEAR YIELD IN MGD

1940 54.85
1941 61.15
1942 78.50
1943 37.80
1944 44.75
1945 39.45
1946 39.35
1947 68.80
1948 59.90
1949 40.30
1950 40.35
1951 51.65
1952 46.05
1953 85.55
1954 69.15
1955 46.30
1956 34.15
1957 70.75
1958 86.30
1959 80.10
1960 84.05
1961 58.50
1962 39.15
1963 87.85
1964 72.45
1965 54.35
1966 77.20
1967 39.40
1968 36.15
1969 78.35
1970 97.85
1971 36.90
1972 86.15
1973 69.10
1974 37.00
1975 32.50
1976 41.65
1977 42.45
1978 94.95
1979 67.45






-52-












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-55-










VII. REFERENCES

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

Bromwell Engineering, Inc., "Safe Yield Analysis of the Lake Manatee Reservoir
by Queuing Theory," 1980.

Croxton, F. E. and D. J. Cowden, "Applied General Statistics," Second Edition,
Printice-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.

Russell and Axon, Inc., "Water Works Project--Manatee County, Florida,"
May 1963.

Seaburn and Robertson, Inc., "Northeastern Manasota Hydrologic Investigation,"
1979.

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.








-56-





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