River basin simulation as a means of determining operating policy for a water control system

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Title:
River basin simulation as a means of determining operating policy for a water control system
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xii, 108 leaves : ill., map. ;
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English
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Kiker, Clyde Frederick, 1939-
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Subjects / Keywords:
Watersheds -- Florida   ( lcsh )
Watershed management -- Mathematical models   ( lcsh )
Upper Kissimmee River basin, Fla   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis--University of Florida.
Bibliography:
Includes bibliographical references (leaves 106-107).
Statement of Responsibility:
by Clyde Frederick Kiker.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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notis - ACH2943
oclc - 03967641
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Full Text















RIVER BASIN SIMULATION AS A MEANS OF DETERMINING

OPERATING POLICY FOR A WATER CONTROL SYSTEM















By

CLYDE FREDERICK KIKER


A DISSERTATION; PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUILRZMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FL3ORIDA


1973

































Copyright by

Clyde Frederick Kiker

1973













ACKNOWLEDGMENTS


My graduate study has been rewarding and enjoyable. Many people

are responsible, and to them I feel a debt of gratitude.

My greatest debt is to my wife and sons for being so patient

with my indulgence. Suzanne's understanding nature and day-by-day vote

of confidence has been invaluable. I thank my sons, Jeffrey, Gregory,

Douglas, and Jason, for their understanding at being fatherless on many

occasions important to them.

Richard Conner as Chairman of my Supervisory Committee has pro-

vided academic and technical guidance in a masterful way, making the

preparation of this dissertation exciting and enjoyable. More than this,

he has provided a warm friendship in trying times. Fred Tyner as Chair-

man in the early stages of my study furnished good advice. John Reynolds'

experience with the technical aspects of the dissertation problem was

helpful. Richard Fluck and Leo Polopolus critically reviewed the manu-

script. For these contributions and many left unmentioned, I wish to

thank the members of my Supervisory Committee.

Special appreciation is extended to Sheriar Irani for his able

assistance with the computer programming. Special thanks also go to

Pam Bunde and Carolyn Crook for their help with the preliminary draft

typing in those last hectic days.

K. R. Tefertiller, the faculty, and my fellow graduate students

of the Department of Food and Resources Economics have contributed







greatly in making this study period significant. My friends in the

Department of Agricultural Engineering have done likewise. To all I

am grateful.

This study could not have been accomplished without the financial

support of the Office of Water Resources Research, U. S. Department of

Interior, through the Florida Water Resources Research Center, the

Central and Southern Florida Flood Control District, and the Florida

Agricultural Experiment Stations. Likewise the University of Florida

Computing Center provided the means of handling such a study.

To the many unmentioned others, I am grateful.













TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS . .. iii

LIST OF TABLES .. . vii

LIST OF FUGURES ... . .... .viii

ABSTRACT : . . x

CHAPTER

I. INTRODUCTION . .. 1

The Problem .. . 1
An Overview . .. 1
Earlier Modeling Work . 4
Management of Existing Systems .. 8
Objectives of the Study .. 10

II. THE PRESENT AND FUTURE SYSTEM .. 12

Man's Dominance . .. 12
The Management Organization .. 14
The Study Area . .. 20

III. THE SIMULATION MODEL . ... 24

Conceptual Aspects. . 24
Hydrologic Models . ... 27
Water Use Activities Models ... 44
Policy Evaluation Capabilities of the
Model. . .. 61

IV. BASIC DATA INPUTS TO THE MODEL ... 63

Hydrologic Data . ... 63
Water Management System Data .. 64
Water Use Data . ... 68





TABLE OF CONTENTS -- Continued


CHAPTER Page


V. POLICY EVALUATION DEMONSTRATIONS .. 80

Temporal and Spatial Water Storage .... 82
Consumptive Withdrawals. .. 88
Minimum Outflows. . .... 91
Land and Water Use Patterns .. 93
Policy Implications. . ... 94

VI. SUMMARY AND CONCLUSIONS . .. 99

Summary . . 99
Applicability of the Model in Policy
Selection . .. 101

LIST OF REFERENCES . .. 106

BIOGRAPHICAL SKETCH . ... 108











LIST OF TABLES


Table Page

1. Relationships of sub-basins, lakes, and control struc-
tures . . . 31

2. Symbols used to represent lakes, structures, and
canals . . .. 33

3. Relationships between water surface elevation and
lake storage . . .. 65

4. Gate structure characteristics. . 66

5. Canal characteristics . . .. 68

6. Evapotranspiration information . .. 70

7. Soil information. ..... .. 71

8. Crop yields, production costs, and prices ... 72

9. Elevations for the percent of maximum monthly recrea-
tional visits functions . .. 75

10. Estimated monthly visits to each lake . .. 76

11. Urban and rural sturcture damage functions .. 78

12. Crop damage functions . .. 79

13. Three-year total dollar benefits and damages resulting
from various regulation schedules . ... 86

14. Three-year total dollar benefits and damages resulting
from irrigation withdrawal demonstrations .. 91

15. Three-year total dollar benefits and damages resulting
from minimum flow simulations . ... 93

16. Crop acreages used . .. ... 95

17. Three-year total dollar benefits and damages resulting
from land and water use change demonstrations .. 95












LIST OF FIGURES


Figure

1.


Page

17


A schematic diagram of the FCD system in south Florida .


2. Operational water management policy and execution model 19

3. The Upper Kissimmee River Basin . .. 22

4. Water management information flow diagram ... .25

5. Flow diagram of streamflow simulation model ...... .29

6. Schematic diagram of the Upper Kissimmee River Basin
water management system . .. 32

7. Water inflows and outflows for Lake Tohopekaliga 35

8. Sequence of calculations in the water surface elevation
management model . . .. 37

9. Consumptive withdrawal functions . 38

10. A typical regulation schedule . .. 38

11. The gate operation function . 39

12. Schematic diagram of the lake, canal, and control
structure relationship. . 40

13. Potential evapotranspiration function ... .46

14. Typical production, average product and marginal product
curves . ... . 49

15. Typical marginal value product curve . .. 49

16. Residential water demand function . .. .54

17. Recreational visit functions . .. 56

18. Recreational demand function . .. 58


viii






LIST OF FIGURES Continued


Figure Page


19. Flood damage functions for a typical lake ........ .. 60

20. The recreational use function . ... 75

21. Regulation schedules for lakes in the Upper Kissimmee
River Basin . . 84

22. Proposed regulation schedules . ... 85

23. Proportional consumptive withdrawal functions ... 90







Abstract of Dissertation Presented to the Graduate Council of the
University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy


RIVER BASIN SIMULATION AS A MEANS OF
DETERMINING OPERATING POLICY FOR A WATER CONTROL SYSTEM


By

Clyde Frederick Kiker

June, 1973


Chairman: J. Richard Conner
Major Department: Food and Resource Economics


The handling of water management problems requires integration of

technical detail with the social consequences of water availability and

control. Nature provides the water, and man attempts to deal with the

variable supply and put it to his use. This study suggests simulation

as a means of considering alternative policies for an existing water

control system. Specifically, the problem of dealing with the formula-

tion of water management policy for the area of south Florida within the

Central and Southern Florida Flood Control District was undertaken.

The objectives of this study were to (a) propose an organizational

framework in which hydrologic, economic, and institutional aspects of the

region may be used in policy development, (b) develop a simulation model

which includes the salient hydrologic, economic, and institutional fea-

tures of the Upper Kissimmee River Basin to serve as a guide, (c) demon-

strate the usefulness of the simulation model in policy evaluations, and

(d) determine the appropriateness of the approach for use in policy

problems encountered when dealing with a large region.

x







A framework merging the technological aspects of the hydrology, water

management, and economic water use activities with the social attitudes of

the region was suggested. The essence of the framework is the use of

simulation models in conjunction with an evaluation process by a group

representing the people of the region.

A first-generation simulation model of the hydrologic phenomena and

water-oriented activities in the Upper Kissimmee River Basin was developed.

Models of the surface water management system, the water use activities,

and the institutional constraints were interfaced with rainfall and water-

shed runoff models. The model of the surface water management system

included sub-models of the gate-type control structures, the canal systems,

and the water storage system. The water use activities model was made up

of sub-models for crop irrigation, residential water consumption, and

property floating. The institutional constraint model included sub-nodels

of lake surface elevation, consumptive withdrawal, and minimum flow regu-

lations.

The model uses as input rainfall over time, which is transformed

into watershed runoff in the form of a time series with a short interval.

The runoff values thus incorporate the stochastic properties of the

rainfall. The water management model, operating under a given set of

policy conscra-ints, attempts to cope with the hydrologic events. The

hydrologic variability is passed on to the water use activities in the

form of water in storage and lake surface elevations. The water use

activities model calculates the levels of the activities and the benefits

accruing.

The usefulness of the model was demonstrated by considering four

policy areas: (a) temporal and spatial storage of surface water,







(b) consumptive withdrawals, (c) minimum flows, and (d) land and water

use patterns. In all demonstrations the results were sets of water flow

data, lake surface elevations, water use activity levels, and dollar

benefits. These data provided the information used in the policy evalu-

ation by the decision makers.

The methodology, because of its detailed approach, lends itself to

the refinement of operational policy for individual basins. The method

could be extended to cover an area as large as the entire Central and

Southern Florida Flood Control District, but, rather than construct

one large model, it would be best to work on individual basins. Each

could then be tied together by a large, much less detailed model of the

entire region. This model could be a linear programming model or an

aggregate simulation model and would consider broad policy alternatives.

The reduced number of alternatives could be submitted to the individual

basin models and shaped into final operating policy for each basin.


xii












CHAPTER I


INTRODUCTION


The Problem


An Overview


Man, from the very beginning, has had water problems. He developed

a rudimentary agriculture where water was available in desired quantities

but failed in-areas of extremes. As time passed, he learned to control

the effects of nature's extremes and civilization flourished.

Twentieth-century man still finds himself beset by water problems.

In many parts of the world, these problems involve simply water for food

and fiber production. In the advanced nations, however, other problems

have arisen which often bring conflict among water users. Water is now

used for recreation and aesthetics, waste disposal, and preservation of

natural ecological systems as well as the traditional crop production.

Florida is encountering many such problems, and the situation here

is dramatic because of the oscillation between too much water and too

little water. The users of water in this state -- agriculturalists,

naturalists, recreationists, industrialists, and municipalities -- often

find themselves in disagreement as to how water should be used. One

need only consult the daily newspaper to see evidence of the running

debates presently underway.

Recent legislation, primarily the Florida Water Resources Act of

1972, has been enacted to create a governmental framework in which these

-1-








problems can be attacked. Foremost in this framework is the broadening

of the powers of the Department of Natural Resources and the creation

of five water management districts which would take in the entire state

land area and water resources. The portion of south Florida under the

management of the Central and Southern Florida Flood Control District is

typical of most water management areas and, because of the high degree of

urbanization, agricultural development and a unique natural environment,

has been facing many of the problems the new water management districts

will confront. This area and the management of it may serve as a guide

in establishing the new organizations.

The Central and Southern Florida Flood Control District (FCD), a

statutory agency, was created in 1949 and given responsibility for

managing the water resources in this location, with the major objective

of flood control. To accomplish this, a physical system consisting of

a complex of canals, levees, pumping stations, spillways, navigation

locks, and retention basins was constructed in the 15,700-square-mile

area in the intervening years. This system has been operated with

criteria which were derived primarily for flood control by the U. S.

Army Corps of Engineers in the early years of the project.

Many groups representing water users in the District are concerned

about water allocation and believe the present operational management

does not provide maximum benefits. Each wants to have its needs met.

The property owners and business interests want flood protection,

the municipalities and agriculturalists want a consistent water supply,

the recreationists want quality water, and the environmental groups

want water for the natural systems such as the Everglades and the




-3-


coastal estuaries. The FCD, responding to water-related changes in the

area, has taken on other management responsibilities which include water

conservation, water supply, preservation and enhancement of fish and

wildlife, improvement of navigation, and public recreation.

The FDC realized that operational "rules" based on flood control

design criteria and previously existing demands can fall short of

generating maximum benefits when the complexion of land use, drainage,

urbanization, pollution, and industrialization, within the project

boundaries, changes. Desiring to develop a rational system of water

management which would better satisfy the various users of water, the

FDC has undertaken a program to derive new criteria by which to operate.

It is thought that a model incorporating the salient features of the

hydrology and the various water-using activities of the area would give

greater insight into the interaction among users and thus greater

knowledge of how to manage the system. Such a model would not be possi-

ble immediately because of the lack of knowledge about both the hydrologic

characteristics and the water use activities. The model, instead, could

evolve.

A logical first step in developing a model which involves such

complexities is to consider an area smaller than the total 15,700 square

miles and the use of this as a pilot for the larger study. The Upper

Kissimmee River Basin can be studied since sufficient information is

available to prepare a simulation model of the hydrology and the economic

activities in the area. The model would provide guidelines for water

allocation and management by reflecting the interaction of the various

economic activities and the effect the stochastic nature of the hydrology

has on benefits accruing to the area due to the use of water. It should




-4-


be noted here that the model could be used to generate a response

surface which could be explored with an optimum-seeking method. But

the main purpose of the model (rather than being to obtain an optimal

operation policy) will be to provide greater knowledge of the workings

of the system much as an experimental apparatus is used in the physical

sciences. Potential operating procedures obtained from the simulation

model will then be considered by the FCD governing board and a policy

derived. The policy most likely will not be optimal in an economic

sense, and it will probably not be wholeheartedly supported by any group,

but it will reflect their point of view better than a policy based

solely on economic optimality or on flood prevention.

The general purpose of this study is thus to (a) prepare a first-

generation simulation model of the economic activities in the Upper

Kissimmee River Basin and interface it with a hydrologic model of the

area and (b) evaluate the potential of this model in the determination

of operational policy.


Earlier Modeling Work


The majority of previous economic analyses of river basins have

dealt with the design of water resource systems. These studies have

been primarily concerned with determining the optimum size and combina-

tion of structures to maximize benefits given an operating procedure.

This procedure specified the allocations among areas. The present study

deals with the case in which a water resources system has been completed

and in use for a period of time. No major physical changes in the water

management system are possible but many changes in land/water use




-5-


patterns have evolved. Now only the operating procedure can be modified

to move to a point of higher net benefits.

Two approaches have been employed in the investigation of water

resources systems and both are being used to study the allocation of

water in the Upper Kissimmee River Basin. Reynolds and Conner [20] are

using mathematical programming in the form of a dynamic linear programming

model. This model will determine the optimal temporal allocation of

water among alternative uses and watersheds. The pertinent literature

dealing with this approach was reviewed in their project statement. The

present study will utilize simulation as an alternative method.

Simulation has several advantages. Foremost is the ability to

readily change formulations and parameters, thus allowing the model to

be viewed as an apparatus with which experiments can be performed.

Changes in the availability of water and the physical, political, and

institutional constraints are easily handled. The model is not limited

to the optimization of a given objective function but can be used to

consider a number of different objectives. The necessity of systematically

laying out the economic activities and the physical movement of water

in the model assists in providing greater insight into the real system.

This, coupled with the ability to handle many variables and nonlinear

formulations, gives simulation much intuitive appeal for use in water

resource studies.

Probably the best known of the early simulation models is that

of the Harvard Water Program [14] in which a hypothetical river basin

system is simulated. Twelve design variables consisting of reservoirs,

power plants, irrigation works, target output for irrigation and elec-

trical energy, and specified allocations of reservoir capacity for flood








control were considered. The economic benefits of the system were

determined on the basis of use and control of water moving through the

system. The design of the system was obtained both by sampling from

the many combinations of design variables and the use of optimum-seek-

ing methods to determine the design that provided maximum net benefits.

The Harvard Water Program later used this approach in a model of the

Delaware River Basin and Hufschmidt and Fiering [12] applied it to the

Lehigh River Basin in Pennsylvania.

The Battelle Memorial Institute used a somewhat different approach

in their work on the Susquehanna River Basin [10]. This study was con-

cerned with the economic interrelations existing in the river basin and

attempted to delineate the factors influenceing the economic growth of

the area. The entire area was broken down into sub-regions, each

described by a series of equations which related the interrelations and

feedbacks of three major factor groups: (s) size and distribution of

the population, (b) kind and level of employment, and (c) water avail-

ability and control. The sub-factors concerning water were water

quality, water supply (agriculture, urban, and industrial), water for

recreation, flood control, and water for electric power generators.

The researchers saw simulation as an evolutionary process where an

operational model is developed, then continually modified as time

passes. The model was seen not as a tool for finding an optimal solu-

tion but as the key to a cohesive planning effort where the model

served as a central focus by relating parts of the study and tending to

keep them in balanced perspective.

Bathke [1] developed a simulation model of a simplified river

basin in which he included hydrologic risk due to the variability of




-7-


rainfall and evaporation. Actual flow data from the South Concho River

for a 39-year periodwere used to develop a response surface relating

the variables. From this the optimal combination of reservoir capacity

and irrigation project size was obtained by selecting the maximum total

net benefit combination. Conner [5] extended this work to include the

full effect of the risk element inherent in the system by considering

the water users' reactions to risk and the effects of these reactions

on optimal levels of the design variables.

The Corps of Engineers has realized the need to investigate the

operation of existing water resource systems and has initiated a simula-

tion study of the Arkansas-White-Red River system. The major purpose of

the 23 reservoir projects located in the three river basins was initially

power generation. The Corps' simulation is a hydraulic model in which

the operational rules can be varied and results are evaluated on how

well the operational objectives, primarily power generation, are met.

A major problem in the study has been the inability to quantify the

operational objectives for the existing system. There was no way to

compare operational procedures when competitive uses of water were con-

sidered [7]. No attempt was made to simulate the economic activities

associated with water use and determine the dollar benefits accruing

to operational procedures.

Bredhoeft and Young [4] used simulation in the consideration of

temporal allocation of ground water. The objective was to determine

operational procedures for an existing irrigation system over a ground

water basin. Water level in the basin was the connection between an

economic and a hydrologic model.








Packer et al. [16] simulated the hydrologic-economic flow system

of an agricultural area in Utah. The hydrologic characteristics of the

Cache Valley were simulated first with an analog program and then as a

digital program. The physical management system was taken as given and

different management techniques were investigated. The only use of the

water in agriculture, and net income accruing to the sector because of

water use was the measure of management effectiveness. The link between

the economic and hydrologic system was the production function, which

related the actual evapotranspiration to the yield of the crop, while

other variables affecting crop production were assumed to be relatively

constant.

This literature and other peripheral works give insight into the

approaches that can be used in the development of the hydrologic and

economic simulation models for the Upper Kissimmee River Basin. It

does not provide the guidelines that are needed for the development of

operational procedures that provide an acceptable allocation of water

to the various users over time. The next logical step is to develop

a methodology that can provide tentative answers to the difficult

allocation problems.


Management of Existing Systems


The planning and design studies mentioned above dealt primarily

with determining the number, size, and location of components within the

system to meet certain functional objectives. Generally, simplistic

operating rules, independent of system configuration and invariant from

alternative to alternative, were used resulting in operating policy being

ignored as a planning or design variable. This was an adequate approach




-9-


for the planning and design of the system but, as soon as a significant

number of components are completed, operating policy as a variable

becomes important.

Simplifications were needed in the design problem to be able to

deal with long periods of time and the resulting uncertainty. It was

necessary to hypothesize how the system would operate and how water would

be allocated for the life of the project. When the system is completed,

however, the managing staff must deal with changing multipurpose opera-

tional objectives with which daily operations must be compatible.

Emphasis is no longer on the very long-range operational policy; the

day-to-day, month-to-month, year-to-year operation is now the major

concern.

The activities and hydrology of the region are recognized to be

dynamic, not static. Land and water use patterns are continuously modi-

fied by new crop plantings, livestock operations, urban development,

recreational enterprises, and numerous other man-conceived ventures.

Various other groups object and want water to maintain the natural system

and wildlife. Conflict arises and pressure is applied to the institutions

dealing with water management. Thus, public opinion points out that new

operational objectives must be considered and integrated into the day-to-

day operation of the system. The question is, how does the responsible

agency deal with these varying influences and manage the system so as to

provide the highest possible benefits to society as a whole?

Modeling, such as was used in the design studies, appears to be a

partial answer. However, now the real world must be dealt with, not a

hypothetical world that is to exist in the distant future. The models

must incorporate the salient features of the hydrology, the water




-10-


management system, the economic activities, and the constraining

institutions if the necessary interactions are to be considered ade-

quately. Through experimental use, models can provide insight into

the effects of potential operating policies. Changes in land and water

use, economic activities, and institutions likewise can be incorporated

into the models and their influences examined.


Objectives of the Study


Management of water resource systems is difficult under conditions

where hydrologic variation is the major concern and water use activities

are essentially static. In situations where man's activities are expand-

ing at a phenomenal rate, also, intelligent management decisions become

nearly impossible. The multitude of interactions are beyond the compre-

hension of the human mind. Computer simulation models have been used

in other fields to extend man's analytical ability. It is believed that

modeling can assist in the formulation of water management policy in

south Florida.

Therefore, the objectives of this study are to

1. Propose an organizational framework in which hydrologic,

economic, and institutional aspects of the region are used

in policy development. The ability to meet long-term social

goals depends upon the day-to-day physical management and

use of water. This, in turn, is dependent on the water

management policies in effect. So, in policy selection a

framework incorporating feedback on the consequences of

proposed policies is needed.




-11-


2. Develop a simulation model which includes the salient

hydrologic, economic, and institutional features of the

Upper Kissimmee River Basin. More specifically, develop

and interface models of rainfall occurrence, runoff

quantities, surface water management, water use activities,

and institutional constraints.

3. Demonstrate the usefulness of the simulation model in policy

evaluations. Policies concerning spatial and temporal

storage of surface water, consumptive use withdrawals,

minimum streamflows, and land and water use patterns will

be considered.

4. Determine the appropriateness -- from the standpoint of

validity of the models, data requirements and availability,

and cost of operation -- of such an approach for use in

policy problems encountered when dealing with a large

region such as the Central and Southern Florida Flood

Control District.














CHAPTER II


THE PRESENT AND FUTURE SYSTEM


Man's Dominance


The southern portion of the Florida peninsula was originally an

area where the most striking feature was water. The region just south

of present day Orlando and east of the central ridge was a large, flat,

swampy, pine forest with many small and large shallow lakes. In times

of heavy rains -- in the summers and early fall -- the lakes would

overflow their banks and flow in large sheets southward to other lakes

and into the Kissimmee River, a wide, very flat flood plain which

remained swampy all year. The water next moved into Lake Okeechobee,

the large body of water that dominates south Florida. Water from heavy

rains swelled the lake causing it to overflow the banks southward into

a sea of sawgrass covering virtually the entire southern tip of the

peninsula. Wildlife was profuse. Reptiles, mammals, and birds were

tied to the water in a fine balance. The fresh water moving into the

salt water of the Atlantic and Gulf of Mexico formed brackish

estuaries which were teeming with fish and shell fish.

The area remained uninhabited except for Indian hunting parties

until the nineteenth century when a few hundred Seminole Indians escap-

ing from white settlers in central Florida moved into the area. Later

in the century, the state sold large blocks of the Kissiummee Basin to


-12-




-13-


individuals who drained the land and put cattle on it. At the turn of

the century, crop farmers began to drain the muck lands below Lake

Okeechobee. A small settlement, Miami, grew on the coastal sand ridge.

The early part of the twentieth century saw more farmers moving

into the area just below Lake Okeechobee, and the towns of Belle Glade

and Clewiston came into existence. In the twenties, storms swelled the

lake causing great floods and thousands of deaths. At the same time,

the Atlantic coast was experiencing a boom, in which speculators were

buying and developing land to sell to people from the North. The warm

tropical climate was now accessible by railroad.

The series of events caused strong pressure to control the water.

The Federal Government began to dike Lake Okeechobee and to dig large

canals to the coast,allowing great quantities of water to be released

quickly into the Atlantic. Smaller canals laced the marshlands and tied

into the larger system. Developers dug canals in the coastal areas to

make way for homes. Drainage of the area below Lake Okeechobee continued

through the 1960's. In the fifties, land owners above the lake were

pressing to control the water in the Kissimmee River Basin. The river

was channelized, canals were dug between the lakes and a number of con-

trol structures were built. Man now played a dominant role in south

Florida.

The ability to control water opened the way to expansion of man's

activities at an even greater rate. The population of the area is

presently three million and is concentrated around Orlando in the Upper

Kissimmee Basin and in a megalopolis running from Fort Pierce south to

the Florida Keys. Tourist attractions in these areas swell the popula-

tion each year. The population is expected to continue to grow. Crops




-14-


and native pasture now occupy much of the land, and expansion of improved

pasture and citrus have taken place at a rapid rate.


The Management Organization


The Central and Southern Florida Flood Control District's role has

expanded as south Florida grew and now includes the following responsi-

bilities:

1. Flood Control protection of life and property from floods

and hurricanes is provided through the use of dikes, levees,

canals, and pumping stations.

2. Water Conservation -- excess surface water is stored for

beneficial use in dry times in a network of interconnected

reservoirs including the Kissimmee River Basin, Lake

Okeechobee, and 50 percent of the original Everglades, and

ground water levels are maintained through management of

the surface water.

3. Salt Water Intrusion Prevention -- water storage in the

Everglades wilderness areas provides a head on fresh water

necessary to prevent salt water intrusion into coastal well

fields.

4. Fish and Wildlife Preservation -- through careful planing

and operation of the physical system, water is provided to

maintain the natural wildlife systems.

5. Everglades National Park -- water is provided from conserva-

tion storage areas to assist in restoring and maintaining

natural conditions within the park.




-15-


6. Agriculture -- flood protection, drainage, and water supply

are provided to foster efficient use of the farm lands in

the District.

7. Recreation -- provides recreational areas throughout the

District so stored water can be used for recreational

activities.

8. Pollution Abatement -- through protective works and controls,

the FCD is working to provide and maintain quality water.

9. Navigation -- small boat navigation is provided in canals

whenever practical and economically feasible.

The FCD's organization is structured to reflect the prevalent

attitudes of the people of south Florida. Policies are established by

a nine-man governing board of local people appointed for four-year

staggered terms by the governor and confirmed by the Florida Senate.

Daily activities are carried out by a staff of 750 in engineering, oper-

ation and maintenance, planning, land, legal, financial, and administra-

tive divisions. An executive director heads this organization.

The Florida Water Resources Act of 1972 makes the FCD one of five

water management districts in Florida and greatly increases their power

to carry out the above responsibilities. The district is granted

authority to issue permits to all consumptive users of water except

household (domestic) use. Broad powers are granted in the management

and storage of surface water and procedures for imposing restrictions

on water users in periods of water shortages are to be established to

protect water resources from serious harm. The governing board with

authorization of the Department of Natural Resources may determine,




-16-


establish, and control the level of water to be maintained in all canals,

lakes, rivers, channels, reservoirs, streams, or other bodies of water

controlled by the District. The board is also empowered to acquire fee

title to real property and easements for flood control, water storage,

water management, and preservation of wildlands, streams, and lakes.

These powers, along with regulation of wells, will allow coordinated

use of waters in the District.

The FCD, as an agency operating a complex physical system (see

Figure 1) in an area in which user demands have become greater and more

involved, has realized that more informed and versatile operational

procedures may extend the project's performance beyond that which was

originally anticipated. An approach which reflects the natural hydrology

and the potential of the physical system in conjunction with the economic

activities and institutional constraints occurring in the area is needed.

Computer models are thought to be feasible and practical. They would

feature the quantifiable characteristics of the hydrologic, physical

management, economic, and institutional systems while the Governing

Board would reflect the subtle nonquantifiable factors which must also

be considered. The result would be a short-term operational policy

compatible with long-term objectives but which is derived from greater

knowledge of the interactions of the various systems than would be

possible without the models.

The resulting operational policy would be programmed into daily

execution. This system uses as input actual rainfall over the area which

is automatically measured and the resulting data transmitted to the

operations center by telemetry. Various models digest the information

and determine a set of gate operations compatible with the short-term




-17-


Orlando


Atlantic
Ocean


Basin


Gulf of
Mexico


S, West
Palm
Si\Beach

|Cor er ioz




I Miami
Legend L


- -- Central and Southern Florida
Flood Control District boundary Vrga
tional-

Everglades National Park boundary P

Conservation Area boundary

Major canals



Figure 1. A schematic diagram of the FCD system in south Florida.




-18-


policy, and these in turn are beamed back to the field and executed.

Figure 2 illustrates a conceptual model designed to develop

operational water management policy and then execute it by prescribing

a short-term gate operation schedule. The manner in which the policy

development side functions is as follows:

a) A proposed long-term regulation policy is specified. This

could be in the form of a gate regulation schedule (rule curve), water

use regulation, land use change, or any other modification.

b) This policy affects the form of the surface water management

model or the institutional constraint model.

c) Hydrologic data are the primary input to the surface water

management model, and the output is a set of lake surface elevations,

the lake system states.

d) The lake system states are input to the economic activities

model, which gives as output the levels of the various water use

activities and the net dollar benefits accruing to various activities

as a result of the regulation policy.

e) The lake states, benefit states, and institutional constraints

provide information on the reasonableness of the proposed regulation

policy. If not accepted, the policy is modified in light of the

evaluation results and another run is made.

f) If the policy is accepted, it is next evaluated by the

Governing Board in the light of considerations that cannot be quanti-

fied. If rejected, modifications and a new series of runs are made until

the policy is acceptable at the first level.

g) If accepted by the Governing Board, it becomes the short-term

operational policy and is used in execution.




-19-


J LJ j




-20-


The policy execution side functions in a similar manner.

a) Actual rainfall is continuously monitored and the data

transmitted to the operations center via the telemetry system.

b) The rainfall data provide input to the streamflow simulator,

which produces as output runoff into the lakes.

c) A set of gate operations is specified by the gate operations

model.

d) The gate operations and runoff values are the input to the

water surface elevations model, which gives as output a set of lake

surface elevations or the lake system states.

e) These states are evaluated in terms of what the short-term

operational policy specifies. In addition, Governing Board and staff

judgment can be used to establish evaluation criteria. If rejected,

a new set of gate operations is specified.

f) If accepted, the set of gate operations becomes the short-

term operations schedule.

The present study will investigate the decision-making procedure.

More specifically, it will interface the various models involved and

demonstrate the procedure by considering several types of policy changes.

The Upper Kissimmee River Basin was selected as the study area because

of the wealth of information available about the hydrology, water manage-

ment system, and water use activities.


The Study Area


The Upper Kissimmee River Basin lies in the central part of

Florida, as shown in Figure 1. The city of Orlando is located on the




-21-


upper boundary, with Walt Disney World and the towns of Kissimmee and

St. Cloud nearby. The area is approximately 1600 square miles and

topographically flat. The western boundary lies along the lower part of

the central ridge of Florida. The central, eastern, and southern parts

are very flat, with a slope seldom exceeding five feet per mile. The

elevation runs from 100 feet in the upper end to 60 feet in the Lake

Kissimmee district. The region originally had many shallow lakes and

swamps with small streams running between them. Water moved south in a

broad path and into the Kissimmee River, a poorly defined stream con-

sisting of many small channels and a two-mile-wide swampy flood plain.

This was the major source of water for Okeechobee and South Florida.

In recent times the basin has been greatly modified. Canals have

been dug and control structures installed to control flooding. The major

lakes are connected by these canals and small streams connect the smaller

lakes. The basin consists of 14 sub-basins or watersheds that empty into

ten major lakes. Figure 3 illustrates the location of these sub-basins,

lakes, canals, and structures.

The predominant use of surface water has been for recreation.

Swimming, water skiing, and boating are popular. Traditionally, the

lakes have provided some of the best fishing in the South. The wildlife

is not unique, but hunting of deer and fowl is good.

Drainage has made agriculture more profitable. The major portion

of the land is unimproved native pasture; however, much improvement is

underway. Pasture is not generally irrigated, but, when it is, ground

water is most often used. Citrus is predominately on the western ridge

and is irrigated with ground water. Increasing acreage is being

developed on the flatwood soils and requires extensive drainage to




-22-


Legend

.-- Upper Kissimmee River Boundary
Sub-basin boundary
Lake outline
-II Canal and control structure
---5gp Water flow

Figure 3. Upper Kissimmee River Basin.




-23-


provide 60 inches of unsaturated root zone. Most of these new plantings

are irrigated with ground water, but groves near lakes and canals use

surface water. Small quantities of vegetable crops and ornamentals

are grown with ground water irrigation. Urban development in the northern

part has been occurring at an ever-increasing rate. Walt Disney World

has caused even greater growth in the area between Orlando and Kissimmee.

The basin is a popular one for retired people as well as for tourists.

These activities are, in general, placing heavy demands on the ground

water and causing severe deterioration of surface water quality.













CHAPTER III


THE SIMULATION MODEL


Conceptual Aspects


The FCD, in developing an approach to study operational policy

alternatives, must find one which will include the essence of the

complexities involved in surface water management. The influence of

the natural hydrology, the existing water management system, the water

use activities, and the formal and informal institutions must be reflected.

Inclusion of these is difficult because of the diversity in each but is

essential if reasonable policy alternatives are to be found. This study

suggests simulation as a means of considering various interactions. It

is believed that many characteristics can be mathematically modeled,

and quantitative parameters defined, to assist in policy evaluation.

This, tied with the Governing Board's reflection of subtle nonquantifi-

able factors, would provide a means of evaluating policy alternatives.

Figure 4 illustrates an information flow model, which is an expansion of

the area enclosed by dotted lines in Figure 2 and provides a framework

for a simulation approach.

The present study, more specifically, develops this conceptual

model into an integral operational model. Rainfall data for the basin

areeither synthesized or obtained from historic records, then distributed

over watersheds, and runoff determined. This in turn flows into the lakes

and is stored or released through management of gate-type structures.

-24-




-25-




-26-


Management criteria are specified by the long-term policies of the water

management authority. Lake surface elevations are generated, providing

information on the availability of water for various activities and the

level of these is determined. The quantified economic benefits, along

with the system states and the institutional considerations provide the

input into the policy evaluation. This evaluation is a technical

weighing of various parameters by the staff and is not itself modeled.

It does, however, provide a feedback into long-term policy and suggests

modifications.

The approach allows the water management authority to take

initial hydrologic information on very short intervals and assess on the

basis of long-term results the acceptability of the operational policy.

This is accomplished by inputing rainfall at 12-minute intervals,

thereby reflecting the natural variability. Runoff is determined at

three-hour intervals and lake surface elevations at six-hour intervals.

Economic activity levels are determined at varying intervals depending

on the activity, and net benefits are totalled annually. Therefore,

by operating the simulation, given a specific operational procedure, for

an extended period of time, information is produced which is used in the

policy evaluation.

The specific components or models making up the simulation are

illustrated in Figure 4. Each of these, the rainfall model, streamflow

model, water surface elevation model, gate operation model, and economic

activities model will be discussed in detail. The institutional con-

straint model is incorporated in the other models.




-27-


Hydrologic Models


The rainfall input can be provided from either of two sources.

The first, which is used in the present study, employs historic data

from rain-gauging stations in the basin to determine the rainfall over

each of the sub-basins. This is accomplished in two steps. Step one

distributes daily rainfall values at a geographic point into 24-hourly

values and then divides each hourly rainfall value into five equal

parts, thereby obtaining rainfall values at two-tenths-of-an-hour inter-

vals. The development of the relationships is based primarily upon the

work of Pattison [17], which considers a well acknowledged characteristic

of persistency in daily rainfall values. The distribution of rainfall

values at each gauge station is determined by statistically estimating

the hour of start of daily rain and the expected value of the hourly

rainfall. Step two estimates the two-tenths-of-an-hour-interval

rainfall values at grid points between the widely separated rain-gauging

stations. This approach is based essentially upon a square grid system

where the rainfall at any grid point or node is computed by applying an

appropriate weighting factor. These factors for each node are based on

the relative distances from the rain guages which are within a specified

distance of the node of interest. From these two-tenths-of-an-hour values

a single rainfall value for an entire sub-basin is computed by averaging

the weighted values over the sub-basin. Sinha and Khanal [22] have

described the two steps in detail and presented values for the Kissimmee

River Basin.

The second source utilizes a stochastic model to synthesize daily

rainfall input data. Rainfall at a point is a continuous hydrologic

process which can be transformed into a discrete process with a given




-28-


time interval. Rainfall amounts observed during different, short time

intervals (hours, days) are not independent events, and conditional

probabilities for these events can be estimated. The daily rainfall

process is similar to a Markov process. Due to these similarities, a

first-order Markov chain has been used to simulate the daily rainfall

process in the Kissimmee River Basin. Khanal and Hamrick [13] have

reported the details of this approach and the results for the basin. Data

from this source replaces the historic daily rainfall values obtained

from the twelve gauging stations.

The sub-model for simulating streamflow from rainfall events

involves using mathematical relationships for determining four broad

activities of the hydrologic cycle. These are (a) infiltration,

(b) water losses due to evaporation, transpiration, and deep ground

water percolation, (c) recovery of water into the stream channel from

soil reservoir and overland flow, and (d) routing the water from chan-

nel to watershed outlet. Figure 5 illustrates the relationship these

activities have to each other. The mathematical functions used in

the Kissimmee River Basin model have been developed by several re-

searchers and are presented by Sinha and Lindahl [23].

The volume of water moving into the soil profile is found by

empirical infiltration equations, which are primarily functions of soil

moisture. These are evaluated at the beginning and end of a time inter-

val. Water loss, water that reaches the ground surface but never appears

at the watershed outlet, is the total of these activities. An empirical

expression that reflects the fluctuations in depth to the water table is

used to specify the evaporation loss. The rate of loss is assumed to

never exceed the pan evaporation rate. Transpiration losses are assumed




-29-


Interception &
expressionn Stora


Figure 5. Flow diagram of streamflow simulation model.




to be primarily a function of pan evaporation and an overall growth index

for the existing vegetation. Deep percolation is a function of the rate

that gravitational water moves through the soil. Recovery of water into

stream channels is from two sources, subsurface flow and overland flow.

The mathematical relationships used to estimate the net surface discharge

are based on the continuity equation and a storage/outflow expression

developed empirically. These are solved in an iterative procedure. With

the subsurface discharge available, total storage is obtained from a

balance equation. Overland flow is the difference between the precipita-

tion and infiltration when surface depression storage is full. Two

routing equations have been used to obtain a time distribution of water




-30-


at the watershed outlet. The first was Nash's equation but this has been

replaced by a simpler expression. It uses an empirical time constant

associated with the source of the water -- surface or subsurface flow --

along with the average inflow and discharge at the beginning of the time

interval. The present streamflow model uses rainfall input on a 12-

minute interval and provides watershed discharge on a three-hour interval.

This in turn is used as input into the water surface elevation management

model.

The water surface elevation management model is the first point

at which management decisions can be made and water output affected.

Figure 3 shows the relationship of the actual watersheds, lakes, canals,

and structures in the Upper Kissimmee Basin. The fourteen watersheds or

sub-basins empty into the ten major lakes as presented in Table 1. Water

in Alligator Lake can move north through Lake Myrtle and around the

western chain, or south through Lake Gentry and into Cypress Lake, where

the western and eastern flows come together. The water movement is then

southward through Lake Kissimmee and down the Kissimmee River to Lake

Okeechobee. This series of lakes, canals, and structures provides the

management capability. By controlling the lake levels with nine control

gates, water can be retained or released.

The management components of the Upper Kissimmee Basin can be

generalized as shown schematically in Figure 6. Table 2 presents the

nomenclature that is used for each component. Water can be retained in

lakes 1-7 by management of the structures 1-9. The water discharged

moves down one of the canals 1-13 and into the next lake. All runoff

from the sub-basins entering the management system and all water with-

drawals are assumed to occur only at the lakes. Lake Tohopekaliga is




-31-


Table 1. Relationships of sub-basins, lakes, and control structures.



Sub-basin With Areaa Drains into Lake Controlled by Structure


60.50

37.91

57.68

89.67

52.93

185.66

132.77

198.75

89.22

119.63

109.85

197.78

197.78

94.70


Alligator

Myrtle

Mary Jane and Hart

East Tohopekaliga

East Tohopekaliga

Tohopekaliga

Tohopekaliga

Tohopekaliga

Gentry

Cypress

Hatchineha

Hatchineha

Kissimmee

Kissimmee


aArea is in square miles.


S-58 and S-60

S-57

S-62

S-59

S-59

S-61

S-61

S-61

S-63 and S-63A

S-65

S-65

S-65

S-65

S-65




-32-


Figure 6. Schematic diagram of the Upper Kissimmee River Basin water
management system.




-33-


Table 2. Symbols used to represent lakes, structures, and canals.



Symbol Represents


L Lake

1 Alligator
2 Myrtle
3 Mary Jane and Hart
4 East Tohopekaliga
5 Tohopekaliga
6 Gentry
7 Cypress, Hatchineha
and Kissimmee


J Structure

1 S-58
2 S-57
3 S-62
4 S-59
5 S-61
6 5-60
7 S-63
8 S-63A
9 S-65


K Canal

1 C-32 above S-58
2 C-32 below S-58
3 C-30 above S-57
4 C-30 below S-57
5 C-29 above S-62
6 C-29 below S-62
7 C-31 above S-59
8 C-31 below S-59
9 C-35 below S-61
10 C-33 above S-60
11 C-33 below S-60
12 C-34 above S-63A
13 C-34 below S-63A





-34-


shown schematically in Figure 7 to illustrate typical water flows into

and out of a lake. No return flows from consumptive uses are assumed.

The mathematical representation of water flow and management in

this generalized system can best be handled by considering several funda-

mental activities. The major purpose of the model is to determine lake

surface elevations at regular intervals, which is accomplished by deter-

mining the change in storage resulting in the flows illustrated in

Figure 7.

The general flow equation is


QNL, i=SUBQLi+QJup i-Qdowni-ACSL,i


where.

QNL,i = net flow rate for lake L in the time interval,

SUBQL,i = total runoff flow rate into lake L,1


Qj .u = flow rate into lake L from the upstream structure,


QJ down = flow rate out of lake L through the downstream
down'
structure, and

ACWSL,i = flow rate of consumptive withdrawals for lake L.

The lake surface elevation at the end of the present time interval,

STL,i, is then a function of the water stored in the lake at the end of

the previous time interval, STORL,i_,, and the net flow rate or


STL,i = s(STORL,il, QNL,i)-

With the ability to obtain the lake structure elevation it is possible


1
Water entering the lake from rainfall and water leaving the lake by
evaporation is included in SUBQL.
Li





-35-


Actual water
withdrawal for
domestic supply


S-61


Lake
Tohopekaliga


Outflow
to lakes
downstream


Actual water
withdrawal for
irrigation


Water losses due to
evaporation, seepage,
lock operations, etc.


Water inflows and outflows for Lake Tohopekaliga.


S-59


Inflow
from
lakes
upstream


Figure 7.




-36-


to compare these with institutionally established desired lake surface

elevations, DSTL,i. The manner in which these compare then specifies a

set of gate manipulations or operations, GO .. That is,
J ,1


GOJi = g(STL,i -1, DSTL,i)-

The gate operations and head and tailwater elevations at the end of the

previous time interval, HWSj,i 1 and TWSj,i 1' respectively, allow

calculation of the flow rates for the structure, QJ,i. Or, mathematically,


QJ,i = q(GO,i HWS,i 1, TWSji 1)

The consumptive withdrawal flow rate, ACWSL,i is an institutionally

-established function of the lake surface elevation and consumptive water

needs, in this case irrigation, IRLi, and domestic consumption, DCL,i.

Implicitly,

ACWSL,i = c(STL,i I' IRL,i. DCL,i)

The sequence of calculations is shown in Figure 8, and considera-

tion of the mathematical make-up of each component will be ,considered in

this order. Initially sub-basin runoff values are provided as input data

from the streamflow simulation model and a set of system states --

headwater, tailwater, and lake surface elevations are available from the

previous time interval. The consumptive water withdrawals are determined

from the irrigation and domestic consumption needs found in the water use

model and the institutionally established withdrawal functions. In this

study linear segmented functions specify the percentage of water needs that

can be met using surface water. These are illustrated in Figure 9 for

irrigation and domestic consumption.

The desired lake level is specified on any given day by an insti-

tutionally established linear segmented function, generally called the




-37-


System states at end of previous time interval,
STL,i HWSJ,i 1 TWSJ,i 1



Determination of total water withdrawals from
lakes during present time interval, ACWSL,
Lii


Determination of the desired water surface
elevation for present time interval, DSTL,



Establish the gate operations for the present
time interval, GOJ
J,i


Determine the discharge rate for the structures
for the time interval, Q



Determine the net flow rates for the lakes for
the time interval, QN
L,i


Determine the change in water storage and the
resulting lake surface elevation for the time
interval, ST
L,i


Determine the head and tailwater elevations for
the structures for the time interval,
HWS_ and TWS.
J'i Ji


I Continue to next time interval


Figure 8.


Sequence of calculations in the water surface elevation
management model.




-38-


100
Percent of
water needs
available for
irrigation,
PWNAIL



0 --
ZIWST DST
L L

Lake surface elevation, STL

(a) Irrigation withdrawal function


100
Percent of
water needs
available for
domestic
consumption
PWNADL

0
ZDWSTL RDWSTL DSTL


Lake surface elevation, ST

(b) Domestic consumption function

Figure 9. Consumptive withdrawal function.




55
Feet
above 54
mean 53
sea
level 52


0


J F M A M J JLA S O N D

Months of the year


Figure 10. A typical regulation schedule.




-39-


lake regulation schedule or rule curve. A typical one, in this case

for Lake Tohopekaliga, is shown in Figure 10. The gate operation, the

number of feet a given gate is opened, is a function of the difference

between the actual lake level at the end of the previous time interval

and the desired lake level for the present interval, and is specified

by DDAL. The function used is illustrated in Figure 11. The percent of

the maximum gate operation is determined and multiplied times the maximum

gate opening.



100
PGOMj = 0, DDAL < 0
Percent of maximum 2
gate operation, PGOMj = 400 (DDAL),
PGOM
0 DDAL 0.5

PGOM = 100, 0.5 I DDAL



0 1
0 0.5

Difference between actual lake level
and desired lake level, DDAL, in feet


Figure 11. The gate operation function.



The flow rate through a given structure during the time interval

can be obtained from the gate operation and the effective head across the

structure. It is assumed the difference between the headwater elevation

and the tailwater elevation at the end of the previous time interval

represents the effective head during the present interval. That is,

EJ,i = HSJ,i 1 TWSJi I1.




-40-


flow through the gate-type structures is given by


Q i= PJ (GO i)rJ (EH i)sJ
Jsi J J,i J,i

where pj, rj, and sJ are regression-determined characteristic coefficients

for the individual structures.

With these values the net flow rates for each of the lakes during

the time interval can be found. And this, along with the stored water, is

used to determine the lake surface elevation at the end of the present time

interval. The set of lake surface elevations is the basic input into the

water use models.

Headwater and tailwater elevations occurring at the end of the

present time interval must be calculated as they are needed for determining

the effective head in the next time interval. In the study, two situa-

tions occur. These are illustrated by using East Lake Tohopekaliga and

Lake Tohopekaliga schematically in Figure 12. In the first case

structure 4 has a canal, 7, leading to it and one, 8, leading from it.

When structure 4 is open, the headwater elevation for it will be different

from the water surface elevation for lake 4. Likewise the tailwater

elevation will differ from the water surface elevation for lake 5.






J=4 J=5
Inflow 3 L=4 > ----B- L=5 -- Outflow


Figure 12. Schematic diagram of the lake, canal, and control structure
relationship.




-41-


The second case has the structure at the lake exit so there is no upstream

canal. The headwater elevation for structure 5 will be the same as the

water surface elevation for lake 5. The tailwater elevation will be

different from the downstream lake.

A technique developed by Prasad [19] and suggested by Sinha [21]

was used to compute the water surface profile along the canals. A change

in water surface elevation, WSE, with respect to space can be represented

by,

d(WSE) = dB + dy where B = C + z.
dx dx dx

Integrating we get:

WSE B + y = C + z + y

where

WSE = water surface elevation,

B = stream bed elevation from mean sea level at upstream point

of the reach,

c = stream bed elevation from mean sea level at downstream

point of the reach,

x = distance along the stream bed,

z = change in bed elevation between upstream point and

downstream point of the reach, and

y = depth of water.

The differential equation of gradually varied flow provides the relation-

ship between water depth and distance and can be expressed:

dy SO SE
dx 2

gA3




-42-


where

SO = slope along the stream bed

SE = energy gradient

a = velocity head coefficient

Q = discharge through a given control structure,

T = top width of the channel cross-section,

g = acceleration due to gravity, and

A = cross-sectional area of the channel.

Manning's formula can be used for energy gradient.


SE = (RN)2 V2
2.22 (HR)4/3

or substituting

V + Q and HR = A
A P

SE = (RN2 2 P/3
2.22 A10/3

where

V = velocity of flow,

RN = Manning's roughness coefficient,

HR = hydraulic radius, and

P = wetted perimeter.

Substituting the energy gradient expression into the gradually varied

flow equation, the result is:

2 2 4/3
(RN)2 Q2 P4/3
d SO 2.22A10/3
dx
1 2T
gA3




-43-


This differential equation is a nonlinear function of y and is not

readily solved analytically. Prasad 119] has developed a digital

algorithm for solving the equation. The technique readily handles

non-uniform channels and allows water surface profiles to be computed

moving upstream or downstream.

Headwater elevations are thus found by starting at the lake outlet

where the water surface elevation is the same as the lake surface eleva-

tion, or

WSE = STL.

The water surface profile is then determined by moving downstream to the

structure. The intersection of the water surface profile and the structure

gives the headwater elevation, HWS .. The tailwater elevation, TWS .,
J, *,1
is found in a like manner except the profile is calculated moving upstream

from the lower lake. The headwater and tailwater elevations at the end

of the present time interval are now available for use in determining the

flow rate through the structure during the next time interval.

The time interval used in this portion of the simulation is six

hours in length. The sub-basin runoff values are aggregated to six hours.

The results from the water surface elevation management model are,

therefore, lake surface elevations for all lakes every six hours.

The institutional constraint model is not a distinct entity as

are the other models but is a series of constraint functions incorporated

in the others. The institutionally established regulation schedules for

the lakes (see Figure 9) are built into the water surface elevation model.

Each specifies the lake surface elevation for every day of the year. The

schedule in this way reflects attitudes of society, through the FCD, as

to how water in the lakes should be managed. Attitudes about the discharge




-44


or export of water from a basin to another area are handled likewise.

Minimum flows through outlet structures are handled in the water surface

model thus satisfying the institutionally established water export

requirements. The water withdrawal functions (see Figure 10) are built

into the water use activities models in a similar manner. They indicate

how the water should be allocated when the water availability is at

certain levels. Society's attitudes about distribution of a scarce water

supply are again reflected through the FCD.


Water Use Activities Models


The present study assumes four economic activities related to

surface water. The net benefits accruing to these for spatial and

temporal control of water are the primary indices of the management

system's performance. Crop irrigation and domestic water supply are

consumptive uses while recreation simply uses stored water. Property

flooding is a result of excess surface water. All of these are functions

of the amount of water in storage. The two consumptive uses gain more

when larger quantities of water are conserved. The potential for flood

damages increases with greater quantities of stored water and decreases

with lesser quantities. Recreational use is only influenced at the extreme

high and low water levels. Therefore, management of the system is pri-

marily a trade-off between consumptive uses and flood control. This

section of the study considers the determination of the benefits

accruing to each of the activities from a given management procedure.

Surface water available for irrigation is a function of the amount

of water available, and, as mentioned above, the function is institutionally




-45-


established. With the lake levels known, the percentage of the irriga-

tion water needs that can be furnished can be determined. During the

growing season the water needs for a crop are based on the irrigation

water required to bring the soil to field capacity. Irrigation water

is not applied until the soil moisture is depleted to one-third of the

soil moisture available between the permanent wilting point and field

capacity. When rainfall is applied the total moisture available to

the crops during a given time interval is the sum of the moisture at

the end of the previous time period, SMA. and the water entering

the soil profile from irrigation, WESI., and rainfall, WESR..

Plant water use is based on the evapotranspiration equation pro-

posed by Blaney and Criddle [3]. A modified form proposed by Phelcn [18]

was used to estimate monthly potential evapotranspiration rates. It is

given by


ET = k k TaPd
p ct 100

where

ET = monthly potential evapotranspiration rate in inches of
P
water,

k = monthly crop coefficient which is a function of physiology
c
and stage of growth of the crop,

k = temperature coefficient which is given by

kt = 0.0173 Ta 0.314,

T = mean monthly temperature in OF, and

Pd = monthly percentage of daylight hours of the year.
d




-46-


The potential evapotranspiration for a given time interval is obtained

by dividing the monthly potential evapotranspiration by the number of

time intervals in the month. The actual evapotranspiration occurring is

assumed to be a function of soil moisture. Studies at the United States

Salinity Laboratory in California [8] indicate transpiration occurs at

the full potential rate until a critical point in the available soil

moisture is reached; thereafter the actual evapotranspiration lags

the potential. Figure 13 illustrates the function used to obtain the

proportion of the potential that gives the actual evapotranspiration




1.0

Proportion of
potential
evapotranspiration,
PET



0 ^ Z -- ,.---------
SMPW SMCR SMFC

Soil moisture, SMA, inches of water.





Figure 13. Potential evapotranspiration function.



in a given time interval. Therefore

AET = ET SMCR < SMA
i pi i

AET. = PET ET ., SMPW < SMA. < SMCR
1 p,i.


AET. = 0, SMA < SMPW
1




-47-


where

ET = potential evapotranspiration during time interval i,

AET. = actual evapotranspiration during time interval i,

PET = percent of potential evapotranspiration actually occurring,

SMA. = soil moisture during time interval i,

SMFC = soil moisture at field capacity,

SMPW = soil moisture at permanent wilting point, and

SMCR = soil moisture at critical point.

The soil profile moisture at the end of a time interval is

SMA. = SMA + WEST + WESR AET..
i -i 1 i 3
It was assumed deep percolation occurs only when available soil moisture

is at its capacity level. The soil moisture is used in the next time

period to determine whether irrigation water will be applied and the

rate at which evapotranspiration will occur.

The actual evapotranspiration occurring during each time interval

is accumulated through the entire growing season to obtain the total water

used by the crop. This is done for each crop, first, with both rainfall

and irrigation water as the total water available and, second, with just

rainfall as the total water available. At the end of the growing season

there are two effective water inputs for each crop, ETtotal, the actual

total evapotranspiration when irrigation as well as rainfall is available,

and ETr the actual total evapotranspiration when only rainfall is used.
rain
The availability of effective water on crop yields can be trans-

lated into benefits accruing to the users of water and used along with

the benefits accruing to other uses of water as an index of water manage-

ment effectiveness. To do this, the concept of producer surplus will be

used, and the surplus is assumed to be the benefits accruing to society

as a result of irrigation water being available. The producer surplus




-48-


is readily demonstrated by using traditional neoclassical production

theory and assuming perfect competition in all markets. First, a crop

production function is used which translates available effective water

to crop yields when all other production factors are held constant.

The traditional idealized production function is, implicitly,

YIELD = y(ET, all other factors held constant)

and is illustrated along with the marginal physical product curve, MPP,

and the average physical product curve, APP, in Figure 14. The crop

yields with and without irrigation water, YIELD and YIELD ,
total rain
respectively, are obtained by solving the production function with

ET totaand ETrain, respectively. Multiplying the marginal physical

product by the price of the crop, P the marginal value product, MVP,

is obtained. Mathematically,


MPP = TP)



MVP = P (TP)
y (ET),

and, graphically, Figure 15. The price of the crop is assumed to be

independent of activities in the river basin and constant, and is

therefore the marginal revenue. First, substituting ETtotal, and

integrating, the total revenue for the irrigated crop, TRtotal, is

obtained,

ET
E total
TR = a(TP) d(ET),.
total y D(ET)




-49-


Production
per acre
(YIELD)


Effective water, ET
inches of water


Figure 14.


Typical production, average physical product, and marginal
physical product curves.


Dollars
per
unit


rain total


Effective water, ET
inches of water


Figure 15. Typical marginal value product curve.


APP




-50-


doing likewise with ET in, the total revenue for the crop without

irrigation water, TR is obtained,
rain

ER
rain
TRin= P 2T) d(ET).
rain 7Y 3(ET)
0


The producer surplus, PS, for each of these cases is the total revenue

minus the price times the quantity. In the case of rainfall, no price

was paid so the total revenue due to the effective water is the producer

surplus. In the case of rainfall and irrigation, there is a price paid for

just the irrigation water, so


P = 0, 0 < ET < ETrain
w rain


and


P = P ET < ET < ET
w wa rain total


where

P = price of water, and

P = price of irrigation water actually paid.
wa

The producer surplus for this case is

PS = TR P (ET ET .).
total total wa total rain


This is the producer surplus accruing to all the effective water without

regard to its source. Only the irrigation water is available as a result

of the water management system. Therefore, only the producer surplus




-51-


associated with the irrigation water is an appropriate indication of

benefits due to the system management. The producer surplus for

effective water from rainfall is subtracted from the producer surplus

for the total effective water. Mathematically, this is

ET
total
PS = P 3(TP) d(ET) P (ET ET )
y a(ET) total rain
S0


ET

P (TP) d(ET)
y 3(ET)
0

and graphically,the shaded area in Figure 15.

The present study considered two crops, irrigated pasture and

citrus. Irrigation water is assumed to be available in only sub-basins

in which lakes are located. The growing season is the entire year, so

actual evapotranspiration is determined daily and accumulated for the

entire year. The management of water in each lake causes the available

water to vary so that the actual evapotranspiration varies. The result-

ing producer surplus for each crop provides the benefits due to irri-

gation water being available for each crop grown near each of the lakes.

Surface water available for residential consumption is a function

of the amount of water stored, and, as mentioned above, the function is

institutionally established. The amount of water that can be removed

from a lake is given as a percentage of the water needed. To obtain the

maximum amount of water needed, an average consumer is assumed and his

needs determined. Howe and Linaweaver [11] in an extensive study have

formulated residential water demand models and estimated the relevant

parameters from cross-sectional data. Their equation for total




-52-


residential demand was used and is


qs = 86.3 v0474 (w 0.6r )0.626 p-0.405


where

qa = average annual quantity demanded for domestic purposes

in gallons per dwelling unit per day,

v = market value of the dwelling unit in thousands of dollars,

(ws 0.6rs) = lawn irrigation water needs in inches of water, and

pa = the sum of water and sewer charges that vary with water use,

evaluated at the block rate applicable to the average domestic

use in cents per thousand gallons.

The average market value of the dwellings in the Kissimmee Basin,

the average irrigation water needs for lawn grass, and total water price

at the block rate applicable to the average domestic use were used in

this equation to obtain the maximum daily water desired by each

dwelling, WCPD. The actual daily water provided from surface water, GPD,

is the product of this desired quantity and the percent of needs allowed.

The balance of water the consumer demands, WCPD GPD, is obtained from

ground water.

The consumer surplus for domestic water consumption is assumed to

be the benefits accruing to the water for residential use. The total

residential water demand equation above is assumed to represent the

demand for water up to a specific price, PRIU. At this point the demand

function becomes perfectly elastic and is therefore a horizontal line to

the origin (See Figure 16). It is assumed that at this price other

sources of water become feasible. The consumer surplus for residential




-53-


use is

PRIU

CSURP = f q(p a) dp (PRIL WCPD).

PRIL

The portion of consumer surplus gained from surface water is



PRIU PRIW

J qa(Pa) dpa / a(Pa) dpa + (PRIW PRIL) GPD

PRIL PRIL

or simply

PRIU

S a(Pa) dpa + (PRIW PRIL) GPD,
PRIW

where

CSURP = the consumer surplus for residential use of surface

water in cents,

q a(p) = the demand function for residential water,

pa = price of residential water,

PRIU = highest price consumers will pay for water, in cents per

thousand gallons,

PRIW = price consumers would pay for the actual quantity of

surface water they received, in cents per thousand gallons,

PRIL = the price the consumer must actually pay for water, in

cents per thousand gallons, and

GPD = quantity of surface water actually received in gallons per

day.




-54-


PRIU


Water price,
cents per
thousand
gallons


PRIW


Figure 16.


PRIL ( J_ X/_/_/_r
APRIL


I i

I I

GPD WCPD

Average daily water consumption,
gallons per dwelling per day

Residential water demand function.


The shaded area of Figure 16 illustrates the consumer surplus for

all residential water, and the lightly shaded area is the consumer surplus

for surface water. Or, the consumer surplus for surface water is the bene-

fits accruing to the availability of surface water for residential use. The

actual quantity of water used by residents from each lake is determined

daily, and these quantities accumulated for the entire year. This

quantity is then used to calculate the consumer surplus for the yearly

consumption of surface water from each lake.

The lakes of the basin are used extensively for recreation, and

the level of use is influenced by the depth of water. This is true

because the lakes are quite shallow, and several feet of fluctuation

drastically affects boating. When the water surface elevation is low,




-55-


large areas of the bottom are covered with only a foot or two of water,

and, when the lake surface is high, access is limited and boat launching

is difficult. Therefore, recreational use is assumed to be a function

of water surface elevation as illustrated in Figure 17. Implicitly this

may be written [2]

V = V(WL, T, D2, Rd, WV),

where

V = number of visitors to lake per day,

WL = lake surface elevation in feet above MSL,

T = daily temperature in 0F

W = highest daily wind velocity in mph,

Rd = number of days of rain, and

D2 = season of the year.

If this is assumed to be similar to a production function, the first partial

derivation with respect to water level can be taken and considered as a

marginal physical product. That is,


3V
MPP =- ,
r aWL

and the marginal value product is


MVP = P
r v aw


The price of a visit, Pv, is assumed to be independent of the number of

visits and is used as the marginal revenue of a visit. Benefits to

recreational use of water can then be written

W
Lo


L v L L
m
m





-56-


Number of
recreational
visits, V


v(WL, all other
factors constant)


WL WL
m o


Lake surface elevation,
WL, feet above MSL


MVP P av
r V aWL


Lake surface elevation,
WL, feet above MSL


Recreational visit functions.


Dollars
per
visit


Figure 17.




-57-


where

W = the actual lake surface elevation, and
L

W = the elevation of the bottom of the lake in feet above MSL.
Lm

There is no price for water level management; therefore, the benefits are

the entire area under the marginal value product curve. It should be

noted that the water surface elevation may be at any level and that

recreational visits will be made. That is, limiting consideration to

Stage II of the production function is no longer correct. This results

in the situation shown in Figure 17, where the water surface elevation is

above the point of highest use. The benefits accruing to this water level

are shown by the shaded area above the axis minus the shaded area below.

The value of a visit, Pv, is not readily attainable, because there

is no true market for recreational visits to the lakes of the Kissimmee

Basin. McGuire [15] has estimated a demand function for recreation on

these lakes by an average individual, Dr. In doing this, he assumed that

the average individual's demand for recreation on the lake is not affected

by the lake level. Some marginal users stop using the lake, but the

average individual's demand remains the same. Since this is the case,

the consumer surplus for an average individual making an average visit

remains constant for varying water levels. Figure 18 illustrates this.

Here q is the average length of stay per visit, p is the corresponding

price, and p* is the highest price the average visitor will pay. The

consumer surplus is

P*

/ Dr dp




-58-


Visit price,
dollars/visit




p


Dr


q Length of stay per
visit, days

Figure 18. Recreation demand function.



and is illustrated by the shaded area in Figure 18. The value of a visit

to be used in the benefit function is the consumer surplus for an average

individual making an average visit to the lake.

Benefits are higher in the first three water use activities when

greater quantities of water are conserved. But, in the case of flood

prevention, the lower the lake surface elevation and conserved water, the

lower the probability of floods occurring. The higher the level, the

higher the probability of flooding and the resulting flood damages. So,

when flood protection becomes a concern in lake water management, there

are conflicting operational objectives. The stochastic nature of rain-

fall aggravates the situation and makes the finding of a reasonably

balanced operational policy difficult.

Flood damages are a function of the lake level and the activities

at various elevations. In the case of agricultural crops, the duration

of the flood is also a factor. Damage to crops increases with the time




-59-


of exposure to saturated soil conditions until finally the crop is killed.

The tolerance of crops to wet conditions varies; some crops can survive

adverse conditions for long periods. Urban property and rural structures

are considered to be damaged immediately; duration of flooding is not a

factor. Momentary wetting of structures and machinery causes maximum

damages.

The lack of demand functions for flood protection makes it impossi-

ble to use the surplus concept to determine benefits as was used for the

other water use activities. The only avenue open for placing an economic

value on the flooding phenomenon is to use the market value of replacing

the damaged property. Lost net revenue to productive activities should

also be considered. Flood damages resulting from lake water management

policy are thus considered negative benefits.

Water surface elevations in the lakes are available every six

hours from the water management model, making it possible to monitor all

floods occurring. Urban and structure damage is determined by entering

the maximum flood stage in an aggregate damage function. In the present

study a simple linear segmented expression is used. It is assumed that

thirty days are required to repair urban and rural structure damages, so

property previously damaged cannot be redamaged until thirty days has

elapsed. Figure 19a illustrates the function for a typical lake. Crop

damages are obtained by determining the mean flood stage during the

duration of the flood. These, the mean stage and length of flood, are

entered in a crop aggregate damage function. Figure 19b illustrates

such a function for a given crop growing adjacent to a given lake.




-60-


Aggregate
damages to
urban property
and rural
structures,
dollars


0 zero
damage
stage


Lake stage, feet above mean
sea level


(a) An urban property and rural structures damage function.








Aggregate
damage to /
crops, o/
dollars Z


approximate
maximum stage


Lake stage, feet above mean sea level


(b) A crop damage function.


Figure 19. Flood damage functions for a typical lake.


r I




-61-


Policy Evaluation Capabilities of the Model


Simulation models, by their very nature, allow easy modification

of function specification. This provides a ready means of considering

policy changes and the resulting effect on the overall management system.

The proposed changes, however, must come from an understanding of the

nature of the management and not a haphazard altering of variables and

functions. The suggested policy changes will come from the technical

staff after thorough study of the problems facing the water management

authority.

The simulation model can readily handle investigations of policy

concerned with spatial and temporal allocation of surface water as well

as changes in surface water demand by specific economic activities. The

water stored in the system of lakes is a function of the management of

the control gates. The actual day-to-day operation of the gates is

specified by the regulation schedules or rule curves for each structure.

These rule curves are the long-term management policy. Briefly, they

indicate that on a given day the water surface elevation of a given lake

should be at a certain level. The schedule is given for an entire year.

It is by varying the shape of these rule curves that alternative spatial

and temporal allocations can be considered. In this case, the informa-

tion flow in Figure 4 is from the long-term surface regulation policy box

into the gate operation model.

A typical investigative simulation would be as follows: Basin

input into the water management sub-model is a generated set of sub-basin

runoffs from the rainfall and streamflow sub-models. The gate openings

during the run are determined by the specified rule curves. The




-62-


resulting set of lake states is submitted to the economic activities

model, and the net benefits accruing to this management procedure

determined. The run would be made over a sufficient period of time to

allow the stochastic character of the hydrology to be reflected in the

sets of lake states and benefit states. Alternative regulation schedules

would be examined in a similar manner using the same input data set.

Variation of the regulation schedules for structures within the

basin allows study of spatial and temporal allocation within the study

basin. In a similar manner, the effect of water exported from the basin

on the benefits accruing to the basin can be investigated. To accomplish

this, specific flow rates through the outlet structure are set, and the

effect on the lakes determined.

The effects of land and water use changes on net benefits accruing

to the basin can also be readily explored. Particular changes in land

use, the resulting change in water demand, and the regulations allowing

surface water withdrawal are considered. In the land use case the

particular changes are entered by modifying the appropriate variables in

the water use activities model. When the water withdrawal regulations

are altered, the function changes are made in the institutional constraint

model. In both cases, a set of runoff values is used, and a set of

lake states determined. The net benefits to this set of states and water

uses are calculated and provided an indication of the effects of the use

changes.

The use of the simulation for each of these policy considerations

and activity changes will be demonstrated. A complete study of each will

not be performed; but, rather the type of information resulting from a

study and used in the policy evaluation by the staff will be generated.













CHAPTER IV


BASIC DATA INPUTS TO THE MODEL


Many interesting simulation models can be conceptualized, but

never materialize into useful tools. They are seen to have real

potential in considering the complex interactions of water resource

allocation problems, but often are not used because there are insuf-

ficient, low-cost data. A first attempt at modeling a system, however,

can often be made with very limited data, and this can point out where

more precise data are needed. A working model should be developed as

early as possible.

In this present study some of the data are quite accurate, while

others are only approximations. An early working model was desired, so

the usefulness of an integrated approach could be demonstrated. The

following describes the type of data and functions used in the working

model.


Hydrologic Data


The hydrologic input is obtained from the FCD rainfall and

streamflow models. These models were developed and put into operational

form by the FCD [22, 23]. Rainfall can be either historic or synthetic,

but for the present study, daily historic data collected from twelve

gauging stations in the basin are used. The daily values are distributed

in the twenty-four hours and over the fourteen sub-basins. The

-63-




-64-


distributed values in turn are translated into three-hour runoff quanti-

ties for the sub-basins. The FCD generates the three-hour runoff values

for each of fourteen sub-basins and these provide the fundamental hydro-

logic input to the models constructed for the present study.


Water Management System Data


The water management model consists of a series of components

describing the lakes, gate structures, and canals, and the manner in

which they are used. Water surface elevation is a function of the

quantity of stored water and the lake configuration. The relationships

for the seven lakes are presented in Table 3, and were obtained using one

foot-interval contour maps. The gate structure relationships were

obtained empirically by the FCD, and are presented in Table 4. The canals,

although actually having somewhat irregular bottom slopes and cross-

sections, were assumed to have constant bottom slopes and uniform cross-

sections throughout the length of each reach. Data providing cross-

section characteristics at 200-foot intervals are available but would be

expensive to use. The model for calculating the water surface elevations

along the canal can easily accept these data if needed for greater

accuracy. The characteristics used are presented in Table 5.

Surface water available for irrigation and domestic consumption

is controlled by the FCD. Very little surface water is presently used

for either of these activities, and this is managed through permits.

When large quantities of surface water are needed in the future, the

amount allowed will have to be controlled, so the present study suggests

the amount be a function of lake surface elevations or available storage.




-65-


Table 3. Relationships between water storage levels and lake storage.

Lake Surface
Elevations, Lake
ft. above
mean sea
level 1 2 3 4 5 6 7


------ --- Storage in acre-feet -----------

42 1,050 72 64,000
43 1,105 111 81,000
44 1,160 160 103,800
45 1,955 226 130,530
46 2,750 318 8,000 179,030
47 3,390 444 17,000 217,630
48 4.025 653 24,900 26,000 259,700
49 4,745 955 33,400 40,500 306,100
50 5,478 1,381 42,400 55,300 357,300
51 .6,400 1,989 51,900 69,000 414,100
52 7,365 165 2,890 61,800 84,000 475,900
53 9,482 602 4.032 71,800 101,200 541,800
54 12,659 1,137 5,151 82,700 122,600 5,600 625,200
55 15,010 1.679 6,520 94,200 144,200 6,700 727,900
56 17,970 2,436 8,105 106,000 170,500 8,000 851,200
57 21,387 3,296 9,827 118,300 194,700 9,300 986,000
58 25,296 4,286 11,739 130,000 222,600 10,800 1,181,500
59 29,545 5,446 14,000 143,700 250,000 12,300
60 34,440 6,805 16,248 158,600 280,500 13,900
61 39,518 8,077 17,480 176,400 306,000 15,500
62 44,950 9,632 20,900 194,300 335,000 17,200
63 50,555 11,421 23,940 210,500 360,000 20,000
64 57,430 13,611 27,200 227,500 390,000 23,700
65 66,966 16,456 33,400 250,000 420,000 29,000
66 80,615 35,600
67 98,434 42,000
68 120,348 48,300






-66-


C4


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C14 a






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S4 5 I 1 M .





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-67-


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-68-


Table 5. Canal characteristics.


Bottom Manning's Upper End Length of
Canal Width, Side Roughness Elevation, Bottom Reach,
No. Ft. Slope Coefficient Ft. MSL Slope Ft.


1 5 1/2 0.168 52.80 5.8x10-6 4,751

2 5 1/2 0.168 51.50 5.8x10-6 6,200

3 5 1/2 0.168 51.25 7.0x10-5 7,245

4 5 1/2 0.168 49.90 1.21x10-4 5,762

5 10 1/2 0.168 48.60 l.11x10-4 898

6 10 1/2 0.168 47.00 1.43x10-4 6,912

7 20 1/2 0.168 46.60 1.48xi0-4 2,425

8 20 1/2 0.168 45.00 1.26xl0-4 18,280

9 20 1/2 0.168 34.00 5.6xl0-5 23,200

10 10 1/2 0.168 53.45 2.47x10-4 4,016

11 10 1/2 0.168 51.00 5.2x10-5 9,602

12 40 1/2 0.168 46.70 4.22x104 15,080

13 60 1/2 0.168 40.50 9.6xl0-5 15,461




The functions used are given in Figure 23 (see Chapter V). The actual shape

of these will be varied to determine the effect of different consumptive

withdrawal policies (see Figure 23, Chapter V).


Water Use Data


The irrigation simulation produces the crop yield possible with the

water available and determines the net revenue for the crop. Surface

water and rainfall provide the available water. Sixty percent of the

rainfall and seventy percent of the applied irrigation water are assumed




-69-


to be available in the root zone. The evapotranspiration by the crop is

utilized in a production function, and variations in this cause different

crop yields. The maximum monthly evapotranspiration values for pasture

grass and citrus in the Kissimmee Basin were obtained from the Soil

Conservation Service and are presented in Table 6. The actual evapotranspir-

ation is a function of soil moisture, and daily calculations of both are

made. The moisture retention capacity of the soils is important, and

the parameters for the sandy soil of the Kissimmee Basin, assumed to be

predominantly Leon fine sand, are given in Table 7.

The crop yields and production costs were obtained from data

collected by Conner and Reynolds.* For this first generation simulation

simple linear production functions are used, and are assumed to approxi-

mate Stage II production with all other factors held constant. The

source data showed costs were a function of crop yield as well as the

amount of irrigation water applied, indicating all other factors were

not actually constant. These were, however, the best data available

at the time. Prices of all goods were assumed not to be affected by the

activities in the basin. That is, perfect competition in all models was

assumed. Since the production function is linear and prices perfectly

elastic, the marginal value product line is horizontal, and the producer

surplus for a crop with irrigation is


PStotal,L = y (YIELDtotal) COSTtotal,L




*J. R. Conner and J. E. Reynolds, personal communication.




-70-


r. -: in en r- 0 -4U
.0 *o ** W 0m

U,


NMNOc C,-- O m m cMO
*1* *


C
0
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ca u

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Ta r-A c i o n m ,-4 cno Mcn
* *m*


\0 o 00r 0 r


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hmONO


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4s4<4Z n-:4M0 ZQ


0 C In n "M OOM r-4 r--OO m w

orr moo 10 M


co ,-I

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CMO% i 00 C4
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-71-


Table 7. Soil information.


Crop
Soil Characteristics Pasture Citrus


Field capacity (0.1 atm), inches of
water per foot of soil 1.50 1.50

Permanent wilting point (15 atm)
inches of water per foot of soil 0.55 0.55

Root zone, inches of soil 36.00 60.00

Available moisture at field capacity,
SMFC, inches of water 4.50 7.50

Available moisture at permanent wilt-
ing point, SMPW, inches of water 1.65 2.75

Available moisture at point where ET
begins to decrease, SMCR, inches of
water 2.60 4.33


and without irrigation


PSrain = P (YIELD ) COST
rainL y rainL rain,L.


The producer surplus indicating the level of benefits due to the availa-

bility of surface water from a given lake for irrigation is


PSL = PStotal,L PSrain,L.


Table 8 gives the equations used for crop yields and production costs, as

well as crop prices.

The calculation of consumer surplus for residential use of surface

water requires the total amount of water an average household uses, WCPD.

The quantity assumed for the Kissimmee River Basin is 13,500 gallons per




-72-


Table 8. Crop yields, production costs, and prices.


Crop Yield Functions

a. Beef yields in pounds/acre

YIELDB,L = -200 + 14(ETB,L), 20 ETB,L 70


b. Mixed citrus yields in boxes per acre

YIELDCL = -300 + 17(ETCL), 20 ETCL 70



Cost Functions

a. Beef production costs in dollars per acre

COSTB,L = 8.76 + 0.1 (YIELDB,L) + 0.056(ETtotal,B,L,- ETrain,B,L)


b. Citrus production costs

COSTC,L = 172.02 + 0.145(YIELDC,L) + 2.40(ETtotal,C,L ETrain,C,L)


Crop Prices

a. Beef price in dollars per pound

PRIB = 0.25a

b. Mixed citrus price in dollars per 90 pound box

PRIC = 1.40a


a
Average prices for period 1968 through 1970.



month or WCPD is 370 gallons per day.* On the charge rate schedules for

Kissimmee and St. Cloud, this quantity corresponds to a combined water and




* This figure was obtained by questioning officials of the Kissimmee and
St. Cloud utilities departments and is an estimate.




-73-


sewer charge of 60 cents per thousand gallons. The residential demand

function becomes


q = 1930.669 (p )-.405


when an average market value for dwellings of $20,000, and an average lawn

irrigation requirement of fifteen inches per year are used.* Substitution

of qa = 370 gallons per day again gives a price of approximately 60 cents.

The proportion of daily water needs that can be removed from the

lakes is specified by the institutionally established withdrawal functions.

This proportion and the total water needs, WCPD, give the quantity of

water removed from the lake, GPDL. Substituting GPDL into the demand

equation gives PRIWL. PRIU is set at 120 cents per thousand gallons, and

PRIL is then above 60 cents per thousand gallons. With this information

the consumer surplus for each dwelling can be calculated. Only lake 4

and 5 were assumed to have residents using surface water. Lake 4 had

1580 dwellings in the surrounding area and lake 5 had 4750. Using

the consumer surplus on a lake, the benefits accruing to the use of

surface water can be found.

Behar [2] has demonstrated the effect of water surface elevation

on recreational visits to lakes in the Kissimmee Basin with his linear

relationship for Lake Tohopekaliga. More specifically, he found a

reduction of 25.63 visits per foot decrease in water level below the

minimum desired level. This represents 11.5 percent of the 223.32 visits

per day average, and implies for each foot of drop there is an 11.5 percent




Again, these are estimates obtained by informal questioning of various
people in Kissimmee and St. Cloud.




-74-


drop in the number of visits. Or, in a range of 8.7 feet, there will be a

100 percent drop in visits. There are no data to support a decrease in

visits for surface elevations above the minimum desired level, but it is

reasonable to assume this is the case. Lake Tohopekaliga was assumed to

be typical of the lakes in the basin, and Behar's 11.5 percent per foot

of lake surface drop was used when the lake surfaces were below the desired

level. A 20 percent decrease in visits per foot of water surface

increase was used when the lake surface was above the desired level.

Functions of the type shown in Figure 20 are used. Values for

the elevations for each lake are given in Table 9. Since the relation-

ship between water surface elevations and number of visits is a linear

segmented function, the pseudo-marginal product and the marginal value

product curves are step functions. The benefit to recreational use of

the lakes is found by simply multiplying the number of visits per month

by the value of an average visit, in this case, the consumer surplus for

an average visit.

The number of visits per month is found by entering the mean

monthly water surface elevation for a given lake in the linear segmented

function and obtaining the percent of maximum monthly visits, PRBL. This

percent is then multiplied times the maximum number of visits for that

month, NRECVML. Behar's [2] data were used to estimate the number of

recreation visits when the lakes were at the desired elevations (see

Table 10).

Gibbs and Conner [9], using McGuire's [15] recreation demand

function, estimated the consumer surplus, PCSURP, for an average

individual making an average recreational visit to a basin lake to be




-75-


100

Percent of maximum
monthly recreational
visits to lake L,
PRB
L






0 ZRLSTL DRUSTL FMINL ZRHSTL

Lake surface elevation, STL

Figure 20. The recreational use function.


Table 9. Elevations
functions.


for the percent of maximum monthly recreational visits


L ZRLSTL DRUST FMIN ZRHST
L L L L


53.28

51.28

50.28

47.28

44.28

51.28

40.28


62.0

60.0

59.0

56.0

53.0

60.0

49.0


64.5

62.5

61.5

58.5

55.5

62.0

53.0


69.5

67.5

66.5

63.5

60.0

67.0

58.0


ZRLSTL = the lower lake surface elevation at which there are no
recreational visits; DRUSTL = the lake surface elevation at
which maximum recreational visits occur; FMINL = the lake surface
elevation at which the recreational visits begin to drop from the
maximum; and ZRHSTL = the higher lake surface elevation at which
there are no recreational visits.


Note:





-76-


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-77-


$58.88, the shaded area in Figure 18. This is based on an average visit,

q, of 5.64 days, an average price, p, of $3.23 per day, and a critical

on-site cost, p*, of $17.57. Using the consumer surplus and the number

of visits to a particular lake during a month, the benefits accruing to

the availability of surface water for recreation are found.

Flood damages for each of the lakes was found by investigating

the activities at various elevations around the lake. The FCD gathered

the data which were used to construct the functions. Urban and rural

structure damages are expressed by the linear functions in Table 11.

The land around the lakes slopes away from the lakes at a very flat angle

and the area flooded increases linearly; therefore, linear functions

provide a reasonable approximation. It is assumed that thirty days are

required to repair damages, so property previously damaged cannot be

redamaged until thirty days have elapsed.

Crop damages are a function of the mean flood stage and the dura-

tion of the flood. Again, the area flooded increases linearly, and if

the crops are assumed to be uniformly distributed with respect to land

elevation, a linear increase in damages associated with flood stage is

reasonable. A hyperbolic paraboloid of the general form z = cxy, where

c is a constant and x, y, and z are Cartesian coordinates, is used.

This function has the property, that, when cut in the x-z or y-z plane, a

straight line results. This allows a function to be obtained with very

little data. This was convenient, since the FCD was only able to pro-

vide damage values for pasture and citrus when the crops were completely

destroyed. This is identified as the killing flood duration, and was

assumed to be fifteen days for pasture and five days for citrus. The

functions obtained for each crop adjacent to each of the lakes are shown

in Table 12.





-78-


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-79-


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CHAPTER V


POLICY EVALUATION DEMONSTRATIONS


Policy evaluation capabilities of an organization can be expanded

with simulation model use. The basis for the broadened capabilities

lies in the ability to change formulations, parameters, and variables,

while using the model as an apparatus to give insight into the complex

interactions occurring in the real system. The simulation of the

Kissimmee River Basin* is intended to demonstrate this usefulness in

dealing with the difficult water management problems in south Florida.

Demonstrations illustrating the potential of the model in four policy

areas, (a) temporal and spatial water storage, (b) consumptive with-

drawals, (c) minimum outflows, and (d) land and water use patterns, have

been performed.

A simulation run can provide

1. The flow through each control structure along with the volume

of water in storage and the water surface elevation for each

lake at six-hour intervals.

2. The daily irrigation water applied, evapotranspiration, and

soil moisture for each crop grown in the vicinity of each lake.

3. The crop yields and resulting irrigation dollar benefits for

each crop grown around each lake.




*The computer program written in Fortran IV and the complete set of data
used in these demonstrations are available from the author or Mr. William
V. Storch, Director, Department of Engineering, Central and Southern Florida
Flood Control District, Box 1671, West Palm Beach, Florida 32402.


-80-




-81-


4. The daily quantity of water withdrawn from each lake for

domestic consumption, and the resulting dollar benefits.

5. The monthly number of recreational visits and the accompany-

ing benefits.

6. The floods and resulting damages to urban property, rural

structures and individual crops occurring on each lake.

These data can be aggregated, used to calculate standard statistics, or

put into any form useful in the staff and governing board evaluation.

It should be noted that the dollar benefits can be used to compare the

distributional effects of a policy as well as its overall economic

efficiency. That is, the dollar benefits accruing to a particular

water use associated with a particular lake can be obtained and compared

to another use on another lake, and a policy selected on this comparison.

Or, in the case of the efficiency criteria, a policy which produces the

highest net benefits to the entire basin can be selected. The staff

and governing board have a number of physical and economic indicators

with which to compare policy alternatives.

Only a few of these indicators of policy performance are pre-

sented for the policy demonstrations discussed below. The availability

of water for each water use activity, the floods occurring and certain

aggregated dollar benefits are mentioned. The purpose of these was to

give the reader a feel for the relative change in indicators when a

change was made in certain parameter or formulation. The purpose was

not to give an exhaustive study of each policy.

Two computers were used to perform the demonstrations. The rain-

fall and runoff calculations were performed on the FCD's CDC 3100




-82-


computer. The University of Florida's IBM 370, model 165 computer was

used to run the water management model, the water use activities model,

and the institutional constraint model. No cost figures were avail-

able on the operation of the rainfall and runoff models. The cost

of running the other three models in the policy demonstrations was

nine dollars for a one-year run.

Rainfall occurring over the basin during the period June 1, 1968

to May 31, 1971, was used as the basin input. A set of runoff values

was generated using the FCD rainfall and streamflow models. This set

of runoff values for the three years was used for each policy demon-

stration run.

This was an interesting time period because the first two years

had typical rainfalls,while the third was very dry. The rainfall means

for the fourteen sub-basins were approximately 53 inches and 57 inches

for years 1 and 2, respectively. The third year mean was approximately

37.5 inches. This year was the beginning of the worst drought in the

recorded history of south Florida. The results of this change of rain-

fall were seen in the policy demonstrations. For example, in simula-

tion 1 using the present regulation schedule, group 1 crop acreages, and

proportional withdrawal functions, recreation benefits dropped $440,000,

while irrigation benefits rose $694,000 between year 1 and year 3.


Temporal and Spatial Water Storage


Temporal and spatial water storage is controlled by regulating

the gates at the outlets of the lakes. The gates are opened and closed

so as to maintain a certain lake elevation. The FCD specifies the lake




-83-


elevation for a given day with the lake regulation schedule. Ideally,

the storage policy given by each of these will provide the maximum net

benefits to the area. It is in the development of these schedules that

the FCD will use the simulation model to study the effects of alterna-

tive storage policies.

The regulation schedules are best illustrated by linear segmented

functions as shown in Figure 21. Here, each of the presently used

schedules is shown. Generally, the lakes are allowed to reach a maximum

elevation in the late fall, and then decrease through the winter and

spring to a minimum at the beginning of the summer. This corresponds

to the periods of light rainfall in winter and spring and heavy in the

summer, although there is great variation.

Three configurations of regulation schedules were used in the

demonstrations. The first consisted of three variations of the present

regulation schedules. Simulation runs were made with (a) the present

schedules for each lake, (b) the shape of the present schedules but

with all elevations for a given day lowered one foot, and (c) the

present schedules but with the maximum elevation raised one-half foot.

The second configuration is a set of changes being proposed by the FCD.

The proposed schedules for lakes 1, 2, 4, and 5 are given in Figure 22.

The last configuration, constant lake elevations set at the highest

elevation on the present schedules, is desired by many people with

property fronting on the lakes (6].

Output from the model gives sufficient information to allow

comparison of regulation schedules with respect to physical as well as

economic states. Simulation 1 (see Table 13) using the present





-84-


Elevations,
feet
above 62
mean
sea
level
60




58





56




54





52





50




48


0


Legend:





Figure 21. 1
I


L= 1


Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Months of thP vear


-- Constant elevation schedule
Present schedule presented and used by FCD



Regulation schedules for lakes in the Upper Kissimmee
liver Basin.


-I----




-85-


Elevations,
feet
above
mean 61
sea
level


L= 1


L= 5


SMar A May J J I S I
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec


Months of the year


Figure 22. Proposed regulation schedules.















a


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-87-


schedules and group 1 acreages (see Table 16) resulted in all irrigation

needs being met except on lakes 1, 2, and 3 during the dry period of 1971.

A small amount of agricultural flooding occurred in October, 1969. The

net benefits accruing to the availability of water during the three

years was $71,118,689. (Table 13 presents the three-year total benefits

and damages for the regulation schedule demonstrations.) Simulation 2,

using the present schedule dropped one foot, resulted in a decrease of

flood damages to $8,685, but also decreased the net benefits by $2,762,055.

Both recreation and irrigation benefits dropped substantially. There was

a very definite shortage of water in lakes 1, 2, and 3 during the dry per-

iod. The proposed schedules (simulation 3) resulted in the same flooding

as the present schedule simulation. Recreation benefits rose, but irri-

gation benefits dropped, and the net benefits were $73,129 lower. The

constant lake levels (simulation 4), on the other hand, caused a

$949,871 increase in net benefits. There was an increase in recreation

and irrigation benefits, but there was also a rise in flood damages to

$468,138, with the majority occurring in urban areas on Lake Tohopekaliga.

The water was 1.07 feet above the flood level and remained above flood

level for 37 days. When the maximum elevations on the present schedules

were raised one-half foot, there was very little change in the benefit

levels, but there was in increase in flood damages. A number of small

floods occurred in the late fall and winter because the desired lake

level was the same as the point where flood damages begin. The outcome

was a decrease in net benefits.

It is possible to vary only one lake's regulation schedule to

gain greater insight into the effects of one lake on the entire system.

To demonstrate this, simulation 6 was made identical to 5, except lake 5




-88-


had the present schedule rather than the constant schedule, as did the

others. Flood damages dropped by $417,218, but the increase in net

benefits was only $78,569.

The demonstration runs have shown the model to be effective in

analyzing specific segments of proposed regulation schedules as well as

comparing different proposed schedules. The daily values for lake levels

and soil moisture help pinpoint time periods when greater quantities of

water need to be stored. These lake levels, also, help in identifying

periods in which less water should be stored to prevent undue flooding.


Consumptive Withdrawals


The FCD has the responsibility of providing surface water to con-

sumptive users, and also to protect the water resources in times of

serious drought. Under the Florida Water Resources Act of 1972, surface

water to be used consumptively is to be controlled by withdrawal permits.

To protect the lakes from undue lowering, the water allowed to be with-

drawn should be a function of the water in storage, or the lake surface

elevation.

Different consumptive water use policies can be investigated

because the simulation model allows ready change of the withdrawal func-

tions. The functions -- irrigation and domestic withdrawal -- are

linear segmented functions which specify a percentage of water needs to

be met when the lake surface is at a given elevation (illustrated in

Figure 9). These allow 100 percent of the needs to be met when the

lake surface elevation is equal to or above the level specified by the

regulation schedule, DSTL. And, when the lake is below this level, the

percentage of needs which can be met drops off and reaches zero at certain

elevations, ZIWST and ZDWST .
L L