Title: Man's impact on the phosphorus cycle in Florida
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Title: Man's impact on the phosphorus cycle in Florida
Physical Description: xii, 269 leaves. : illus. ; 28 cm.
Language: English
Creator: Gilliland, Martha Winters, 1944-
Publication Date: 1973
Copyright Date: 1973
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Subject: Phosphorus   ( lcsh )
Environmental Engineering Sciences thesis Ph. D
Dissertations, Academic -- Environmental Engineering Sciences -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
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Thesis: Thesis -- University of Florida.
Bibliography: Bibliography: leaves 260-268.
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
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Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: alephbibnum - 000577606
oclc - 13995803
notis - ADA5303

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MAN'S IMPACT ON THE PHOSPHORUS
CYCLE IN FLORIDA



By


Martha Winters Gilliland


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


UNIVERSITY OF FLORIDA


1973


II


if1







F.-



I-



'U
"P









ACKNOWLEDGMENTS


Foremost appreciation is expressed to Dr. H. T. Odum,

my committee chairman, for his supervision, inspiration,

and guidance. It is rare that a student has the opportunity

to learn from a man who exhibits such a high degree of

creativity and possesses such an immense storehouse of

knowledge in many disciplines.

Many special contributions were made by other members

of my committee: Drs. P. L. Brezonik, E. E. Pyatt, T. E.

Bullock, and M1. Y. Nunnery.

Maurice Sell and James Zuchetto were particularly

helpful with simulations.

This research could not have been completed without

the patience and understanding of my husband, Richard.

The work was sponsored by the United States Environ-

mental Protection Agency Training Grants Branch with a

Research Fellowship. Other aid was provided by the National

Oceanographic and Atmospheric Administration Sea Grant pro-

ject number R/EA-3 entitled "Simulation of Macromodels to

Aid Coastal Planning."












TABLE OF CONTENTS


Page

ACKNOWLEDGMENTS . . . . . . . . ii

LIST OF TABLES . . . . . . . . v

LIST OF FIGURES . . . . . . . ... vi

ABSTRACT . . . . . . . . . . ix
L
INTRODUCTION . . . . . . . . .. 1

Previous Studies on Phosphorus Cycles . 2
Phosphorus Systems in Florida . . ... 15

METHODS . . . . . . . . ... .. . 40

Model Development . . . . . ... 40
Symbols Used in Model Diagrams . . .. 41
Examination of Numbers to Gain
Perspective . . . . . . ... 41
Simulation Model . . . . . . .. 46
Writing and Scaling Equations . . ... 47
Simulation Procedures . . . . ... .48
Experimental Manipulations of Models . 49

RESULTS AND DISCUSSION . . . . . ... 50

Phosphorus in the Peace River -
Charlotte Harbor Estuarine System . . 50
Nitrogen, Phosphorus, and Productivity
in the Peace River Mouth . . . .. 106
Phosphorus in Peninsular Florida . . .. .131
Deposition of Phosphorus in Florida
Over Geologic Time . . . . . 149


iii






TABLE OF CONTENTS (continued)


Page

MAN'S IMPACT ON THE PHOSPHORUS CYCLE
IN FLORIDA . . . . . . . . ... 174

Energy Value of phosphate Mining in
Polk County . . . . . . . 174
Effects on the Larger Systems of Phos-
phorus Mobilization Through Mining . 183
Genesis of Phosphate Rock .. . .... 189
Suggestions Pertinent to Pollution
Regulations and Resource Management . 192

APPENDIX

A NOTES TO TABLES 3, 5, 6, 8, 9, AND 10 . 195

B MODELING DATA AND COMPUTER PROGRAMS . .. 243

C DATA FOR SOLUTION OF BROOKS EQUATION . .. 257

LIST OF REFERENCES . . . . . . ... 260

BIOGRAPHICAL SKETCH . . . . . . ... 269












LIST OF TABLES


Table

1 Statistics for Counties Through
Which the Peace River Traverses . .

2 Cenozoic Time Scale . . . . .

3 Sources, Storages, and Rates for the
Peace River Charlotte Harbor
Estuarine System . . . . . .

4 Residence and Turnover Times for the
Storages of the Peace River Charlotte
Harbor System . . . . . . .

5 Sources, Storages, and Rates for the
Phosphorus-Nitrogen Interaction Model


6 Sources, Storages, and Rates for the
Peninsular Florida Model . . . .

7 Ionic Concentrations in Florida's
Surface Waters and Groundwater . .

8 Sources, Storages, and Rates for
Deposition of Phosphorus System . .

9 Energy Values in Polk County for the
Present Condition . . . . .

10 Energy Values in Polk County Without
the Phosphate Mining Industry . .


Page


25

S 32



S 55



S 66


S 109


. 134


155


. 160


S. 177


179













LIST OF FIGURES


Figure Page

1 Map of Florida showing study area
locations . . . . . . ... .17

2 Map of Peace River Charlotte Harbor
Estuarine System . . . .. . 19

3 Map of Peace River drainage district . 22

4 Flowsheet of a Florida rock mining
and beneficiation plant . . . ... 28

5 Map of the land pebble phosphate
district . . . . . . . . . 35

6 Cross-section through the land pebble
phosphate district . . . . ... 37

7 Symbols of the energy circuit language .. 43

8 Sensor symbol representation . . .. 45

9 Peace River Charlotte Harbor estuarine
model with mathematical terms . . .. 52

10 Peace River Charlotte Harbor estuarine
model with numerical values . . .. 54

11 Summary models of the Peace River mouth 63

12 Differential equations for the Peace
River Charlotte Harbor estuarine
model . . . . . .... . . 67

13 Simulation results for the Peace River
mouth sector ... . . . . . 71

14 Inorganic phosphorus data . . ... 73

15 Simulation results for the northern
Charlotte Harbor sector . . . ... 75






LIST OF FIGURES (continued)


Figure

16 Simulation results for the southern
Charlotte Harbor sector . . . .

17 Simulation results for an increase
in precipitation factors . . . .

18 Simulation results for an increase
in precipitation factors . . . .

19 Simulation results for withholding
mining water from the Peace River .

20 Simulation results for sewage increase

21 Expanded model for slime spill
simulation . . . . . . .

22 Simulation results for a slime spill

23 Simulation results for a slime spill

24 Soluble reactive phosphorus versus
salinity in Charlotte Harbor . . .

25 Model of nitrogen and phosphorus
interaction with production . . .

26 Ecosystem representations . . .

27 Simulation results for models with
and without recycle pathways . . .

28 Simulation results for nitrogen
increases . . . . . . .

29 Nitrogen concentration versus
standing crop and productivity . .

30 Simulation results for phosphorus
increase and turbidity decrease . .

31 Nitrogen concentration versus
phosphorus deposited in sediment . .

32 Simulation results for turbidity
increase . . . . . . . .


Page


S. 77


S. 85


S. 87


S. 90

93


S. 96

99

101


S. 103


S. 108

S. 112


S. 116


. 119


. 121


S. 125


S. 128


S. 130


vii






LIST OF FIGURES (continued)


Figure

33 Peninsular Florida systems model .

34 Summary diagrams of the Peninsular
Florida system . . . . . .

35 Summary diagrams of the Peninsular
Florida system . . . . . .

36 Model of geochemical reactions
involved in phosphate deposition .

37 Stoichemistry involved in phosphate
deposition . . . . . . .

38 Simplified geochemical phosphorus
model for simulation . . . .

39 Simulation results of geochemical
phosphorus model . . . . .

40 Simulation results for changing
rates of new material additions

41 Simulation results for changing
ratios of CaPO4 to CaCO3 in sediment

42 Systems model of energy flow in
Polk County . . . . . .


Page

. . 133


. . 145


. . 147


. . 151


. . 153


. . 159


. . 165


. 169


S. 172


. . 176


viii





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


MAN'S IMPACT ON TIE PHOSPHORUS
CYCLE IN FLORIDA


By

Martha Winters Gilliland

August, 1973


Chairman: 11. T. Odum
Major Department: Environmental Engineering Sciences



A quantitative understanding of the phosphorus cycle

in Florida is essential for resource management and pollu-

tion control of activities that release and utilize phos-

phorus, affecting eutrophication and economic vitality.

Systems models of phosphorus flux were developed here for the

Peace River Estuary, for the state of Florida, and for pro-

cesses which may have been important in the original deposi-

tion of phosphate rock.

Digital computer simulation of the phosphorus flux in

the Peace River Estuary showed the relative importance of

projected changes in mining and population. The entire Peace

River is high in phosphorus (all forms) ranging from 0.3 mg/l

in Southern Charlotte Harbor to 1.0 mg/l in the Peace River

Mouth. Since the natural drainage to the river is high in

total phosphorus, daily mining water discharges to the river

have little effect on total phosphorus concentrations. The





periodic spills from slime ponds in the mining district are

more serious as shown by simulation of slime releases.

Total phosphorus concentrations increase drastically for

several days (20 mg/l total P) and level off at an average

of 1.8 mg/l in the river mouth. Simulations indicate that,

because tidal turbulence reworks the settled slime, phospho-

rus concentrations may remain elevated for many years.

Analog computer simulations were made of a model of

productivity in the Peace River Mouth to show the effect of

additional nitrogen on net photosynthesis and eutrophication.

The simulation suggested that high phosphorus levels keep

nitrogen levels low (less than 0.1 mg/l), the latter limit-

ing net productivity. When nitrogen inputs from sewage and

urban runoff are increased to levels corresponding to a

population of 3 to 5 times the present population, net pro-

ductivity increases to levels generally considered eutrophic

(2.0 g 02/m3/day).

The percent effect on the overall geochemical cycle of

the present phosphorus flows in peninsular Florida was deter-

mined by evaluating an overall phosphorus budget model for

Florida. Overall phosphorus flows total 64 g/m2/year.

Through mining, Florida is draining its phosphorus supply

125 times faster than it is replaced. The phosphorus mobil-

ized through mining is three orders of magnitude higher than

the phosphorus cycling through Florida's waterways. The

ratio of phosphorus in estuarine sediment to estuarine water





is 1,000 to 1. Fifty percent of the total input of phos-

phorus to inland waters is due to man's activities; these

include sewage effluent (6%), agricultural runoff (34%),

urban runoff (3%), and mining effluent (7%). Sewage going

directly into estuaries is 9% of the phosphorus input to

estuarine water. If the rate of phosphorus influx to sedi-

ment in estuaries is indicative, sedimentation rates are

0.76 m/1,000 years in Florida's estuaries. If isostatic

adjustment is keeping pace with erosion, then the present

rate of land elevation is .07 m/1,000 years.

Present ionic concentrations of Ca HCO3, and HPO4

in surface and groundwater runoff indicate that phosphorus

is being concentrated in rock through dissolution and repre-

cipitation with calcium phosphate increasing at the expense

of calcium carbonate. Analog computer simulation of a

systems model of this process suggests that enrichment can

occur in 20 million years. The degree of enrichment depends

on the supply of new phosphorus to Florida through rain and

oceanic exchange processes. If the calcium phosphate con-

tent of original rock is .5 to 1.0%, a formation with 10 to

20% calcium phosphate as in the Miocene Hawthorn formation

may result. Nutrient upwelling along the continental slope

coupled with transport to the estuaries by lateral eddy dif-

fusion can supply an additional 400 mg P/m2-year which, if

deposited, would result in a sediment with a 4.3% calcium

phosphate content. If this is later enriched by resolution,

40% calcium phosphate results.





Using a systems model of the main energy and money

flows, the energy budget of Polk County, Florida, for the

present condition and for the condition without the mining

industry was calculated. The energy budget for the present

condition was 316.0x1011 kilocal/year; that for the condition

without the mining industry was 303.6x101 kilocal/year.

For the present, the metabolic losses from the denuded land

can be absorbed by the system. At the current rate of strip-

ping land, however, within five to ten years the total ener-

gies for the county without phosphate mining will be higher

than with mining.


xii











INTRODUCTION


Often limiting to key processes in nature, agriculture,

and industry, phosphorus is a major part of the systems of

man and nature. Phosphorus moves through the land, air, and

sea with concentrations in some rock deposits as in the phos-

phate deposits of Florida. The natural cycles of phosphorus

have been much changed by the activities of man in mining,

applying fertilizer, and releasing wastes. Phosphorus is

one of the major nutrient elements affecting eutrophication

in lakes, rivers, and estuaries and a critical factor in the

agricultural and industrial economics of Florida. Under-

standing the phosphorus cycle is required for any sensible

plans for resource management and pollution control. Florida

offers a unique opportunity to examine the phosphorus cycle

since one can find here examples of the benefits and problems

associated with man's use of phosphorus (e.g., mining, lakes,

estuaries, agriculture, and urbanization). What are the

effects of man's development on the state's original phos-

phorus cycle? What happens under intensive agriculture and

population growth? At what level are the resources of phos-

phorus? What kind of geochemical process generates these

deposits and what kind of time is required to develop them?







To gain perspective of man's interaction with the phos-

phorus cycle, systems models were developed of the phosphorus

cycle for the state of Florida and for the Peace River phos-

phate district and estuary. The Peace River district is

uniquely rich in phosphorus and is the projected site of the

largest future population growth in Florida so that manage-

ment for phosphorus wastes becomes an important part of the

total ecological engineering concerns of this area. The

systems model of phosphorus flux in peninsular Florida quan-

tifies the rates of flow and present storage so that flows

can be examined in terms of their percent effect on the

overall geochemical cycle. The effect of population growth

and alternatives of water and waste management are tested

with calculations and simulations.

Explaining the origin of the phosphorus concentrations

in sedimentary phosphate rock deposits and determining the

rates of formation requires considerations over geologic

time. A systems model of geochemical replacement is used to

evaluate the pathways of dissolution and reprecipitation of

calcium carbonate and calcium phosphate in the soil and rock.



Previous Studies on Phosphorus Cycles


The literature on phosphorus and phosphorus cycling

is extensive. Surveyed here are theories on the origin

of phosphate rock deposits, three landmark papers on








the biogeochemical cycling of phosphorus, and the history

of theories on recycling phosphorus from the ocean.


Early Papers on Florida's Phosphate Rock Deposits

Sellards (1913) summarized the theories on the origin

of Florida's mineable phosphate rock deposits. Several

early writers (Ledoux, 1890; Cox, 1891; Darton, 1891; and

Dall, 1892) suggested bird guano deposits as the source.

They suggested that phosphoric acid leached out of the guano

and replaced calcium carbonate with calcium phosphate. Dall

suggested that the local character of the bird rookeries

determined the local character of the phosphate rock. More

recently, Vernon (1951) developed the guano theory, stating

that limestone islands existed with bird rookeries on them

during the Miocene and younger epochs. Rainfall dissolving

the guano allowed phosphoric acid to penetrate the limestone

and form a crust of calcium phosphate. He stated that

"large colonies of birds on land may also increase the

amount in solution in adjacent sea waters which then support

a thriving population of phosphorus using organisms." The

guano producing birds (large birds which feed over a wide

area and return to restricted sites for rest) are pelicans,

boobies, and cormorants. Birds began evolving during Cre-

taceous time andwere well established in the geologic record

by Miocene time. Hutchinson (1950) stated that large colon-

ies of birds on a section of coastline, when the form of the

substrate permits guano to be returned to the ocean, steepens








the nutrient gradient resulting in increased littoral pro-

ductivity. A steady state was established in which a phos-

phorus rich ocean supplied food for the birds; excrement

from the birds returned phosphorus to the sea and completed

the cycle. A few guano forming birds have been found in the

Miocene in Florida. They include several cormorants and a

booby (Brodkorb, personal communication). However, the

Bone Valley formation of Pliocene age contains abundant bird

remains (Brodkorb, 1955). Brodkorb identified 135 specimens

of the small cormorant Phalacrocorax wetmorei in the Bone

Valley. He believed that the Bone Valley phosphates were

concentrated from the Hawthorn phosphates through guano

producing birds. Specifically, he stated that erosion of

the Hawthorn formation produced a phosphate rich sea with

high productivity. The excrement of cormorants and boobies,

which feed on the top of the food chain in the ocean and

group on land to rest, was then the means by which the Bone

Valley phosphates formed.

Among the early writers, Davidson (1892), Brown (1904)

and Sellards (1931) believed that percolating water was the

mechanism responsible for concentrating phosphorus. Sellards

stated, "the rainfall (high in Florida) in passing through

the surface materials dissolves a limited amount of the

phosphate which is carried to a lower level and precipitated

in a concentrated form. This process long continued results

in the accumulation of workable phosphate deposits." More








recently, Odum (1951), in noting that phosphorus concentra-

tions are higher in acid surface water than in groundwater,

used tables of solubility of phosphates and pH to suggest

that phosphorus was dissolved by acid surface water but

precipitated again as percolating water became basic.


"The Geologic Role of Phosphorus" by
Eliot Blackwelder, 1916

Blackwelder may have presented the first complete dis-

cussion in the literature of phosphorus cycling. Although

nonquantitative, insights into the overall phosphorus cycle

and subordinate cycles were stated. Phosphorus in meteo-

rites, in igneous rocks, in sediment and sedimentary rock,

and in the ocean were discussed. Theories on phosphate

deposition were examined as well as pathways from one stor-

age location in the cycle to another. He stated that all

igneous rocks contain phosphorus as apatite averaging 0.29%

P205. The basic igneous rocks had the highest content (0.5
to 1.15% P205). High grade phosphate rock could occur in

pegmatites as exemplified by the nelsonite of Virginia.

Primary phosphorus found in igneous rocks was dissolved by

percolating water, providing nutrients for plants and animals

and ultimately the source of phosphorus for sedimentary

rocks. Blackwelder further pointed out that the phosphorus

in the ocean seems to have reached the most dilute state in

its cycle. Its only escape from the sea, he said, is

through birds and fishing. In discussing the origin of







phosphate nodules in the sea and phosphate rock of marine

origin, he stated that phosphorus sedimentation could only

occur where the quantities of decomposing matter were too

great for scavengers to completely decompose. An anaerobic

environment, he contended, was a controlling chemical condi-

tion implying that areas of restricted circulation in the

ocean were the sites for phosphate deposition with cellophane

being the original phosphate compound formed. The amorphous

cellophane was gradually converted to apatite. He briefly

presented the idea that phosphate may be enriched in lime-

stone due to percolating waters when he said, ". . the

lime carbonate is relatively more soluble than the lime

phosphate. Therefore, during the slow process of solution

by rainwater descending from the surface, the calcium phos-

phate, although actually decreased in total quantity, has

been relatively concentrated by differential solution."


"The Biogeochemistry of Phosphorus" by
G. Evelyn Hutchinson, 1952

Hutchinson presented the first real quantitative exami-

nation of the phosphorus cycle. He discussed the cosmic

background of phosphorus, its natural history and its move-

ment in the biosphere. Summaries of the structure of apa-

tites, occurrence of phosphate in primary rocks, in the

pedosphere, in the atmosphere (phosphine gas), in the hydro-

sphere, and in guano deposits were presented. Salient

points with respect to the structure of apatites included








the fact that the hydroxyl ions in apatites of biological

origin are exchanged for fluoride ions in dilute aqueous

solution. Furthermore, it appeared that when apatite skele-

tons came in contact with sea water a considerable amount of

fluorine was incorporated into the lattice structure.

After reviewing the extensive literature on phosphorus

in primary rock, Hutchinson concluded that the best esti-

mate for the mean value is .12% P. Phosphorus content de-

clines with increasing silica in igneous rock; basalt con-

tains .2% and rhyolite .02%. Sediment, he contended, is

intermediate between basalt and rhyolite with continental

regions underlain by granite having less than their share

of phosphorus.

Since phosphates are slightly soluble in water, a small

amount of phosphate occurs in soil solution. After entering

plants, it has a long metabolic industry and is eventually

returned to the soil except where crops are removed to be

eaten elsewhere. The important consideration as far as soil

phosphates are concerned is fixation of soluble forms as

calcium, aluminum, or iron phosphates resulting in a lowered

availability of phosphorus to plants.

In the hydrosphere, phosphorus in inland waterways and

in the oceans is of prime importance to primary productivity.

Hutchinson obtained an average river concentration for the

world of 0.1 mg/l total phosphorus. The importance of the

exchange of phosphorus between mud and water was discussed

in noting the extraordinary dilution at which phosphorus can








be used. In the ocean, there was a continual drain on phos-

phorus in the photic zone due to the sedimentation of plank-

tonic organisms. Hutchinson gave the overall average phos-

phorus concentration of the ocean as 0.093 mg/l total P.

Pointing out that this is the same order of magnitude as

influent river water, he concluded that the replacement of

phosphorus in the ocean must occur almost as frequently as

that of water (once every five million years). A maximum

residence time for phosphorus of twenty million years was

calculated, indicating that the phosphorus in the ocean had

been lost and restored many times. The return of phosphorus

to the land occurs slowly being mediated only by birds, man,

and geologic uplift.

Hutchinson was the world's pioneer in showing the role

of guano in the phosphorus cycle (see Hutchinson, 1950).

He pointed out in this overview paper that divergence of

surface waters in the latitudes of the trade winds along the

west coasts of continents caused upwelling of nutrient rich

deep ocean water. The result was fertile ocean waters with

high primary productivity forming the base of a food chain

which ends with birds. The birds then deposit the phosphate

from the deep ocean in the form of guano deposits which, on

desert islands such as the Peruvian guano islands, simply

accumulates. On islands with occasional rain, the soluble

components of the guano are leached out, leaving the calcium

phosphates.








"The Acceleration of the Hydrogeochemical Cycling
of Phosphorus" by Werner Stumm, 1972

Recently, at the Nobel Symposium in Sweden, Stumm pre-

sented a landmark paper on phosphorus in which he addressed

the question of man's role in phosphorus cycling rates and

storage. Stumm presented a global phosphorus circulation

model which included the abundance in terrestrial and marine

plants, in soils, sediment, and water, and in the earth's

crust. Transfer rates between compartments were given.

From examination of rates, he concluded that man, through

mining, is restoring incipiently marine phosphorus to the

land at higher rates than it washes to the sea. The result

is "ecological imbalance causing pronounced pollution in

inland and coastal waters." Noting that the annual uptake

of phosphorus by phytoplankton in the sea is much higher

than the annual contribution of phosphorus to the oceans,

he concluded that most of the phosphorus flowing through the

Phytoplankton is continuously regenerated from organic

debris. Stumm pointed out from the photosynthetic equation

that for every phosphorus atom respired, 276 oxygen atoms

have been consumed. Thus, any increase in the supply of

phosphorus to the sea, even if it has a negligible effect

on the overall phosphorus content of the ocean, will increase

the fraction of ocean floor which is anaerobic.

In discussing pollution of inland waters, Stumm stated

that the organic material introduced to a lake from sewage

may be quite small in comparison to the organic material







synthesized from the phosphorus in the water. If phosphorus

is limiting, 1 mg of phosphorus allows the synthesis of

about 100 mg of algal biomass. When this biomass settles it

exerts a biochemical oxygen demand of about 140 mg. Estu-

aries are apparently an area of great concern because they

are efficient in trapping nutrients.

In discussing the formation of marine phosphorites,

Stumm proposed three mechanisms: (1) burying of detrital

phosphorus, (2) chemical precipitation of apatite, and

(3) diagenetic replacement of calcite by substitution of

carbonate by phosphate. He believed that apatite precipi-

tation on the seafloor is unlikely unless the relative

degree of apatite saturation has increased and favorable

conditions for nucleation prevail. Unless the system is

anaerobic, regenerating detrital phosphorus does not increase

the degree of saturation because the regeneration also liber-

ates CO2 which increases the acidity. For the degree of

saturation to increase, this CO2 must somehow be lost from

the system. Stumm believed that areas of upwelling are

likely sites for apatite precipitation since the CO2 is lost

to the atmosphere in this system. In other words, increas-

ing phosphorus concentrations may not precipitate apatite,

but increasing the pH of the water may initiate it.

In investigating the kinetics of apatite formation.

Stumm found that three steps are involved: (1) sorption of

phosphate forming amorphous calcium phosphate, (2) trans-

formation of the amorphous nuclei into crystalline apatite,








and (3) crystal growth of apatite. He also found that cal-

cite will convert into apatite in sediments although the

change is quite slow.

Finally, Stumm concluded that mining production, which

increases the flux of phosphorus to inland waters, to estu-

aries, and to the ocean, is creating undesirable conditions

in lakes and estuaries and causing oxygen deficits in parts

of the ocean. As first steps in controlling this, he

suggested a re-examination of the present practice of

excessively fertilizing land and improvement of the pres-

ently inefficient waste treatment systems.


Studies on Phosphorus Recycling from the Ocean

The ultimate recycle pathway and an important one in

the considerations here is the means by which phosphorus

moves from the ocean to the land. Mediation by pelagic

birds has been discussed previously; however, several other

pathways may also be important.

Conway (1943), as cited in Chesselet et al. (1972),

considered a "cyclic salts" hypothesis. He showed that

part of the salts dissolved in rivers had a marine origin.

A steady state salinity for the oceans requires that some

fraction of the salt must be recycled onto land. Barth

(1952) and Goldberg (1963) later demonstrated that these

salts must be injected into the atmosphere at the surface

of the oceans and fall out with rain onto the continents.








Sugawara (1961) demonstrated that the constant proportion

of ions in sea water is not found in the atmosphere; there-

fore, an evaluation of the fraction of salts recycled is

difficult and remains obscure to date. Woodcock (1953)

showed that the mechanism of particle injection into the

atmosphere depends on the action of the wind on the sea.

When wind conditions over the ocean are such that whitecaps

appear, waves and surf splash sea water into the atmosphere,

forming ion-containing aerosols. Probably more important,

however, is the continuous formation of marine aerosols by

bubble collapse at the sea's surface over all the ocean

(Blanchard, 1963). Baylor et al. (1962) and Sutcliffe et al.

(1963) showed that bubbles rising through sea water adsorb

phosphates and that phosphate is ejected from the surface

of the ocean by the bursting of wind and wave induced bubbles.

The bursting bubbles were found to contain a greater concen-

tration of phosphate than the sea water (1.41:1 for P04 in

the aerosol to PO4 in the sea water). Some fraction of

phosphorus in rain, then, originates in the ocean and is

recycled onto the land.

In geologic time, phosphorus may be recycled from the

ocean through estuarine sediment which becomes land as sea

level changes. Phosphorus concentrations in the ocean are

quite small (often less than 0.01 mg/l at the surface) unless

special conditions exist. It is a well-established fact that

upwelling of nutrients occurs in locations where prevailing








strong winds parallel to or off the land push water off the

coast, allowing it to be replaced with deep nutrient-rich

water. The best known example is along the coast of Peru

where nutrient-rich surface waters support large phyto-

plankton populations. The first suggestion of upwelling

as a source of phosphorus for phosphate rock is in a paper

by Kazakov (1937) where he states that upwelling of deep

phosphate-rich ocean waters along steeply inclined conti-

nental slopes brings phosphates onto the relatively shallow

areas of the continental shelf. This "extra" phosphorus

may be taken up in the food chains and eventually be deposited

in the sediment, or it may precipitate directly. Dietz et al.

(1942), in making calculations on the theoretical amount of

phosphate ions that can exist in sea water, found that the

sea is several hundred percent saturated with phosphate.

Although there are many sources of error in this calculation,

such as the effect on the solubility of calcium phosphate of

temperature, pressure, and the presence of other ions, Dietz

et al. believe that sea water, at least in its deeper colder

portions, is essentially saturated with calcium phosphate.

Furthermore, they postulate that slight changes in the

physical-chemical or biological conditions in the sea may

bring about supersaturation. It is known that dissolved

phosphorus is high in the cold waters of deep ocean basins

(Sverdrup et al., 1942). Upwelling of deep water to shallow,

agitated, and warmer zones may cause a loss of dissolved








CO2, an increase in pH and supersaturation of phosphate.

The phosphate nodules occurring off the coast of

southern California are often cited as examples of phosphate

forming at the present time. Similar nodules occur in other

oceanic areas (western coast of South America, western and

southern coasts of Africa, and south of New Zealand).

Kolodny and Kaplan (1970), using radioactive age dating of

the U234/U238 isotopes, which are associated with the phos-

phorite, found all the nodules to have a minimum age of

800,000 years; indications were that they are probably older

than that. No recently forming apatite was detected in their

study. The phosphorite nodules found in today's oceans occur

along the continental slope edge; they are generally not

found in shallow shelf areas.

Assuming phosphorus of oceanic origin is deposited in

shallow water sediment, this phosphorus may become part of

a continent through sea level lowering and uplift of the

land. The geologic record indicates that sea level fluctu-

.ations have occurred throughout geologic time. The details

of large fluctuations during the recent pleistocene epoch

are recorded in coastal rock. What is now Florida has been

below sea level and large expanses of the Florida shelf

have been above sea level many times (Cooke, 1945). During

low sea level stages when the water was in glaciers, exposed

continental shelf areas may rebound isostatically due to the

unloading of water. Studies on Lake Bonneville in western







Utah seem to verify this (Crittenden, 1963). An average

load of 145 m of water covered an area of about 50,000 km2

there. Since removal of the water some 15 to 25 thousand

years ago, once level shorelines have undergone a broad

domical uplift of about 64 m (210 feet) in the center. The

indication is that uplift may coincide with sea level lower-

ing.



Phosphorus Systems in Florida


Several systems in Florida were selected and defined

for modeling, calculations, and simulation. Some background

and introduction to these follows next.


The Peace River Charlotte Harbor Estuarine System

Charlotte Harbor (Figs. 1 and 2),located on the Gulf

coast of Florida approximately 60 miles south of Tampa, is

one of the largest and least contaminated (Alberts et al.,

1970) estuarine complexes in Florida. The system is a

drowned estuary enclosed by a series of barrier islands,

the most famous of which is Sanibel Island located at the

southern end. Tidal exchange is controlled by two major

inlets -- Boca Grande Pass on the West and San Carlos Bay

on the south end. Three rivers drain into the harbor --

the Peace, the Myakka, and the Caloosahatchee. The total

harbor, including islands, occupies an area of 280 square

miles with a total shoreline of about 40 nautical miles

(Huang and Goodell, 1967).































Figure 1. Map of Florida showing the area included
in the peninsular Florida model, the
drainage of the phosphate mining district,
and the edge of the Florida Plateau. The
northwestern boundary of the peninsular
Florida model is the Suwannee River;
total area is 1011 m2.

































GULF OF
1MEXICO
AL


HILLSBOROUGH /
AY \MYA I
\ R



CHARLOTTE
HARBOR



\^


DININGNG
DISTRICT


I




I
I
I
I

I
I
I





UPWELLING
I
I
I


4.-
% EDGE OF -

CONTINENTAL SHELF


-24o


865
!


830
I


--300


UPWELLING


-26o


LOOP
CURRENT


__ _





























Figure 2. Peace River Charlotte Harbor Estuarine
System showing the physical location of
the storage defined in the model
(Figs. 9 and 10).














CHARLOTTE


0 1 2 3
1 -- --- i--1
I cvticl t.ilco


RIVER MOUTH
SECTOR


/...
'C-
b-i


27 0O' N-


CATTLE


NORTHERN
SECTOR


BOCA CFGr;D
FASS


GULF
OF
I EXICO


SAN CAR. LOS
BAY


I I


I
6220' VI


82000'Vi


HARBOR


- 27o00Al


e;cO'O/w


- ? 1-11-~-----


E2":'.o'v


"~-~-~W` -~~--llllr'------UII~~ ~---D ---~--------- --I-I----^I-


- 2Go 5o0'1







The Peace River begins at Lake Hancock, forming one

mile east of Bartow by the juncture of Peace Creek and

Saddle Creek Canal (Fig. 3). It extends 98 miles southward,

emptying into Charlotte Harbor at the town of Punta Gorda.

Average depth of the river is three to eight feet with a

maximum depth at Arcadia of twenty feet (Lanquist, 1953).

The width of the river varies from 60 to 200 feet.

Phosphorus enrichment of the Peace River Charlotte

Harbor estuarine complex is a result of the natural rich

geochemical cycle of phosphorus in the area and a result of

the urban expansion of man. Questions of regulation of

waste discharge in the Peace River Basin require understand-

ing of the present state of phosphorus and factors affecting

its flows.


Natural Areas

The surface geology of the land area consists of post-

Eocene rocks which are primarily limestone and dolomite with

sand, clay, and phosphate (Cooke, 1945). Karst topography

is evident, resulting from heavy rainfall on the calcaceous

rock. The Peace River basin consists of rolling sandy hills,

swamps (some of which have been made into canals), and many

small lakes (some of which have been connected to surface

water drainage and some of which drain through the ground).

These many small lakes exert a buffer effect on streamflow.

Streamflow does not fluctuate rapidly since the lakes store

water in times of excess rainfall, -reducing the flood peaks.





























Figure 3. Peace River from its source north of Bartow
to its mouth at Charlotte Harbor. Sources
of phosphate wastes to the river are shown.






























































































































'Ch.rloile HKrbor


-^----llllllll-CI---~ --


- --------








Along the peace River proper, upland pine and oak forest

predominate, surrounded by pine flatwoods (slash and longleaf

pine). Mangroves occur along the east coast of Charlotte

Harbor. At the mouth of the Peace River is a swamp forest

consisting of water oak, laurel oak, sweet gum, and cypress.

Intermittent cypress swamp can be found from Bartow to Fort

Meade.

Lanquist (1953) in a biological survey of the Peace

River attempted to correlate the chemical and physical fac-

tors with the fauna. He found that the substrate in the

river was usually sand, phosphatic slime, or hyacinth

detritus and is of great importance in determining the

nature of the community. Deposition of phosphatic slime

from spills destroyed animal habitats and vegetation.

J. Dequine in personal communication indicated there may

be direct effects on gill actions of fish.

In a study of the small estuarine fish of Charlotte

Harbor, Wang and Raney (1971) found an abundance and diver-

sity of juveniles and euryhaline fish near the mouths of

the Peace and Myakka Rivers. Dominant fish are the bay

anchovy (Anchova mitchilli), the pinfish (Lagodon rhomboides),

the silver perch (Bairdiella chrysura), the silver jenny

(Eucinostomus gula), and the seatrout (Cynoscion arenarius).

The geochemistry and hydrography of Charlotte Harbor

have been examined by Alberts et al. (1970). They sampled

the system for salinity, temperature, and dissolved








phosphorus in surface waters, bottom water, and interstitial

water. Water temperature in August averaged 30'C, in

December 160C and in March 190C. The salinity structure was

one of decreasing salinity from Boca Grande Pass to Punta

Gorda at the Peace River Mouth (Fig. 2). Just inside Boca

Grande Pass at high tide the salinity was 30 0/oo; at low

tide 15 0/11. At Punta Gorda at high tide the salinity was

12 0/oo; at low tide 1 0/oo.


Human Settlements

Man's technological systems affect the great diversity

in ecosystem types in the Peace River area. These include

agriculture, urban areas, and especially the phosphate

mining district in Polk County. Table 1 has statistics

related to agriculture and urbanization for the four coun-

ties through which the Peace River flows. The large, grow-

ing population of Charlotte County is significant since it

surrounds the estuarine portion of the Peace River. Sewage

from 200,000 people is presently discharged into the Peace

River. Manufacturing in the area includes principally food

processing and chemicals employing 17,300 people in Polk

County and 780 in the other three counties. The fishing

industry in Charlotte Harbor grosses 3,444,000 pounds of

fish per year which sells for $646,000.

Most of the farm land (Table 1) is pastureland which

receives little subsidy in terms of fertilizers. The area

is a major citrus producer with about one-fourth of Florida's

production coming from Polk County (Fla. Stat. Abst., 1971).
















(n I--,


C) t3 oC










S O4- O
-O 0 il
















(d


Sr c







C C
cd H oo
rtA r-
r-4 ,









I-l
















0
















u
Uo
C C























C-O
0 cI\s/-
W t-Clo\
rtr 11^












3 u


- co a m


0 0 vo r-4

-4


0O 0 r-l 14

C 0 '-0 co

C(N







'-0 C0 tn C0


















(N i-l r-
r--1










(1 00 0 0






o" co o O





0 0 0
0) + r-1
k rt 0 -
h C-


(r-
C






o,
SC)









r- 0 >



SU --i
CCli
0












4-a c




*H C)
U4-




rf
4-
)


.-
















cd
C4-
0'











-4
Ud
+-.




'--4






?-
(-







Vegetables grown include cabbage, cauliflower, tomatoes,

beans, cucumbers, squash, and strawberries. Few field crops

are grown. Total dollar value of the farm products sold in

the four counties is $157,646,000 (Table 1).

The phosphate mining industry in Polk County exerts

the greatest influence on the entire Peace River Charlotte

Harbor system. Commercial grade phosphate rock occurs as

pebble size nodules (>1 mm) to a fine clay in the lower

half of the Bone Valley formation. Pebble phosphate is in

a deposit five to forty feet thick and ten to sixty feet

below the surface (Boyle, 1969). The matrix, a term used

to mean the ore or that part that can be economically mined,

is 30 to 60% phosphate rock, 10 to 25% quartz sand, and

15 to 40% clay and colloidal phosphate. Obtaining the high

grade rock involves strip mining where draglines with bucket

sizes up to 40 cubic yards remove the overburden and deposit

it in spoil banks along the side of the cut. Nine cubic

yards of overburden must be removed to obtain thirteen cubic

yards of matrix (Boyle, 1969). The phosphate rich material

is slurried into a pit by hydraulic guns which use 10,000

gallons of water per minute. This slurry of phosphate,

quartz sand and clay is pumped through fourteen-inch pipes

to the washer plant where the sand and clay are removed by

washing, screening, and flotation (Fig. 4). The waste water

is routed to hydroseparators which separate clear water from

slime. The clear water is recycled and the slime is routed

to settling ponds. Total water usage of the industry is































-I
Cz r1











U
04 0
0
O,









4J
rCE
1RO








*H










; -.
O6



4-c
rt *



U
&, *H





t.o.-

h41
0 **-
CI-























-J

I-



cnci)


I-


C-
<:

0
C:








0
-o
CO

o



u"


I-.
1-







0'0
CQ

Lt-


_ __ 1_~__~_1_







77,200 gallons per minute with 22,000 gallons (26%) coming

from deep wells and 57,200 gallons (74%) reclaimed from

processing and settling ponds (Boyle, 1969). The slimes

are nine to twenty-six percent solids by weight (Specht,

1950) and would take as long as 30 years to settle (Specht,

1950). Since the major constituents of the wastes are clay

minerals whose retention of water increases their volume six

to ten times, the volume of wastes exceeds the original

volume of rock removed by 1.25 times to 1.5 times. As a

result, the waste will not fit entirely in the mined-out

pits and diking above grade is required. This is hazardous

due to potential spillage and, in fact, dozens of slime

spills have occurred in the past 25 years (Dequine, personal

communication). Major slime spills, due to the toxicity and

high turbidity, kill river fish and cause heavy mortality of

the benthic invertebrates.

Other problems in the industry include air pollution

(particulate dust, sulfur dioxide, and fluoride emissions)

from beneficiation of the ore. Wastewater with high phos-

phorus, nitrogen, and fluorine contents at one time was

discharged to the rivers. However, presently it is par-

tially recycled.

In summary, the mining industry in Polk County has

transformed about 50,000 acres of farms, forests, and pas-

tures into spoil banks, slime impoundments, and water-filled

pits. Natural plant succession has produced young forests

in some areas.








Peninsular Florida

Since benefits and problems associated with man's use

of phosphorus are exemplified in Florida, it offers a unique

opportunity for examining phosphorus cycling and man in a

quantitative manner. Florida produces three-fourths of the

nation's marketable phosphate rock and one-third of the

world's (Florida Phosphate Council, 1973); a sophisticated

agricultural system, with its associated superphosphate

fertilizer use, exists in the state; Florida's many lakes

are subject to nutrient enrichment; its highly urbanized

areas have the usual associated nutrient waste disposal

problems; and its many estuaries acting as the final

nutrient trap are subject to enrichment and associated

depleted oxygen supplies.

The Environmental Protection Agency as well as Florida's

State Pollution Control Board is currently attempting to fix

wastewater effluent standards for phosphorus. For example,

the Wilson-Grizzle Bill'passed in the Florida State Legis-

lative session of 1972 requires the city of Tampa to use

advanced waste treatment processes for phosphorus removal

to 1 mg/1 P. Tampa sewage is discharged into Hillsborough

Bay which experiences the algal blooms and anaerobic bottom

waters associated with nutrient enrichment.

Criteria presently used to determine effluent standards

are often qualitative or refer to concentrations. For

setting standards for effluent, limits stated as







concentrations may be less useful than limits on percent

effects on existing flows. Few quantitative data on

flows have been prepared for regional or statewide systems.

Demonstration of this new approach is done here in evaluat-

ing phosphorus cycling in the state; the percent effect of

each flux on the overall chemical cycle is determined.

State water quality programs based on this sort of quanti-

tative data may be more meaningful and efficient.

As higher standards for phosphorus in domestic waste-

water and mining wastewater effluent are met, Florida's

population continues to grow exponentially so that the net

gain in water quality may be negligible. In order to

evaluate this, a clear quantitative understanding of phos-

phorus storage and rates of flow from storage to storage

must be acquired.

The evaluation of phosphorus cycling in peninsular

Florida (Fig. 1) done here examines the magnitude of the

outside sources of phosphorus to the state, of the storage

and recycling pathways within the state, and of the phos-

phorus losses from the state.


Florida's Phosphate Rock Deposits

In order to understand and calculate rates of formation

of Florida's phosphate rock, data on the geologic formations

and their phosphorus contents are pertinent. For reference

a Cenozoic time scale with the principal Florida formations

is included as Table 2.




















a H I
*U O n1 =
r> .,-Ir

*- 0 -n o I

SGOCH II o

(1) H* (3) 1 k
u EoI
) o C1 0
q() .
H ;-4 H 4- 4 4-J +-J

oo _H













*H O0 0 C )
H C -*





0- If 0 0 O .
I nn 4 0 + _
-1*H 4-J
1= r-i C: Lf) r( )a







0 0 0 0 -
) r s0

u i- I C)) -C







oo He o ( o *
0o e. o a 0 o o o o
r-I 0 I





S U 4I > -) *H rIn
4- 0 4- I ( )











N fC) I O a, Cd 0
oU w .,- I EfO .r- O 4- r ,-










I rq I rz o c d 0 -
C) 0 1 -4 - () 4-0 0






U Zdo < 0H 0 00
wU rw r-i E o o 4-

SE E 4-O E r4 0 (4 r-





0( o 0 U)
.l ri aI C) os C
04 U I UU- C w) U -i c is -4





w0 C 0 m) 4-J Nc)
PQ O > 0 u .1 W 0)








0 4- C! I u 4- Z r C
0 C) *H 0 u 00 C 0 Q C
( *H e O 0 H tt u ( O
IU O-r PC I 0 H U 0 UOr
Sw. 0
) I C) (U > (




0 E a e o




(4 C)
SU 4-4-)


p 0C 0 O
OP I EU
O' I ? 1 M
0- E- I r r e







Florida stratigraphy is dominated by a thick series of

shallow marine deposits, principally limestone, ranging in

age from Lower Cretaceous to Recent. The principal struc-

tural feature is the Ocala Uplift, a broad oval arch trend-

ing N-NW and centering in Levy or Marion County (Cooke,

1945). The Ocala limestone of Eocene age is exposed at the

surface on the Ocala arch. This limestone is the dominant

stratigraphic unit underlying most of Florida; solutional

features in the Ocala limestone cause the Karst topography

typical of much of northern peninsular Florida. Although

Oligocene rocks are absent in much of Florida, the Suwannee

limestone of late Oligocene age occurs in West Central

Florida in the region of the land pebble phosphate district.

Both the Ocala and Suwannee limestones are quite pure, being

91 to 98% CaCO3. The Tampa limestone of early Miocene age

lies on the eroded surface of the Suwannee limestone (Cooke,

1945) in the northern part of the phosphate district. It

is an impure sandy and clayey limestone containing chert

nodules and trace amounts of phosphate (Altschuler et al.,

1964). For reference, the location of the land pebble phos-

phate district and a stratigraphic cross-section through it

are shown in Figs. 5 and 6, respectively.

Of particular interest in this study is the Hawthorn

Formation of middle Miocene age. It consists chiefly of

gray phosphatic sand and lenses of green or gray clay

(Cooke, 1945). It is thought to consist of the deposit of

























4-)
,*H

Er- *















C) 4-).
i-l CP


*H



Orl






0 ;4- 4J













r-i 04
C) <












(1) 0
C-, CO






* r--- U)
o -H e -





4-- ,,C
C)




"U 0
F.-














onC)
*H





---























I'
O 0
I I
It
a


C

,c-,


- -


C l

rU
<0





















04-
U
*H Co
- 0 I-
P *Hrl \0
tU) -m


.( U
ri *I r--*

U, ,I

04-1
o 0-


d 00


b 0 t-
0 0


Cd
ce o






0 *H C)

0 cd










4U)
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t zo
o *H








bt



















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C,

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C:
r- o
o o

c'
















00






-00


z
co





































<-o
ro



































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00











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a transgressing sea that flooded an eroded land surface.

Cooke (1945) and many others-believe that it was deposited

over all of what is now Florida and has since been eroded

from the Ocala arch. Vernon (1951), however, believes that

the Ocala arch was already above sea level during Miocene

time and that the Hawthorn formation was never deposited on

it. The Hawthorn formation averages 4 to 17% CaPO4 (Carr

and'Alverson, 1959).

Although there are seven Pliocene age formations in

Florida, only the Alachua formation and the Bone Valley

formation are of interest here. The Alachua formation is

unique in Florida in that it is a terrestrial deposit con-

taining bones of land animals of middle Pliocene age. It

always overlies the Ocala limestone, the Hawthorn formation

having been leached away (Cooke, 1945). The lower part of

the Alachua formation contains phosphate rock (35% P205)

occurring as plates and boulderlike masses. Cooke believed

that the phosphate originally occurred as grains in the

Hawthorn formation. He stated that the grains were dissolved

by downward percolating rain water; when the solution reached

the underlying rock, the phosphate was reprecipitated. He

believed this process began as soon as the Hawthorn forma-

tion emerged from the sea and has continued ever since,

although interrupted during the Pleistocene epoch.

The Bone Valley formation, which is the only formation

mined today, consists of clayey sand in its upper part and







phosphate particles, sand, clay and gravel in its lower

part (Altschuler et al., 1964). It is believed to have been

deposited in the broad delta of a stream opening into the

ocean with parts being deposited in the open sea. The

average P205 content of the nodules is 35% (Vernon, 1951).

The phosphatic portion contains both land and marine verte-

brate fossils (Sellards, 1913).

In summary, the oldest stratigraphic unit containing

phosphate is the Hawthorn formation (middle Miocene);

Pliocene formations deposited on or partially derived from

the Hawthorn formation are enriched in phosphorus to the

extent of being economically mineable. An explanation for

the origin of the phosphorus, then, must account for the

phosphorus in the Hawthorn formation as well as that in the

mineable rock of later formations.














METHODS


Model Development


From the review of the literature and from conferences

with many people concerned with the area under study, pre-

liminary models were developed. These can be written in

mathematical language or diagrammed in pictorial represen-

tation of flows, storage sites, and process pathways.

First, the state variables (stored properties) of the system

were listed; these became the storage tanks in the model

diagrams. A list of outside energy sources and forces

which affect the level of the quantity in the storage tanks

was compiled. These became the circular forcing functions

of the model diagrams. The storage tanks and forcing func-

tions were connected by lines with the intersection of path-

ways being some function indicating their interaction.

Intersection functions may be additive, multiplicative,

exponential, logarithmic, or switching (on or off action).

The model building process led to the identification of

major pathways and state variables. Then numerical data on

magnitudes were obtained from the literature. All numbers

refer to some base line year and to the specific area being

modeled. Where observed data from the area were unavailable,








numbers for the same process in another similar area were

used.



Symbols Used in Model Diagrams


All models are depicted in the energy language devel-

oped by H. T. Odum. A description of each symbol and its

mathematical meaning can be found in Odum (1971b and 1972).

The symbols used in the models in this thesis are pictured

and described in Fig. 7. The Peace River estuarine model

involved fluid transport of a solute (phosphorus in water).

The sensor and other symbols needed for these models devel-

oped by H. T. Odum after his original book are included in

Fig. 8. In the Peace River estuarine model the sensor was

used both with and without a backforce.



Examination of Numbers to Gain Perspective


After each pathway was identified and estimated numeri-

cally, it was possible to do an overall budget calculation

of the whole system and of unit models within the system.

Missing values in some instances were calculated by differ-

ence as if the system were in steady state. Associated with

each state variable are inflows and outflows so that the

budget for the storage was easily calculated. This made

possible identification of the relative importance of each

pathway. A pathway with a numerical value several orders

of magnitude less than others does not exert a major effect














Figure 7. The symbols of the energy circuit language
used in this thesis (from Odum, 1971b).

a. Outside source of energy delivering
forces according to a program con-
trolled from outside; a forcing
function (N).

b. A pathway whose flow is proportional
to the quantity in the storage or
source upstream (J = kN). The heat
sink represents the energy losses
associated with friction and back-
forces along pathways of energy flow.

c. A compartment of energy storage
within the system storing a quantity
as the balance of inflows and out-
flows (Q = J kQ).

d. Multiplicative intersection of two
pathways coupled to produce an
outflow in proportion to the product
of both; control action of one flow
on another; limiting factor action;
workgate (KN1N2).

e. A combination of "active storage"
and a "multiplier" by which potential
energy stored in one or more sites in
a subsystem is fed back to do work on
the successful processing and work of
that unit; autocatalytic (Q = kQ(N -
Q/C) and many variations.

f. Production and regeneration module
(P-R) formed by combining a cycling
receptor module, a self-maintaining
module which it feeds, and a feed-
back loop which controls the inflow
process by multiplicative and limit-
ing actions. The green plant is one
example. On a large scale the module
may represent plants and consumers
of ecosystems or agriculture and cities.















Output


Steady State Flow


Energy Source
(A)


Input


Heotsink
(B)


Output


State Variable

(C)


Output


Multiplier Interaction

(D)


Input


Group Symbol
(Self Maintaining
Consumer Population)


Group Symbol
(Plant Population)


Output


__


Input





























Figure 8. Diagrammatic representation and mathematical
description of the sensor symbol for use in
modeling the fluid transport of a solute,
taken from Odum, memorandum number 11, 1972.
The sensor delivers a force to a diverging
pathway that is proportional to the flow
sensed and derives its energy from it.

















KJ KJ
Sensor of Flow Sensor of Flow
J from left J from right


(a)




er









Q2
- KI QI =K Q2

No Backforco
(b)


L Q
L6-
lC,


With Backforce
(c)


_ __








on the system, and conversely a pathway several orders of

magnitude larger than others is one to be considered care-

fully since it may be the controlling pathway for the system.

To gain further perspective on the importance of pathways,

residence times and turnover rates for each state variable

were calculated. The residence time is the quantity in the

storage divided by the sum of the flows into it, and the

turnover rate is the inverse of the residence time. These

calculations yielded insight into times involved for change

and stability.



Simulation Model


Computer simulation of the entire model developed for

each system was not readily done or useful since the models

were large. However, at this stage in the methodology,

the relative importance of each pathway was estimated, and

insight into expected model behavior gained. Then a simpli-

fied diagram was developed. It included the pathways and

compartments which play a major role in model behavior and

which are important for variations to be simulated. A test

simulation was made of the simplified model in order to

identify unexpected model behavior. Although the whole com-

plexity of the system was not simulated with the simplified

model, it represented the essence of the system and identi-

fied unexpected complications (e.g., if a state variable

decreased when it was expected to increase).








Writing and Scaling Equations


The set of differential equations associated with each

system was written directly from the energy language diagram

of the system. Each storage or state variable is the inte-

grated sum of the inflows minus the sum of the outflows

plus initial conditions. The mathematical terms for each

inflowing or outflowing pathway are shown in Figs. 9, 25,

and 38 (refer to Odum, 1972, for the theoretical derivation

of the mathematics associated with the energy language).

The set of differential equations of the real systems

all required magnitude scaling to keep outputs within the

range of voltages on the analog computer. In scaling, the

values of the voltages in the computer are related to the

values of the corresponding dependent variables in the

system. Thus, the scale factor is a constant of propor-

tionality which tells how many volts on the computer repre-

sent one unit of the corresponding variable in the system.

Since the constants chosen for scaling must have a magnitude

at least equal to the maximum value of the associated origi-

nal variable, some knowledge of the maximum values of the

variables in the system is required. The numerical coeffi-

cients of each of the terms in the equations are transformed

into potentiometer settings on the analog computer. These

settings may range from 0.001 to 0.999 so that all coeffi-

cients must be scaled to fit into this range.







Simulation Procedures


There are advantages and disadvantages to both analog

and digital computer simulation procedures. The analog com-

puter allows for continuous rather than step-wise integration

and gives the user closer communication with his model;

however, the size of the model is limited by the hardware

on the computer. Digital simulation has errors if steps

are too large, costs more, and takes longer to debug. Both

were used in the simulations done here.


Digital Simulation Procedure

The Peace River Estuarine System model was simulated

on an IBM 1800 computer. The differential equations were

written in Digital Simulation Language (DSL); a language

developed for continuous simulations on the 1800 computer.

The program was prepared directly from the set of differen-

tial equations and utilized a fixed format for input and

output. These features greatly simplified the programming

and allowed the user to concentrate on the problem rather

than on the mechanism for implementing the simulation. The

language utilized centralized integration to ensure that

all integrator outputs were computed simultaneously at the

end of the integration cycle. These simulations utilized

fourth order Runge-Kutta integration with a fixed step size.

The step size programmed corresponds to one day except during

the slime spill when it was one minute for four days. All

DSL programs are included in Appendix B.








Analog Simulation Procedure

A submodel of the estuarine mouth of the Peace River

System with nitrogen and phosphorus interactions and a

geologic time model of phosphorus deposition were simulated

on the Electronic Associates, Incorporated, MiniAc analog

computer. An analog diagram or program (Appendix B) was

written directly from the differential equations and

patched onto the MiniAc board.



Experimental Manipulations of Models


Alternative management choices related to man's impact

on the system were involved in each model simulation (see

discussion). Each issue was tested separately; appropriate

calculations to incorporate changes in the numerical values

were performed and the model simulated for this variation.

The models were used as though controlled experiments had

been performed for one factor at a time.













RESULTS AND DISCUSSION


Phosphorus in the Peace River Charlotte
Harbor Estuarine System


Data Evaluation

The simplified model for the Peace River system is

given in Fig. 9. Included are the mathematical terms for

each source, storage, and flow. Figure 10 is the same dia-

gram showing the numerical values calculated in Table 3

using data obtained from the literature. Table 3 describes

the parameter defined, gives its numerical value and the

source for the number. Notes found in Appendix A

describe in detail the derivation of each numerical value.

Since the large model represented in Fig. 10 is diffi-

cult to conceptualize, the relative magnitude of the flows

of water and of phosphorus into the river mouth (into Q4

and Q5) are shown in summary diagrammatic form (Fig. II).

Note that the river flow, mining water, and tidal

input are all the same order of magnitude (Fig. lla).

Sewage effluent is less by two orders of magnitude and

water from a slime spill is higher by one order of magni-

tude. Note that mining water is a significant percentage

of the river flow (26% when the river is at intermediate
























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Figure 11. Summary models for a unit area.

a. Flux of water into Phe Peace River
Mouth; units are 10 m3/day.

b. Flux of phosphorus into the Peace
River Mouth; units are 106 g/day.













- -- 10.0

- -- 5.0

- - - - - -- 1


River


TIDE=5.76


Slime


------15.0

---- 7.5

-------------- .15


River Proper


TIDE=


(b)


__ C_ ~II


__








flow). When a slime spill occurs, the water discharged

into the river greatly increases; the data indicate river

discharge approximately doubles.

With similar considerations in mind, note the relative

magnitude of the phosphorus flows into the river mouth

(Fig. llb) from rivers and tide.

Clearly, the total phosphorus contribution of each

source to the river is dependent not only on the phosphorus

concentration but also on the amount of water from the

source. For example, except for slime pond water, sewage

effluent has the highest concentration (5 g/m ). However,

phosphorus contribution to the river from sewage is the

smallest of all flows. On the other hand, tidal water which

enters the river mouth with a flood tide has a relatively

low concentration (0.35 g/m3) but the tide contributes a

significant amount of phosphorus to the system. In the

first case small amounts of water are involved and in the

second case large amounts of water enter with the tide.

Except during the dry season the river proper, whose phos-

phorus comes from the natural drainage of the Peace River

system (approximately 1,400 mi2, Lanquist, 1953), is the

major phosphorus contributor.

Phosphorus in mining water, in the drainage water proper,

and in the flood tide input is the same order of magnitude.

Contributions from sewage and sediments are one order of

magnitude smaller while, if a dam break with a corresponding







slime spill occurs, the contribution of phosphorus is five

orders of magnitude larger than all other contributors.

The phosphorus contribution of the Myakka River (Fig.

10) to the northern part of Charlotte Harbor is also one

order of magnitude less than the flows from major outside

sources.

As calculated for the amount of phosphorus in and out

of the sediments, the model is in steady state unless a

slime spill occurs so that no net erosion or deposition

takes place.

Residence times for each estuarine storage were calcu-

lated by dividing the quantity in the storage by the sum of

all flows entering the storage (Q/EJ). Turnover rates are

the inverse. The results are given in Table 4. All the

residence times are similar (three to six days) except the

phosphorus in sediments, most of which is inactive.


Simulation Evaluation

Figure 9 depicts the mathematical terms which represent

each storage and flux in the system. Differential equations

needed for a simulation of the system are written directly

from this diagram (Fig. 12).






66










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x = Q4/A4+z a = Qs/Q4
y = Q6/A6 b = Q7/Q6
z = Q8/A8 c = Qg/Q8
w = H+D


Q1 = -k lQJ3B-k2QJ3A

if Q 2>R and J 4>7
2 = J3B-k3Q2

if Q2>R1 and J4>7
3 = klQ1J3B-k3Q3
if Q2>R1 and J4>7
Q4 = +3A+J-k5(x-y)+k32
if y S = JlJ2+J J6+k2QJ13A-k7J9Q5+k8J10Q10-k9a(x-y)

if y>x if Q2>R1 if a>R
f yx and J4<7 2
-kl0b(x-y)+k 3Q3 -k6Q


6 = J7+k5(x-y)-kll(Y-z)

if yx if zy
Q7 7 J8+k9a(x-y)+ b(xy)-k12b(y-z)- 5(y-z)

-k13J 11Q7+kl4J12Q1


Q8 = kll(y-z)-k6 (z-w)


Figure 12. Differential equations.







if zy if w>z if w Q k12b(y-z)+k c(-z)-k7 1(z)-kc(

-k19J13Q9+k20J14Q12

if a>R
Q10 = k7JgQs5-k8J1oQ


611 = kl3J11Q7-kl4J12Ql1


Q12 = k19Q9J13-k20J14Q12


(continued)


Figure 12.







The computer program in Digital Simulation Language

(DSL) for the entire set of differential equations is found

in Appendix B. That simulation takes out the daily tidal

effects and assumes mean low tide for all values (Appendix

B). All programs with corresponding data changes for the

simulation variations are found in Appendix B.

Results of the digital simulation for five years are

shown in graphical form in Figs. 13, 15 and 16. Figure 13

depicts the water, the total phosphorus, and phosphorus

concentration in the Peace River Mouth. Note that steady

state was immediately attained and continued. The fluctu-

ations in quantity of water (Fig. 13a) in the river mouth

correlated in shape directly with the sine wave input

(Fig. lla). Huang and Goodell (1967), Dragovich et al.

(1968) and the USGS Water Resources Data for Florida -

Surface Water Records (1964-1968) all give Peace River dis-

charge data which indicate maximum discharge in August and

September as the simulation showed; however, the literature

indicated a second, less significant peak in January and

February. The water in the river mouth rises and falls

with the order of magnitude shown in the simulation; however,

there is a second high in January and February. During the

period of maximum flow the model predicted a depth (volume/
7 3 7 2
area) for the river mouth of 5.16 meters (9.2x10 m /1.78x10 m )

or 16.5 feet, and at low flow a depth of 2.35 meters

(4.2x107m3/l.78x107m2) or 7.55 feet was predicted. These


























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values agree well with depths given on the U.S. Coast and

Geodetic survey map, 1971.

The fluctuations in quantity of phosphorus in the Peace

River mouth (Fig. 13b) correlated in shape directly with the

sine wave input (Fig. llb). The simulation indicated that

the total quantity of phosphorus in the river mouth depended

largely on the total volume of water present. In support of

this is the statement from Dragovich et al. (1968), "the

quantity of nutrients contributed by the river to the sea

is determined largely by the volume of river flow, not by

actual concentrations of nutrients. The maximum amount of

phosphorus is discharged in August and September when maxi-

mum runoff occurs."

The amplitude of fluctuation in phosphorus concentra-

tion (Fig. 13c) was considerably less than fluctuations in

total water volume or total phosphorus (Figs. 13a and 13b).

This flatter curve implies that input concentrations are

staying relatively constant while volume of water varies,

which is the case. The curve is flat except for dips in

concentration during the dry season. The curve is shaped

in this manner because the main contributor of phosphorus

except during the dry season was the water draining the

region (river proper) which was high in total phosphorus

(1.5 g/m3 ). During the dry season the major water flow

came from mining operations at a concentration of 1.0 g/m3

The result was that the overall concentration drops. This







result does not correspond exactly to the data given by

Dragovich et al. (1968) or the data in the USGS Water

Resources Data for Florida publications. These sources

indicated that fluctuations in concentration were more

severe; however, their data indicated that concentrations

were high for a longer period of the year than they were

low, and they were low during the dry season. Figure 14 is

a graph of dissolved phosphorus concentration for four years

as given in the USGS Water Resources Data for Florida at

Arcadia, Florida, fifteen miles north of the portion of the

river under study. Concentrations of total phosphorus indi-

cated for the river mouth by the simulation ranged from

1.13 g/m3 to 1.39 g/m3 Alberts et al. (1970) stated that

90% of the phosphorus in the area was dissolved and found

an average concentration of 0.6 g/m3 dissolved phosphorus

which, assuming it represents 90% of the total phosphorus,

is lower than that predicted by the simulation. However,

total phosphorus was not measured. The USGS data at

Arcadia (Fig. 14) were higher than those predicted by the

simulation. Dragovich et al. (1968) obtained an average

total phosphorus concentration for the river mouth of

0.93 g/m3 which agrees quite well with the simulation pre-

diction. John F. Dequine of the Southern Fish Culturists,

Inc. (personal communications), found inorganic P values

for the river mouth ranging from 0.233 to 3.27 mg/l P.

The average value was 1.9 mg/1 P.







Dequine's values also agree well with those predicted by

the simulation.

Figure 15 shows the simulation results for water, total

phosphorus, and total phosphorus concentration in the

northern sector of Charlotte Harbor. Similar seasonal fluc-

tuations in water volume and total phosphorus with river

discharge were observed, but the amplitude of the seasonal

change was less than that in the river mouth. This was the

expected result due to the dampening effect of the tide and

the larger area in the harbor over which the river discharge

was spread. The volume of water present (Fig. 15a) during

the dry season predicted an average depth (volume/area) of

3.4 meters (5.0x10m3 /1.468x108m2) or 10.9 feet. During

maximum river discharge period depth was 6.1-meters

(9x108m3/l.468x108m2) or 19.6 feet. These depths agree well

with those given on the U.S. Coast and Geodetic survey map

(1971).

The graph of phosphorus concentration in the northern

sector of the harbor (Fig. 15c) was not as flat as it was

for the river mouth but followed more closely the shape of

a sine wave. The larger tidal input of total phosphorus in

this area predominated over fluctuations farther up the

river. Concentration during the low water volume period

was 0.45 g/m3 and during the high water volume period was
3
0.75 g/m3. These values are somewhat higher than those

reported as dissolved phosphorus by Alberts et al. (1970);







the maximum values reported there were about 0.5 g/m3 and

the average is 0.35 g/m3

Note that all three graphs of Fig. 15 show a time

lag between minimum and maximum points for this area rela-

tive to the up river area given in Fig. 13. The lag was

about 7 days.

Figure 16 has the simulation results for the southern

sector of Charlotte Harbor. Seasonal fluctuations in water

volume and total phosphorus were greatly dampened by the

large tidal effect. Simulation graphs indicated a depth for

the harbor at the low volume period of 2.9 meters

(3.5x108m3/l.871x108m2) or 9.3 feet. At maximum volume
83 82
period the depth is 3.47 meters (6.5x10 m 3/.871x10 m ) or

11.1 feet. These depths agree well with the U.S. Coast and

Geodetic survey map (1971).

The graph depicting phosphorus concentrations in the

southern sector of the harbor (Fig. 16c) indicated little

seasonal change in concentration. Minimum concentration

was 0.3 g/m and maximum was 0.41 g/m3. These values were

slightly higher than the average value of 0.25 g/m for

dissolved phosphorus found by Alberts et al. (1970). There

is no question, however, that the phosphorus concentrations

of Peace River water did affect the entire southern sector

of the harbor. Alberts et al. (1970, p. 9) stated,"the

wedge of high phosphorus Peace River water maintains its

integrity to Boca Grande Pass."








The time lag in the minimum and maximum was seven days

from the northern sector of the harbor to the southern

sector and fourteen days from the river mouth to the southern

sector.

Graphs for the total phosphorus in sediment storage

(Q10' Q11' Q12) are not given since the values remained
constant at the initial conditions throughout the simulation.

Huang and Goodell (1967) stated that no net deposition or

erosion has taken place in the harbor for at least the last

100 years. In the river mouth there was evidence that net

deposition due to slime spills (Harriss, 1972) has taken

place (see discussion following, page 94); however, for

the purpose of initial modeling a steady state was assumed

and the simulation indicated the same.

With the hope of gaining some insight into the effects

of increased pollution pressures in the area which may arise

as population increases in South Florida, four variations

of the simulation were run: adding nitrogen flux, reducing

mining effluent, increasing sewage, and following a surge

from a slime pond dam break.


Deposition of Phosnhorus in Sediments

Several factors including a nitrogen increase or

increased pll could cause deposition of phosphorus in the

sediments of the estuary. Pathways J9, Jll, and J13 of

Fig. 9 pump phosphorus into sediment.







Total dissolved nitrogen concentrations were low in the

estuary ranging from .1 mg/l (Connell and Associates, 1972)

to .34 mg/l (Odum ct al., 1955). High phosphorus may stim-

ulate organic use of nitrogen, keeping it low. As a result,

nitrogen may be an important factor in limiting phytoplankton

in the presence of high dissolved phosphorus concentrations.

If, in the future, nitrogen concentrations increase sub-

stantially due to sewage disposal, urban runoff, or indus-

trial waste disposal, eutrophication problems may arise.

For example, Hillsborough Bay (Fig. 1), receiving phosphorus

from the Alafai River and sewage from Tampa, has high phos-

phorus and high nitrogen; it experiences eutrophication

characterized by frequent phytoplankton blooms and low dis-

solved oxygen in bottom waters where large amounts of organ-

ic material are respired (Federal Water Pollution Control

Administration, 1969).

As a first step in understanding effects of phosphorus

deposition, the pathways (J9, Jll, and J13 of Fig. 9) were

increased by a factor of ten. The results are presented in

Figs. 17 and 18. Total phosphorus and phosphorus concentra-

tions decreased sharply in waters with an increase in phos-

phorus in sediments. The new minimum value for the river

mouth was 0.4 and the maximum was 1.0 g/m3 (1.13 and 1.39

previously). For the northern sector of the harbor, the

new value ranged from 0.037 to 0.097 g/m3 (0.45 to 0.75 pre-

viously). In the southern sector, the new range was 0.023

to 0.025 g/m3 (0.3 to 0.41 previously).

































Figure 17.


Simulation variation of the model in Fig.
in which the factors causing phosphorus
precipitation (J9, Jll, and J13) were
increased by a factor of ten, pumping
phosphorus from the water to the sediment.


















Precipitation Fcctors Increased


River Mouth


YEARS
(a)


Precipitation Factors Increased


2 YEARS
River Mouth (b)


-Precipitation Factors 'Increased


Northern Sector
Charlolte Harbor


YEARS
(c)


10'-


Q5
Phosphorus,

0
0 1


07
Phosphorus
9


___~111~


----






























Figure 18. Simulation variation of the model in Fig. 9
in which the factors causing phosphorus
precipitation (J9, Jll, and J13) were
increased by a factor of ten, pumping
phosphorus from the water to the sediment.





















1.0-

Q7/Q8

Phosphorus
Concentration,
g/m3


Precipitation Factors Increased


Northern Sector
Charlotte Harbor


PreciFitction Fcctcrs increased


Southern Sector
Charlotte Harbor


1.0-

Q9/08

Phosphorus,

g / m3
0-


Southern Sector
Charlotte Harbor


YEARS
(a)


Phosphcrus,


0


YEARS
(b)


YEARS
(c)


_ _I_ ____


I __ _


Precipitation Factors Increcced







In eutrophic lakes and bays, which have pathways

returning nutrients to the surface waters, concentrations

often remain high. Hillsborough Bay maintains a total phos-

phorus concentration of 3 to 7 g/m3 with the highest value

at the mouth of the Alafai River (Federal Water Pollution

Control Administration, 1969). This estuarine model (Figs.

9 and 10) may not depict the complete dynamics of phosphorus

sedimentation and regeneration which develops under eutro-

phic conditions. For this reason, a more detailed model of

phosphorus and nitrogen interaction was developed (Fig. 25)

and simulated.


Mining Water Effluent Decreased to Zero

At the present time, part of the clear effluent from

the slime ponds in the mining district is not reused but is

wasted to the river (Boyle, 1969). The volume of water dis-

charged is 1.3x10 m (J3A in the estuarine model, Fig. 9)

at a concentration of 1.0 g/m3 (J3D in the estuarine model,

Fig. 9). In order to determine what effect the constant

influx of mining water has on the phosphorus concentration

of the river mouth and harbor, these two quantities (J3A

and J3D) were set equal to zero and the model simulated.

The results are presented in Fig. 19. Water volume was

lower in the river mouth and northern sector of the harbor

(Figs. 19a and d) by 25% and 4% respectively during the dry

season and 10% during periods of maximum flow. Total phos-

phorus was reduced by 11.5% in the river mouth and 6.2% in




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