Systems analysis of nutrient disposal in cypress wetlands and lake ecosystems in Florida
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Title: Systems analysis of nutrient disposal in cypress wetlands and lake ecosystems in Florida
Physical Description: xvi, 421 leaves : ill. (part col.) ; 28cm.
Language: English
Creator: Mitsch, William J
Publication Date: 1975
Copyright Date: 1975
 Subjects
Subjects / Keywords: Eutrophication -- Florida   ( lcsh )
Water -- Pollution   ( lcsh )
Water -- Analysis   ( lcsh )
Sewage disposal   ( lcsh )
Environmental Engineering Sciences thesis Ph. D
Dissertations, Academic -- Environmental Engineering Sciences -- UF
lakes
cypress
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 410-420.
General Note: Typescript.
General Note: Vita.
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Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000159831
oclc - 02639875
notis - AAS6162
System ID: UF00098316:00001

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SY'STEPlS ANALYSIS OF NUITRIE~NT DISPOSAL IN\
CYIPR~ESS WEITLANVDS AN~D LAK;E E~COSYISTEM1S IN FLORIDiA





By



WILLIAM JOSEPH1 PIlTSCH













A DISSERTATION PRE~SENT'iED TO THE GRADUATE C~OUN:CIL OF
THE UN\IVERSITY' OF FLOR:IDA
INd PARTIAL FUILFILLMENT~I OF THE REQUIICIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHYI



UNIVERSITY OF FLORIDA


1975














ACKN OWLED AGENTS



A systems analysis, by its definition, requires inputs

from many sources and disciplines. The author was fortunate

to have Hl. T. Odum as chairman and K. C. Ewel as co-chairman,

both of whom saw the similarities rather than the differences

in systems and helped me cross into new fields of study.

Mly supervisory committee also included P. L. Brezonik,

W. C. Huber, F. G. Nordlie, and E. E. Pyatt. P. L. Brezonik

provided data critical to this study. Data were also given

by J. L. Fox. Ml. K'eirn, C. L. Coultas, and J. Steinberg.

Climatological data were supplied by G. Prine of the Agronomy

Department and tree growJth data were supplied by J. Lewis of

the State Division of Forestry and W. Schlitzkus of Owens-

Illinois Inc.

Some of the field data were collected with the coopera-

tion of others, including Ml. Bishop, R. Bloom, T. Butler,

G. Bourne, S. Brown, T. Center, L. Chesney S. Cowles B. Cut-

right, K. Dugger, K. Heimburg, R. Klein, D. Layland, T.

Morris, D. Post, D. Price, R. Smith, and P. Straub. J. Ordway,

site manager for the cypress domes, provided man-power and

engineering.

Lake Alice work was supported by the National Science

Foundation on Grant GK-34232 entitled "Data Acquisition and








Manag~emen for Water Quality' Control" to the Depar~tment of

E~nvironmnental Engineer~ing Sciences, WJ. C. Huber and J. P.

HeaneY, co-pr~incipal investigators. Cypress dome work was

supported by! the N~ational Science f~oundation's RANN Div~ision

with Grant GI-38721 and Rockefeller Foundation's Gr~ant RF-

73029 entitled "Cypress wetlandss for IWater Mlanagemnent,

Recyclin g, and Conserva'tion"' to the Center for Netlands,

H. 1. Odum and t:. C. Ewel, principal investigators. Compulter

facilities at thle N~or'theaSt Regional Data Center of the State

Ulniversity System of Flor~ida wJere utilized.


111

















TABLE OF CONTENTS


Page


AC KN OWLEDGMENT S ..........

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


LIST OF FIGURES ...


. . ix

. . xv


ABSTRACT


INTRODUCTION


1


Eutrophication and the Waterhyacinth System
Wetlands as Potential Nutrient Sinks ...
Mathematical Approaches to the Concept
of Limiting Nutrients .........
Study Areas . . . . . . . .

lE TH-iODS . . . . . . . . . .


. . 24

. . .31
. . 45

. . 68


Data Collection for Lake Alice...
Data Collection for Cypress Wetlands
Modeling Mlethods..........


RESULTS .....


. . 88


Data from Lake Alice .....
Lake Alice M~odel .......
D~ata from Cypr-ess W~etlands ..
Cypress Dome Mlodel ......
Cypress Pond M~ini-Mlodel ...


88
125
177
243
284


. . .
. . .
. . .
. . .
. . .


DISCUSSION . . . . . . . . .


Comparison of Eutrophic Cypress Dome
and Eutrophic Lake ..........
Comparison of Nutrient Uptake ......
Preliminary Evaluation of Nutrient
Disposal Alternatives .........
Succession in Lake Alice .........
Cypress Tree Production .........
Cypress Domes and Fire ..........
Analysis of the Limiting Nutrient Concept
Recommendations for Management ......


. . 303


.303
.309


319
331
336
342
344
349










TABLE OjF CONTENTS continued


Palge


APPENDLIX

A A REVIEW OF TH1E LITERATURE ON LAN~D
DISPOSAL OF N~UT`RIEN!T WASTES .......

Literanturee Cited in Ap~pendix A ...

8 SUPPLEMENT~AL IATERIAL FOR LAK;E ALIC~E
IOD)EL AS G~'IVEN IN FIGURE 33 A1ND TABLE S .

C SUPPLEMENTAI-L IATERIAL FOR CYPRESS DOMlE
IMOiDEL A~S G'IVEN lIN FIGURE 62 A4ND TABLE 23

D SUPPLEIMENTATL 1.1ATERIAL FOR CYPRESS PONDU
MIN;1-GIODEL AS GIVEN IN FIGURE 76 ANJD
TABLE 25 . . . . . . . .

LITERATURE CITED . . . . . . . .

BIOGRAPHICA L SKETCH . . . . . . . .


. . 352

. 70


. 75


. 3 1




. . 40

. 10

. 32
















LIST OF TABLES


Page


Tab le

1 SUMMI~ARY OF ANALYTICAL PROCEDURES AND
ASSOCIATED REFERENCES FOR N\ATER CHEMISTRY
ANALYSIS OF LAKE ALICE AND CYPRESS DOM1ES .

2 LAKE ALICE HIYACINTH~ COVERAGE FOR THREE
DATES IN 1973 . . . . . . .

3 W~ATERH~YACINTHI blETABOLISM AND BIOM1ASS DATA
AT LAKE ALICE ON AUGUST 11-13, 1973 ...

4 NET PRODUCTIVITY OF WATERHYACINTHS TAKEN
FROM PUBLISHED MATERIAL .........

5 STANDING BIOMIASS OF: WATERHYACINTH~S TAKEN
FROMl PUBLISHED MIATE3RIAL .........

6 WATER COLUMN METABOLISM FOR OPEN LAKE
COMlMUNITY IN LAKE ALICE .........

7 RANGES OF N\ATER QUALITY PARAMETERS
(MlONTH-LY AVERAGES) FOR LAKE ALICE,
J AN UARY -SE PT EMBE R, 19 73 .........

8 STORAGE AND PATHWAYS FOR LAKE ALICE MODEL
SHOWN INJ FIGURE 33 . . . . . ..

9 DIFFERENTIAL EQUATIONS AND SPECIAL FUNC-
TIONS FOR MODEL IN FIGURE 33 .......

10 FORCING FUNCTIONS FOR FIRST THREE LAKE
ALICE MlODEL SIMULATIONS .........

11 SUMMI\ARY OF MONTHLY LOADING RATES IN
EXPERIMENTAL CYPRESS DOMIES ........

12 MONTHLY AVERAGES OF HYDROLOGIC FLOWdS
IN SEWJAGE DOIE . . . . . . .

13 POND CYPRESS BIOEASS DATA ........

14 REGRESSION ANALYSIS FOR POND CYPRESS
B I OMAS S . . . . . . . .


. .73


. .98


. . 105


. .106


. 107


. 109



. .110


. .129


. .153


. .158


. .181


. .186

. 189


. .196








LISTI OF: TABLES continued


Table Page

15 POIND~ CYPRESS BIOWASS ATr SEWAGE DOMlE .. .. 197

16 PO[ID CY'PRESS BIO:ArSS AT GROUIIDWATER D~OMEE .. 198

17 RESULTS OF CY'PRESS NET PRODUCTIVITYI
CA~LCUJLATIONS FOR: 23 PLOTS IN W~ITHLACOOCHEE
STA~TE FOREST .. .. .. .. .. .. .. .. 0

13 SUMMARY~l' OF IJET PRODUCTIVITY~ CALCULATI~ON S
FOR~ 23 CYPRESS SITES IN TIlE JITH1LACOOCHIEE
STA'rTE FOREST AS GIVENI INJ TIABLE 17 .. .. 0

19? RESULTS OF CYPRFEISS NET PRODUCTIVITYI
CALCULATIONS FOR DRKY ANDJe W~ET SITE`IS IN
ALACilUA COUNT Y . . . OS

20 COMIPAR~IOISO OF CYPRESS NET PRODUCTION WI'lTH
OTHER FOREST' PRODUCTION VALUES.... ... 211

21 AIIR ANDC WJATER TEM'PERATURE, SOLARi RDIACITION
AND PONlD HlETABOLISMl IN AUSTI' N CARYI CY'PREISS
D)OME . . . . . 220

12 SUIMARY` I OF CHENlICA~L CHAIRACTERISTrI CS OF
DOMEIF STAND~JING( NA~TERS (APR~IL-AUUGUST 197-1) .22

23STORAGES AND~ PATHWAY'IS FOR CYPRESS DOMIE
;ODEL L SHlOiBJ Ill FIGURE 62 4

24 DIFFER~ENT'IAL EQUATIONS FOR CYPRESS )OMIE
tMODEiL Ill FIGURE 6'~ 56

25 STORAGES ANDJL PATHWAYIS FOR CYPRESS PONDI~
MlINI-MlOD EL SHOWN:~ IN FIGURE 76 .. .. .. . 7

26 COMPARISON OF CYPRESS POND r'II-l~l-MOEL
SINlULATION~iS (CASES 1,2 3, ANjD 41) FOR
MODEL SHOWN IN FIGURE 7; . . .. . .. 299

27 NITR~OGENI AND PHOSPH1ORUS REMlOVAIL EFFICIEN~-
CIE~S OF LAK;E ALICE W~ATERHYA'.CINTH MARSH .. .. 3,11

lS NITR'OGENI ANDI~ PHOSPHIORUS REMOliVAL EFFICIENl-
CIES OF CYIPR~ESS D)OME RE~CEIVING SEWAGE .. .. 1

'9 QUA~LTY` FACTORS RELAITIN:G DIFFERENT TYPIES
OF ENEKCRG FLOiW . . 2


l'll










LIST OF TABLES continued


Tab le Page

30 CHANGES IN ENERGY FLOWJS CAUSED BY THE
DISPOSAL OF 2.8 MlILLION GALLONS PER DAY
SECONDARY SEWdAGE UNDER DIFFERENT
ALTERNATIVES . .. ... .. .. .. ... 327

31 EFFECTS OF FIRE ON BIOMASS AND NUMlBERS
OF TREES IN CYPRESS DOMES ...........343

A-1 EXAMPLES OF AGRONOMIC AND GRASS SYSTEMlS
USED AS LAND DISPOSAL SITES FOR WASTEWATER .. 355

A-2 EXAMPLES OF SOIL FILTER SYrSTEMIS USED AS
LAND DISPOSAL SITES FOR W"IASTENJATER ......361

A-3 EXAMPLES OF: FORESTED SYSTEMlS USED AS
LAND DISPOSAL SITES OF WASTEWATER .......36 3

B-1 CALCULATED COEFFICIENT VALUES FOR LAKE
ALICE MODEL IN FIGURE 33 .. .. .. .. .. 376

C-1 CALCULATED COEFFICIENT VALUES FOR CYPRESS
DOMIE MODEL IN FIGURE 62 ............392

C-2 POT SETTINGS FOR ANALOG DIAGRAM IN FIGURE C-1.. 394

D-1 CALCULATED COEFFICIENT VALUES FOR CYPRESS
POND MINI-MODDEL IN FIGURE 76 403

D-2 POT SETTINGS FOR ANALOG DIAGRAM IN FIGURE D-1.. 405


viii






























. .10





. .16

. .18








. . 20


... 27









. .50

. .527


... 57


. .60


LIST OF FIGURES


F i gu re


Page


1 Production-respirat ion model showing broken
nutrient ricycle pathu~ay ....

2 nergy- n u tr1i e nt f'low dia gr am s howJi ng
nutrient disposal alternative ... ..

3 IMap of research areas in Alachua County .

-1 Malp of Lake Alice watershed ...

5 M~ap of experimmental c:,press dome ariea .

6 AInalogous models of lake and c>'press
s s es .' . . . . .

7Systems diaram1i of Lake..t Alice ......

8 S:,stems diagram of cypretss dome .....

9 Mlap of wetlands inFlor-ida....

10 Sketch of' a cy~pr~ess dome profile .....

11 Limiting factor' curves . . .. . .

12 Limiting factor concepts described in
energyl language .

13 Limiting nutrient schemets pretsentl! used
in energy, language modeling .......

1-1 Ge ner1ali ze d crIos s- se c tion o f Ga3i n e s il1le ,
Flor~i da . . . . .

15 Bath!met ric map of Lake Al ice ......

16 Aerial photographs of Lake Alice ...

17 Site plan of Dw\ens-Illinois c)'pr'ess
r'esear 'ch1site . .

18 Location map of Aus tin Calry Cont~rol
Cy ress Dome . . . . . . . .










LIST OF FIGURES continued


Figure Page

19 Aerial photographs of OwJens-Illinois
cypress research site .. .. .. .. .. 2

20 Aerial photos of control cypress domes .....64

21 Mlap of the cypress wetlands in the Richloam
Tract of the Wdithlacoochee State Forest.... 67

22 Energy language modules .. .. .. .. .. 82

23 Lake level and rainfall for Lake Alice .. .. 90

24 Area-depth curves for Lake Alice ........93

25 Hydrology budget for Lake Alice ........ 95

26 Wdaterhyacinth coverage on Lake Alice...... 97

27 Carbon dioxide metabolism curves for
large wJate rhyacinths .. .. .. .. . 12

28 Carbon dioxide metabolism curves for
small rate rhyacinths ... ......... 104

29 Wdater chemistry for Lake Alice ......... 112

30 Changes in water chemistry across water-
hyacinth marsh . . . . . . . . 117

31 Changes in temperature across wJater-
hyacinth marsh . . . . . . . . 122

32 Lake Alice sediment analysis .......... 124

33 Lake Alice model ................ 126

34 Summary models for nitrogen and phosphorus
in Lake Alice . . . . . . ... 141

35 Wdaterhyacinth module used in Lake Alice
mo del 143

36 Nutrient limiting factor curves for water-
hyacinth module . . . . . . . . 145

37 Empirical relations for waterhyacinth
module . . . . . . . . . . 147









LIST OF FIGURES continued


F i g ure P age

38 IWater- column module for Lake A\lice module .1439

39 Bottom det ri tus- decomposer modules for
Lake Ali ce model . . . . . . . 151

410 Lake A\lice model simulation results for.
present conditions .. .. .. . .. .. 160

411 Lake Alice model simulation results for
sewa:ge div~e r~sio . . . 1641

42Lake ALlice mnodel1 simulation re suil ts fo r
heated effluent div~ersion . . . . .. 168

43Lake Alice model simulation results for1
w~aterbya!' cint hl mechanical harv'~esti ng. .. 172

44 L~ake ALlice model simnulation r-esults for
wa3terbyacinth chemnical spr'aying . .. .. 175

45 Lake Alice model simulation comparisons
of dissolv'ed oxygen w~ithl hyncinth manage-
mentaslter-nati vres ... . . . 179

46 Waster level, rainfall, and pumpage for
experiment al1 cvpres s domes . .. . .. .18

417 Wa~ter level and r-ainfall for- Austin Caryv
control dome . . . . . . 135

48 Hydr-oloGy' budget for- sewa~ge cypress dome .. 18

419 Biomaiss of hasrvested cpr~ess trees .. .. .. 192

50i: Cypress biomass r~e gre s sion .. ..... 195

5 1 Cypress biomass and diameter as func ti ons
of age . . . . . . . . . 201

52 Energy model definition of net pr-oductivity 203

53 Cypress production curves for- Alachua
Coiunt)sites . 1

51 Sunlight pa7tter'ns in cpr~ess dome ..... 2141

55 Diur~nal oxygEen curves for cpr~ess dome
pond . . . . . . 21










LIST OF FIGURES continued


Figure Page

56 Annual patterns in cypress dome .. .. .. 222

57 Understory biomass from cypress domes . ... 226

58 Water chemistry for cypress domes...... 232

59 Chemical analysis of cypress dome sediments .. 237

60 Total organic matter, inorganic matter,
nitrogen, and phosphorus sampled from
cypress dome sediments .. .. .. .. ... 239

61 Nitrogen and phosphorus sediment profile
for sewage dome prior to wastewater
application . .. . . . 242

62 Cypress dome model .. ... .. .. .. 245

63 Sunlight limitation models used in cypress
dome model . . . . . . . . . 248

64 Nitrogen and phosphorus summary models
for cypr-ess dome model ...... ...... 255

65 Cypress model simulation undisturbed
gro w~th . . . . . . . . . . 259

66 Cypress model simulation harvesting
from small dome ... .. .. .. .. .. 262

67 Cypress model simulation harvesting
fromn large dome .. .. .. .. . .. . .64

68 Summary graph of cypress harvest simulation .. 267

69 Cypress model simulation 10-year fire ... 269

70 Cypress model simulation 100-year fire ... 271

71 Cypress model simulation 10-year fire
plus harvesting ... ... .. .... ... 273

72 Cypress model simulation 100-year fire
plus harvesting .. .. . .. .... 25

73 Cypress model simulation sewage addition
wdith no shading by canopy ........ 278


X11









LIST' OF FIGURES continued


Page


Fig:ure

741 Cypress model simulation sewage addition
with shadin by canopy......

75 Sewage addition summaries from cvpr-ess
model simulations .

76 Cypress pond mini-model .........

77 iMini-model simulation stead\' state ...

73 Mlini-model simulaltion half canopy

79 Mlini-modell simulation no ca7nopl,

SO blini-modell stimulation no stem blockage .

31 Mlini-modell simulation nondeciduous
canop y . . . . .

Q3 Comparison of low~ and high nutrient
conditions of lake and cypress domne ..

S3 Relativ;e storasges of organic matter,
nitrogen, and phosphorus in lake and
cvpress domne . .. .

341 Energy! quality of wlaterbyacinths and
cy ar'ess wood . . . . . . . .

55 E~ner'g! diagrams of various alternatives
for the disposal of 2.3 million gallons
per dayv of secondary! se\.age .......

86 Lake Alice open lake community production
efficiencies . . . . . . . .

37 W~ithlacoochee cvpr~ejs association pr-oduc-
tion v;s. trlee dens i t: .....

SS Ev~aluated energy! modules for limiting
fact rs . . . . .

-1Ilutr-ient balance for- land application of
secondaryv sewage to reted canar gra~ss ..

C-1 A~nalog diagraml of cvpr-ess dome model ...

D-1 Anl\,7og diagr~am of c!press pond model ...

X111


283















219





. 29


. . 3








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

SYSTEMS ANALYSIS OF NUTRIENT DISPOSAL IN
CYPRESS WETLANDS AND LAKE ECOSYSTEMS IN FLORIDA


by

W~illiam Joseph Miitsch

June, 1975
Chairman: H-. T. Odum
Major Department: Environmental Engineering Sciences


Models field measurements, and computer simulations

were used to evaluate alternative systems of man's nutrient

recycling using a freshwater lake and cypress swamps in

Florida. Ecological characteristics, nutrient budgets,

organic productivity, energy r-elations, and interface with

man's economy were compared between the two ecosystems.

In Lake Alice in Gainesville, Florida, treated sewage

and thermal effluent were 82% of the inflow to the lake.

Waterhyacinths dominated the system and reduced temperature

fluctuations. Gross primary productivity measured as 15.6

to 19.4 g-C/m2-day in summer. Production by phytoplankton

and submerged macrophytes in the open water ranged from 1.3

to 19.4 g-C/m2-day and was damped by high flushing rates.

Nutrient levels were high in the water (0.8-2.8 mg-P/1 of

phosphorus and 0.6-2.4 mg-N/1 of Kjeldah1 nitrogen) and in

the sediments (2.2 mg-P/g dry w~t for phosphorus and 6.2

mg-N/g dry wt for nitrogen). The waterhyacinth marsh absorbed

11% of phosphorus and 49% of nitrogen inflow~s.
XIV








Simulated divcr-sion of the serwage flowJ from Lake Alice

w~ith a digital com~puter model r-educed waterbylacinths by 50?%

or- mor-e. Dissolvecd oxyvgen r-emained low. Simulated dlivlersion

of the diluting etffect of the heating plant effluent led to

complete hyvacinth takeovecr andl much greater seasonal oscilla-

tions in chemical par-ameter-s. Simulated hyacinth control

caused thc greatest dissolved ox~gen fluctuations w~hen spr~ay-

ing and per-iodic harve~stingg er~e tested and the least wJith

continuous harv\.esting.

Field data fr-om a cypress domne receiving secondary sew-

age showed overf-low~ if the w~ater flowJ was gr-eater- than 2.5

cm /w k. Loading ra3tes of up to 13.3 cmi/wk werie tested. CyrprIes s

tr-ee biomass in tw~o experimental domes was estimated to be

13.6 and 17.5 kg/m Nlet pr-imairy productiv'ity was 600 g/m"-)yr

in sites in the Wlithlacoochee State Forest, 1923 g/mi-yr in a

w~et site w~ithl diver-ted drainage, and j16 g/m--yr- for a drained

site. Diu~rnal oxygen changes in the pond of a contr-ol cypress

dome indicated a peak of pr-oduction in early spring. Light

was limited in summer by the canopy and in wJinter by the

shading effect of th~e stems. In the dome r-eceiv.ing sewage ,

standing water w~as coated with a mat of duckweed stimulated

by high nutr-ient levels (up to 12 mg-P/1 of phosphorus and

-1 mg-N/1 of nitr-ogen). Aterci S months of sewage application ,

phosphiorus content doubled in th~e upper sediments, bu~t nitr~o-

gen did not increase. Wlhen loading w~as high and water. o'er.-

flowing, -10 of the phosphorus and 760 of the nitr-ogen were~

r-etained. W~hen loading was low~ without much ov'erflowJ, 5








of the phosphorus and 93% of the nitrogen were absorb-ed.

Simulation of harvesting and drainage of a cypress dome

caused excessive growth of understory and likelihood of

destructive fire. Organic peat doubled in volume and tree

biomass tripled over a 100-year period in a simulation featur-

ing undisturbed conditions. Recovery time of trees after har-

vesting depended on the degree of harvesting and initial bio-

mass. Simulated addition of sewage caused cypress growth

only if the shading effect of the trees on the understory was

significant. The angle of the sun and the deciduous nature

of cypress were significant features in the simulations of

annual patterns in a dome.

The two systems responded similarly to the addition of

nutrients through the introduction of plants with low quality

structure, intermediate in biomass between phytoplankton of

the lake and trees of the dome. Relative C:N:P ratios for the

systems were 38:2.7:1 for the lake and 57:12:1 for the forest.

Cypress wood has an energy quality 40 times that of water-

hyacinth biomass. Preliminary evaluation of cypress dome,

lake, and technologically based nutrient disposal alternatives

suggests that the cypress system may realize a higher work

service per purchased energy invested.


XVI













INTRO DUCTIONl


N~an and natur-e 31re interlconn-cted~! with many' ener~gy path-

~ay~s that cont ribute to the lifei support of man, de-monstrating

his symbiosis Ji th nature. Domestic ecoss tems such as agr~i-

culture andl commercial forests vield food andl fiber in ret~tur~n

for serice;sts supplie~d by man in fert ilization soil tilIling

and petst con trol. Naturl3 landscapes hav~e ecosystems thiat

assimilate air- anJ wa3terl pollution, conServei water., and con-

trol floods. Assimilation of nutrieint waste is one of the

most important of the symbiotic r-ole-s of ecosystems. This

study' compared tw~o types of Flor-ida etosystetms as they) adapt

to receivingn high nutr~ient sew\age~ waste inpults fr~om man. Onne

is a laket dominated by w:ate~rsnhyainhs and the other is a

cypre'css wetland expelrimentally supplied w~ithl nutrients.

Plodetls, measurements and computer simulations were~ used to

help, understand the wihole of man's relations to thleSe etnvir-on-

metntal systems.

The cycsling of nutrients in an etcosystem is a ntcessary!

strategy for the continual surival~a of that sy~Stem (e',g., O~dum,

1960o; Pomneroy, 1970). IM~n attempting to be manager and a

pariit of nature, is faced wJith a broken nutr-ient cycle (Figurte

1) and two immediate pr-oblems. O~n the one hand, hiigh inor-

ganic nutrient f-low~s from miunicipal and agr~iculturl3 SOur1cets



























Figure 1. A generalized diagram showing where man hias
broken thle basic nutrient cycle necessary
for a viable interface of man and nature.
P represents gross primary productivity by
green plants, while R is the respiratory
processes of man and nature. Symb ol
description given in Figure 22.



















BJROKENI~/


)RGANIIC B











---- ENERGY FLOWE
---- NJUTRIENT FLOW~









are contributing to the problems associated with eutrophica-

tion or nutrient enrichment of lakes, rivers, and estuaries.

At the same time, fertilizers for farming and forestry are

becoming increasingly expensive because of their dependence

on fossil fuel-based mining and manufacturing. These two

phenomena are shown in more detail in Figure 2, where three

alternatives for disposal of nutrient wastes are given:

eutrophication of waters, terrestrial recycling, and terti-

ary treatment by technological means. Mlany questions remain

unanswered about the relative costs and benefits of each

alternative.

A comparison between a lake and a cypress swamp, both

receiving secondary sewage effluent, was undertaken to draw

some general principles about hiighi nutrient systems and to

determine relative benefits of each to man. Evaluation of

the newJ cypress disposal test was helped by comparison with

the conventional means of sewage disposal into an available

body of w~ater. The comparison also allowed generalizations

of limiting nutrient concepts with systems models.

T'he lake site under study is Lake Alice (Figures 3 and 4),

located on the campus of the University of Florida in Gaines-

ville. It is a small lake (33 ha) wJith high nutrient loading

due primarily to the 2.8 million gallons per day (10.5 x 103



























riguret 2. A diagrami of enerigy flow! and nutrients showding
disposal alterlnativ'es. Pathw~ay 1 paasses
nuitrie~nt wastes into bodies of water-, the most
common method; pathw~ay 2 passes nutr-ients to
thle land; and pathway 3 uses technological
inputs for- tertiary tre~atment w~ith economic
and energetic costs. T'he wide lines indicate
major nutrie~nt flows fr-om the sources in the
upper. left, through commercial forIe st s agri -
cullture't, and man's economy to the aquatic
systems anid finally to the ocean in the low;er
left. Symbol description givetn in Figure 22.





COMMihERCIAL FORESTS AND
AGRIICULTUJRE


M~AN'S
ECONOMY


LAKES, DRIVERS,
AND ESTUARIES


TO OCEAN

































Figure 3. General map of' research areas in Alach~ua
Count!', Florida, including Lake Alice
r~esearich si te and two cypress research
sl tcS.












GENERAL MiAP OF RESEARCH
SITES IN ALACHUA COUN\TY,a
FLORIDA




SCALE IN MILES




?\ ~~~Austin Cory Cypress~eerhSt


Cypress

















OW


OE





aC 0

nE





On
r-4 e-






*EC




CO








0 Oh



(OO


OC





1000





c4
*H






















WO
J RO
J 10


1


133~1S HI t~~








m3/day)! of secondary sewage effluent being discharged into

its eastern marsh. It has been classified as highly eutr-o-

phiic or ev'en "senescent" by Br-ezonik and Shannon (1971); mats

of waterby)acinths flourish across most of its surface. On ly

the western third of th~e lake is kept open fr~om hyacinth cover

by spraying and harves ting done for sesthietic reasons. The

lake also receives theatre effluent fr~omn thie campus heating

pl1an t. Wdat e rs fr-om the lake discharg,e to groundwater through

pipes installed dow~n to the Floridan Aquifer-. Some water is

pumped from the lake to irrigate surrounding a7griculturall

fields.

Thie cypress wetlands used in this study (Figur-es 3 and

5) are the main r-esearch sites under study in a project of

the Center- for W\etlands, sponsored by Rock~efeller Foundation

and BRANN division of NaJtional Science Foundation, entitled

"Cypress W~et lands for Wanter- Managemnent, Recycling, and Con-

servation" (see O~dum, 1972b, O~dum et al., 19) Co rmmo nly

referred to as cyplress domes or cypress ponds, these pockets

of cypress tr-ees are located in ar-eas of low relief withi

seasonal standing water, amid drier pine flatwroods Figur-e 5

shows thle main experimental site nor-th of Gainesv~ille on land

le ased from Owens Ill ino is Inc. Scondary sewage and gr-ound-

wa3ter arec being applied to var-ious cypress domes at this site.

In addition to sewage disposal, inter-actions between man an1d

these cypress domles involve dra3inage, fire, har~vesting of

wood products, and microclimatic actions on houses.





























Figure 5. Site of experimental cypress domes northwest
of Gainesville, Florida, on lands provided
by Owens-Illinois, Inc. (Contour map obtained
from USGS topographic map, 7.5 minute series,
Gainesville East Quadrangle, 1966.)
























',oWNEirS-lLLINOIlS
CONrT ROL DOME


EXPERIMIEN TA L CYPRESS
W'ETLAN~lDS Own~;S ILLINVOIS SITE
CAiNESVILLE, FLORIDA

~180 TOPOGRAPHIC
CON~TOURS
(FEET AtiOVE Mr.S.L.)
SI LO METERS
-'OC- I~r








Simplified models which display analogous features of

the lake and cypress systems are given in Figure 6. These

models and the more complex models in Figures 7 and 8 guided

field work and were a basis for subsequent computer simulation

of the lake and the cypress dome. Included are both nitrogen

and phiosphiorus, the nutrients cited frequently as the two most

important mineral elements in ecosystems. The main autotro-

phic components in the lake system included are waterhyacinths

and an open lake phytopl ankton-benthic producer community,

while the cypress dome model has cypress trees and duckweed

with some aquatic or semi-aquatic understory. Organic matter

on the bottom is a significant storage in both systems. Dis-

solved oxygen is important to each ecosystem and often limit-

ing to respiration. The hiydrologic inflows are primarily

rainfall, runoff, and man-introduced flowds, while evaporation,

transpiration, and drainage dominate the water losses. Water-

hiyacinth control, in the forms of mechanical harvesting and

chemical spraying, and well injection are shown as the primary

mechanisms of lake management in Figure 7. Manipulation of

the cypress swamp by man is shown in Figure 8 to occur pri-

marily through harvesting of trees and altering of the sur-

rounding drainage patterns.



Eutrophication and the Waterhyacinth System


Eutrophication is the accumulation of nutrients and sub-

sequent increase of aquatic primary productivity. Where man






























Figure 6. Gene ralize d wJo r-kIng models for (a) la3k e
sy~stemn, and (b) cypress w~etlands. Ea3ch
system shares analogous state var1iables
including nutrient, biomass, and sediment
comrponlents. See Figure 22 for description
of symbols.







16



Solar

/Water '*
Inflow
Y/ater

Nut- *-~----i x xy 1 `
rients
Nutrients ttL II IHyocinths









Phytoplonkton
///// ganicand Benthic
rganicProducers
/Sedi-
mnents

R

(a)




Solar








~ I ICpress







\Yater VOter C i
Inflow

Sediments x

INlrtrients xi~~-_ NU~t-\ OrI Understory
rents gamc






W v (b)




















rl







L.L










vi


*M


C
O
*M




U

r J,







E



O~




















\If



r,









* r-




















IZ

>--0
X0














PI


O



LL


ct









If)
*Hl

c








vr








Ou



C


U

O














*H
Ll.






20







III



O



- J-I






Oo L











or 0 0
c o
o r-- c
a r

o



--





O9 V








causes the nutrient additions, it is often called cultural

e ut roph ica t ion Nutrie~nts ar-e tr-ansferr1ed firom one system

(t e rre str1'i al/ urba 3n) to another (aq~cuatic). Whle n e utr1'op hi c a-

tion is ex:tensive,, there may~ be associarted problems for mian's

activ'itieS. The problems are of w;orld-wgide econ-omic concer-n.

Unsigh~tlyI algal blooms and organic depositions miay reduce

rczreational uses of lakes, while prolific aquatic wee~d growth

often imp~edes boat tr~affic. Chemical, biological, and physi-

cal fetureslt3 change significantly,, and it is often postulated

that e~utr~ophicatio n acceleraites nature's slow~ process of lake

succession (cE~g, Hasler, 19417). If nutrients origiinate fr~1om

domestic wa~Ste, disease r'iSkS are inlcreased. These points

an~d other'S hav~e been addrCSesse in several edited v'olume~s

(NoJtional .Academy of Sciences, 1 9~6 C; L i k en s, 192 lle~n and

i:ramer 1972; IMiddlebr~ooks et al., 1974) and individual pub-

lications (M~cCarty,, 1966; Sawyer, 1966; Frzub et al., 1966;

Fr uh, 1967; Lee, 1970; and Hutchinson, 1973) and will not be

discussed hecre fur'thler


Florida Lakes

Florida has a w~ealth~ of freshwatter lakes of varyring: waterl

quality and morphometric character. They~) ae atypical of

temperate lakes as described in the classical limlnology stud-

ies. M~ost of F-lorida's lakes are sinkhiole lakes, a dir~ect

result of thle por~ous karst topogra3phy of thle state in whlichl

lthe acid conditionlS created by r~ainfall and or~ganic accumula-

tion tend to dissolve thle underlying limestone. Because of









the mild subtropical winters, high phosphatic deposits (see

Odum, 195 3; Gilliland, 1973), and general shallow nature of

Florida lakes, moderate eutrophic states may be usual rather

than exceptional in the state. Notable exceptions are the

trail ridge lakes of northcentral Florida where the lake

basins are found in low nutrient, sandy deposits. The trophic

states of these and other Florida lakes were examined by Bre-

zonik and Shannon (1971) and wJere found to coincide well with

calculated nutrient loadings.


W~ate rhyacinth Systemn

One of the more common results of high nutrient and high

flow conditions created by the disposal of nutrient wJastes in

Florida is the dominance of the waterhyacinth (Eichhornia

crassipes). The wJaterhyacinth is a floating aquatic plant

that has proven to be a significant economic burden to many

tropical anid subtr-opical regions of the wJorld wJhere open water

stor-age is desired. It is a highly productive plant (Penfound,

1956 ; Wdestlake, 1963; Bock, 1969) wJhen found in high nutrient

waters, and populations canl double their surface area coverage

in two weeks (Penfound and Earle, 1948). Its floating ability

and sail-like leaves give it mobility to infest new areas

quickly. It generally propagates vegetatively, forming a mat

of thousands of plants connected together as one by a maze of

underwater stolons. The mats become impenetrable to water-

craft and hamper recreational uses of lakes and rivers.








Conditions that allow\ invansion by waterh~vacinths lead

to an ecosystem ve~ry different fromn that whr~ichi preceded it.

There is a not accumullation of organic mat ter under thle mat.

D~issolved oxy'gen is dimninishled due to recduction of oxygeni

diffusion by~ the mat and to r~espira3tion of roots and decom-

posing hyacinths. Carbon dioxide levelsl increase w~ell beyond

open water vanlues (U~ltschl and Anthony', 1973). A weanlth of

i n \erteb rate s (0' Ha3ra 196 7) and vet~rtebrates (Go i n, 19413) a re

attracted by the increased subsstrate and large root structuree

associated wJithl the w~ate rhva'cinth. O'Hanra found over 55

species among 44,000 invetrtebrate specimens including a

diversit) of about 33 species per 1,000 individuals for insect

larvaeP alone. Sire~ns, newts, ?nd somne frogs dominate the

l owe r vle reb rates Fisl li fe is mnostly~ r'ectr~icted to ai r

gurlpers, such as thle mosquito fish (Gambusia aff~inis) and the

topminno\! (Fundulus chrysocus). Highecr trophiic level fishies

apparently use~t the hya3cinth coverage as feeding locales.

The~ hyancinth mat can be a pioneer stage for filling in

a lake, followed by a Su1ccession of r~ooted aquatic plants and

woody plants. In other cases, where sediments are continually

w~ashed awany or re~moved,, a steady state can result. Mlorri-

(1974) found that the plant seems ill-equipped to invade

areas alread! dominated by sone other aquatic plants. The

mat also appears to havet an effect onl heat exchange be~twee~n

the lake and the atmnosp~here stabilizing year-round wJater

t emp er a tu re s ( Ult sch 17








Several feedback schemes have been suggested to enable

the waterhyacinth growth to benefit man, including its use as

a protein supplement for feedlots (Boyd, 1968a,b ; Taylor,

1969), as a possible pulp source for papermaking (Nolan and

Kirmse, 1974), and as a tertiary treatment of sewage wastes

(Clock, 1968; Sheffield, 1967; Boyd, 1970 ; Rogers and Davis,

1972; Furman et al., 1973). Apparently no extensive appli-

cations have been made to date. Control schemes have had

little success except under very intense schedules with con-

troversies raging as to the relative merits and flaws of bio-

logical, chemical, and mechanical control. Baker et al.

(1974), for example, found that white amur (Ctenopharyngodon

idella) at a density of 1,900 fish/ha maintained some control

of hyacinths. This was wJell in excess of normal fish densi-

ties for aquatic weed control.



Wetlands as Potential Nutrient Sinks


Terrestrial recycling of high nutrient wastes one of

the pathways in Figure 2, may take on greater importance as

an alternative to eutrophication and expensive fertilizers.

A literature review of some of the many applications of waste-

w~ater to normally dry terrestrial ecosystems is given in

Appendix A. Mlost of the engineering problems associated with

these projects involve the increased hydrologic loading,

which tends to transform the land system into a w~et forest

little resembling its natural state. Long periods are








required for- adaptation. Distribution of wastewa~ters to w~et-

lands which are adapted to flooded conditions for at least

part of the ycar- may be a more sulitable scheme for nutrient

removal and urlban runoff collection.

"W\etlands" is a v'ery' gener-al term used for any "lowlands

covered w~ith shallow! and sometimes temlporary or- intermittent

w a t ers"' Shaw~ and Fredine, 1956). Malny different names ~avle

evolvetd for these lands as a result of both cultural and eco-

logical di ffe rences Bogs moors swa~mps domes mar-shes ,

and sloughs each inspire a certain image of w~etlands. Hanny of

these areas are being drained and altered as man continues hiis

urban and agraonomic expansion. N~ier-ing (1968)j estimates thant

"as a result of drainage, dredging, fill i ng and/or po lluti on

w~e have in th~e coterminous United States reduced th~e nation's

wetland asset to :0 million acres, slightly! mnore than half'

the original acreage estimated 127 million acres)" (p.17)

Flor'ida's wetlands (Figur-e 9) are experiencing a1 similar

demise as drainage canals continue to make incisions across

the shallows landscape.

Some studies have been undertaken to evaluate potential

con t r ibuti ons of we tl1an ds to nutrient ulptak~e. Grant and

Patr-ick (19 70) report on Tinicum mar-sh, an area of aqulatic

per-ennials and annuals near Pli ladelphia. S ign ifi can t re dulc-

t ion s in phosphorus and nitrates wJere experienced. Wdi sconsi n

marshes hav\e been invecstigated by Bentl3ey ( 1969) and Klopatek~

(1974)j for their- effects on w~terr quality' and nutrient cycling.

Each investigator found seasonal fluctuations in the discharge































Figure 9. Mlap of Florida and Alachua County wetlands
and urban centers (from Odumn, 1972b).





Comr~Fled by Kathenrine C Ewel an~d F.1ark T Brow~n
Wetlands And Urban Centers


27


r?.


*





*


-


~~'


POPULATION CENTERS
a lo.ooo-2oo.ooo
0.000 -100.000


Cypress, Alachua County


1,000-70.000


*)i



*.


*








concentrations of nutrients from the marshes, suggesting a

net uptake of the elements in the summer and a net discharge

in the nongrowing season. Kadlec, Kadlec, and Richardson

(1974) have begun a study, through field measurements and

computer techniques, on the effects of secondary sewage on a
Mlichigan marsh system.

Forested wetlands have only recently been researched to

any great extent for their nutrient uptake capacities. Kitch-
ens et al. (1974), in measuring the effects of South Carolina

forested wetlands on chemical, physical, and biological param-

eters, found significant reductions in phosphorus (on the

order of 50%) although reductions in nitrogen species were

not consistently observed. Brown, Bayley, and Zoltek (1974)

give preliminary evidence that a forested wetlands area in

central Florida receiving sewage for nineteen years proved

to be a nutrient sink with the added benefit of significantly

greater tree growth in the sewage-receiving area when compared
to a control area.


Cypress Domes

Cypress domes or ponds (Figure 10), dotting the land-

scape of pine flatwoods of the Atlantic and Gulf Coastal

Plains (Mlonk and Brown, 1965), may offer suitable sites for

the disposal of high nutrient wastes. These forested wlet-

lands, generally only a couple of acres in size, are dominated

by pond cypress (Taxodium distichum var nutans), although they

often growJ in association with tupelo and black gum (Penfound,

























.0
ril







O


O












E
O


"O

Us





O



O



fl
*M

e--4








ch1
*H























C/J CDI



I


d
'''3
:.



1~4



r4:
rL,



'i
~3a





i




..







i






31


1952). 'Tree species diversity has been given by ;onkl and

M~c~innis (1966) as 1 species per- 1,000 individuals counted.

Charalcterisstic of these domes is a yea~rly period of flooding

and dry)ingS, thie dry! period nieces~sary for seed germination of

cypr-ess (Demar~ee, 1932). Th~e dome gets its name from its

profile of lar~ger trees in thie center and smaller trees near-

the edge. This phenomenon has been suggested to be due to

soil condi tions ('Ha rper1, 1927) fi re (Eur:= and WJagner, 15)

and a gradul~3 increase in thie water table (VerIn on 1)

In addition to nutrient uptake thiese' cypress ~etla~nds

may' prove to be a val1uable par't of thre Flor-ida landscape

through thieir- roles ini timber production, storm water' reten-

tion, wJildlife habitats, and groundwater recharge. Cypress

wood, duie to its dural.ble nature has been especially' valuable

to man f~or many' uses,, fr~om building construction to fenlce

posts. All of thepse functions mnake the cypress dome an1 ideal

syste~m in w~hich~ to stutdy thie fitting of manl and nlatur~e together

in a sy'mbiotic partnecrship.



;asthemat ical1 Aouproa ches to the Conceptt
of Limiting Nutrientss


Th~e treatment of limiting factors inl mothematical form

r~equires unification in order to address, thr~oughl mathemati-

cal modeling, problems such as ioutr~ophication and nutrient

wJas te r-ecy'cl1i ng. Considerablle speculation and some mathe-

matical w.ork have~ been applied to the effects of external

factors on the process of photosynthesis in plants.









Some Early Limiting Factor Models

Early efforts on the question of limiting factors were

led by Liebig (1840) in what is now commonly called Liebig's

Law of the Mlinimum. This law states that a process is limited

by the quantity of one nutrient element present in minimal

quantity relative to its optimal quantity. A second principle,

popular in the last half of the nineteenth century, was that

of the three "cardinal points" (Sachs, 1860) whereby biologi-

cal processes require a certain minimum concentration of a

limiting factor to begin, attain an optimum at a certain level

of the limiting factor, and diminish as maximum tolerable

concentrations are exceeded. Rabinowitch (1951) suggests

three general types of kinetic or limiting factor curves

based, on previous wJriters' hypotheses. These curves, plots

of productivity or growth versus limiting factors have been

a popular means of displaying limiting factor relations. The

first type,or Blackman type (Blackman, 1905), is shown in

Figure 11a and consists of a linear ascending part terminated

by a sharp break and a horizontal plateau. The interaction

between sunlight or nitrogen with phosphorus is given in this

exa mp le. Bose (1924) offers a slight variation (Figure 11b)

in wJhich the initial slope is dependent on the second variable,

in this case, sunlight. This is referred to by Rabinowitch

as a kinetic curve of the second type or Bose type. In a

series of experiments Bose had verified his Law of Product,

wJhich states that "the resultant effect of the simultaneous

variation of factors is not the sum, but the product of the





























Limiting f~actor curves showing possible recla-
tionships among exter'nal factors a7nd primary
prIoduct ion: (a7) first type or- Blackman type
with~ common initial slope and a sha3rp breakk
in curves; (b) second type or- Bose type with
entirely different curves for. different
value-IS of other- factors ; and (c) thir-d type
w ithi d iff~e rcn t ini tial currvcs convergingg to
a7 common a7symptote (Rnb i now i ch 1951).


Figur-e 11.













O
O
O

a I increasing
Sunlight,
rr E~Nitrogen, etc.



PHOSPHORUS
(0)


O

O



Increasing
rr Sunlight,
Nitrogen, etc.


PHOSPHORUS
( b)


O
c- Increasing
o Sunlight,
"o I Nitrogen, etc.


PHOSPHORUS
(c)










effects of the individual fact o rs" (Bose 192-1 p. 26i~5) .A

third type of curv~e as given in Figur~e 11c "is characterIize d

by final convergence in a comml~on saturation plateau" (RPab ino -

vitch,1951).

Mi ts cher~lich (1909) presented one of the first mathie-

mlatical interpretations of the limiting factor' concept in the

forIm


dy/!dx =(A-)k


In(A y) = c kx


where y = production

x = limiting nutr~ient

A = max3imur m ploro-dctivity!

k = constant.

Th~e di fferIe nt ial for~m, assuming ,er~o ini tial1 conditions,

integrates to thle followings:




This equation is further expanded by Baule (1918) for several

limiting factors i nt o the f3m il1iar1 Baule Mi t sche r1 ich eq7ua t i o

as given by. \'erduin(16)

P' = Pma (1 e- 7 / )(1 e- > h ( -' e- 7 /



where P = prima7ry production

Pmax maximuml pr'imary) pr-oduction
.7/h = a factor' addedl to facilitate computation

xi)y;z = limiting factor's.









Verduin gives his modification as follows:


P = P (1 2 )(C1 2 )~(1 2 Z) etc.
max

These mathematical relations produce curves similar to the

Bose plot (Figure 11b) for two limiting factors, but can be

expanded to any number. A general description in energy

language is given in Figure 12a.

The Michaelis-Mlenten equation (Mlichaelis and Mlenten,

1913) is a mathematical description of the velocity of an

enzymatic reaction as determined by the concentrations of the

reactant or substrate. The key to the formulation is the

fact that the enzyme forms an intermediate complex with the

substrate. The mathematical expression, the derivation of

which can be found in Brezonik (1972) and W~illiams and W~il-

liams (1967), is given as

V S
max
Kt + S

where V = uptake velocity or reaction rate

Vma = maximum uptake velocity or reaction rate
S = substrate concentration

K= half saturation constant.

Mlonod (1942) offered what is now\ widely accepted as the

analytical form for limiting nutrients:


1 o C1 + C

where p = growth rate

q~ = maximum growth rate



























FiGure 12. Various limiting factor concepts described
nenr language:: (a~) B a~ul1e ii ts ch~e r1i ch
model for multiplication of individual
limiiting factor functions; (b ) Mi ch aelis -
iMn t en ( 19 1 3 e n me- sub s tra-nte' rLct ion ;
(5) cycling recep~tor model for- sunlight as
givecn in Lumlry and Ries;e (19,59) a~nd
descr~ibed in energy language b! Odum (19 71)
(d) Rasle vs ky (1 6 0) res pi rat ion l imni t i n
faictor- model for- glucose~ and oxygen, a
described b! Odumi (19 72a). S\mbols ar-e
giv~en in Figure 22.















D ,,x( I-ex) (I-e ) (-ez)












VMx S






V=







V= K, I


I
I


(c)


+ -
I-y


X= jy


I= F(C C2)








C' = concentration of limiting nutrient

C' = concentration of nutrient for which the rate
of gr-owth is equal to half the maximum.

Mlonod's w;ork has been described as being an extension of

IMichaelis -Molnten enzyme kinetics to hole organisms, in this

case bacteria (D~ugdale, 196:). A\ tr-anslation of the M~ichiaelis-

rMenten/Monod model into energy language is giv~en in Figur-e 12b.

Lumry and R2ieske (1959) discuss the velocity of the

photochemical activity of isolated chiloroplasts as being

given by

p k kll
k I +k
1 d

where p = concentration factor

kd = high1 light controlling factor

k1 = low~ light controlling factor
I = Liverage light.

In energy language th~is is simply the equation for the cycling

receptor- as shiown in Figure 12c and already discussed by H.

T. Odumn (19:1, 1972a).

k as he ~s ky (i1 960 ) i n d i sc ~s si ng c ell ula 3r r e spIi ra7t ion ,

gives an equation for oxygen consumption as a function of the

external oxygen supply and the supply of glucose:

v = + '
"~~ v)

where x = exiternal oxygen concentration

y = relative oxyg~en consumption

EF = constant

=F (glucose, lactic acid).








This particular case is interpreted in energy language in

Figure 12d. Rashevsky obtained several limiting factor curves

from experimental data similar to those given in Figure 11b.


Ecosystem Mlodeling of Limiting Factors

Several authors have made attempts to apply mathematical

expressions for limiting factors to specific systems models,

generally phytoplankton-nutrient models. Fuhs (1969) and

Fuhs et al. (1972) discuss the growth of diatoms as controlled

by the excess of intracellular phosphorus over the minimum

amount present during phosphorus starvation. The equation is

similar to the one presented by Verduin (1964), except intra-

cellular concentration is now important:


~ = ~~l -(a-aol//So


where 11 = growth rate

1-m = maximum growth rate
a~ = saturation level phosphorus

a = cell phosphorus.

Takahashi et al. (1973), in an estuarine model of phyto-

plankton growth, suggest a formula such that the slope of the

production light curve at the origin is the same, irrespective

of the nutrient concentration (i.e., a Blackman type curve

as in Figure 11a). The mathematical formulation is given as

P = alI exp[1 aIl(+h-N)/(g*N)]


where P = photosynthesis

I = light intensity





411


N = nutrient concentration

a,h,g = constants.

Dugdale (1967) used the Mlicha3elsis-M~ente exupression as

an explanation of the uptake kinetics of nitrate by~ phyto-

plankton. In a later' wor~k, Ma3cTsaac and Dugdale (1969) cau-

tion "that a mathematical and not necessar~ily biochemical

equiv~alence to M~ichaelis-MI~enten kinetics is being considered

here." lialf saturaio constants wJere determined for- several

species of marine phytoplankton for nitrate aind ammonia.

E~ppley et al. (1969) used simnilar1 methods but wJere able to

generate curvesJ showJing both sunlight and nitrate as var~iableCS

for severl- species. The M~ichaelis -Menten/blonod relation has

since been applied to lar-ger mathematical models by~ many

authors, including ChIen (1970), Chien and O~rlob (19 72), Fubs

et al. (1972), Grenney' et al. (1973), O7'Brien 17) Larsen

et al. (19741), Parker' (1971), Bloomnfield et al. 17),and

LaSSiter' and Eearns (19174). Chen and Or-lob (9),for-

example, hav~e described a comprehensive "'ecologic"' models of

cutrophication in which the growJth rate is expr'e~ssd as

L.LI C ? ( P



where a = growth rate

D = mlaximum gr'owth rante

L, = light

C = CO2 concentration

Ni = inorganic nitrogen

P = orthophosphate.








Thiis formulation uses multiplication of several limiting

factor terms in the Dugdale interpretation of the Mlichaelis-

Mienten/M~onod relation. It produces limiting factor curves

similar to the second type or Bose type as shown in Figure 11b.


Modeling of Limiting Nutrients
in Energy Language

The various models for limiting interactions can be repre-

sented in energy language to gain insights about their simi-

larities and differences. These are shown in Figure 13 with

the algebraic equation for steady state conditions. In the

model in Figure 13a, production is proportional to the product

of two concentrations. This model alone has limited applica-

bility, since the concentrations available to the interaction

do not ordinarily hold constant.

In Figure 13b are interactions which operate through two

processes that have internal limits (such as recycling limita-

tions). Both processes are related to the M~ichaelis-Menten

equation and when combined are empirically correct. This

model has no ability to increase responses w~hen nutrients

become enriched beyond the internal limitations.

In Figure 13c a model introduced by Odum (1971, 1972a)

reproduces the Michaelis-M~enten equation, but has a constant

external flow that causes the concentration available to the

interaction to limit. This model represents the Monod usage.

In Figures 13d and 13e there are two limiting flows and

tw\o varying exter-nal concentrations. These also have typical

limiting factor curves and a Mlichaelis-Mlenten relationship at





























Limiting nutrient schemes presently used
in energy language modeling. (a) strictly
multiplicativle limnitation; (b) multipli-
ca7tion of' Michaelis-M~enten factors ;
(c) stea~dy state limiting case as presented
by Odumi (1971,1972a); and (d and e) limiting
flow~ concept of~ two flows. These last two
models sire equivalent. Symbols gSiven in
Figure 97


Figur-e 13.












= K/--/N


P = KIN


(b)


(0)


KNI






K+N










K J2N
K+N


(c)


(d)


(e)








steady state. Applications of the multiplication of Michaelis--

iMenten model of Figure: 13b and the "Jr~" model of Figure: 1,e

wJill be: presented in this studyr, and their differences w~hen

applied to multiple limiting nutrient cases ar~e given in the

Discussion.



Study' Areas


Northeent ral Florida, in the v~icinity of Gainesv~ille,

was thec location of~ most of th~e data collection effort.

General locations of thie study ar-eas in Alach~ua County are

shlown in Figurlle 3~. Theyr include the highly cutrophic Lake

Alie and tw~o sites w~her~e cypr~ess studies h~ave been underway.

A fourth ar~ea of studyv, cypr-ess wJetlands in the WJithlaccochee

State Forest in thie central par't of th~e state, will also be

discussed below~.

Alachua Countyr topography is dominated by the Ocala lime-

c stone formation (Eocene) and an overly~ing Hlawthorne formation

.of phosphatic sands, clays, and limestones (i oce ne). The

limestone allows for a karst topography~ of collapse sinks

formed by solution holes in the limestone and subsequent slump-

age of thie above sediments. Lake Alice occupies an ar~ea of

multiple fractures and caverns in the Ocala limestone and has

been determined to be: the result of the sinkhole phenomenon

(C~ason, 1970). low~ever, to the north and northeast of Gaines-

v~ille, only slight slumpage is observed in the higSher H-aw~thorne/

P'leistocene-sand plateau (Pirkle and Brooks 1959). It is in








these slight depressions that cypress domes develop and dot

the landscape of pine flatwoods. A cross-section of the

Gainesville area (Figure 14) shows the relationship of these

formations to Lake Alice and the experimental cypress area.


Lake Alice System

Lake Alice (Figure 4), located on the campus of the

University of Florida, Gainesville, was once a sinkhole fed

by a small marshy creek. Until an earthen dam was built at

the western end of Lake Alice in 1948, the extent of the lake

wJas about 4 ha. It has since expanded to its present size of

33 ha, due to both the dam and the addition of secondary sew-

age effluent (presently 7.3 m3/min) and once-through condenser

water from the campus heating plant (presently 30.6 m3/min).

The western end of the lake (Figure 15) averages less than

2 m in depth with a few small areas of about 4 m depth --

probably the original sinkholes. This half of the lake,

called the "open lake," covers about 12 ha. The eastern end

of the lake, 21 ha, is referred to as the "marsh" and is a

very shallow waterhyacinth prairie with virtually no open

water areas. The flow through the lake is generally east-

west with the inflow first going through the marsh and then

through the open lake. An arbitrary dividing line between

the two sections is a catwalk fence constructed in 1970 to

retain the hyacinth growth in the marsh. Aerial photographs

of Lake Alice are given in Figure 16.
















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Flgur~e 16. Aerial photographs of Lake Alice showing
(a) view of lake and surroundingg wnter~shed
as seen from th~e west; and (b) an ov;erhead
vliew of the la7ke, shooting the division
between the hyacinth mar~sh and the open
lake.




























(a)





53


The lake dr-ains into twJo disposal wells on the w~ester~n

shor-e whlich were installed in the early 1960s to provide an

outflow for the ma7n-increased hydr-ologic input. One well is

drilled to 72 m and thie others to 13~7 m, putting the lake efflu-

ent in contact wJithl the upper por-tions of Flor-ida's major

undergr-ound \!ater- supply, the F~loridan A-quifor. Lake Alice

is located in an area under'lain by multiple frastur-es aind

cavrerns, but the lake basin is generally per-ched above the

local water~ table because of silty~ clay~ that has accumulated

on the bottom (Cason, 1970). The lake level is usually

between 68 ond 70 ft abovie mean sea level, whlile the local

water table is estimated to be 60 ('5) ft (Pir-kle and Brooks,

1959).

TIhe Lake A~lice w~ter-shed (171 ha) is pr-imar-il ur~ban

(i.e., university comlpus), but a7 substantial ar-ea of agriCUl-

tur-al land operated by\ the university drains into the lake's

souther-n shore, and some forested 7r-eas ar-e along$ parts- of

the norther-n sh~ore. Brezonik and Shiannon (1971) r~epor't 60.3%:

of the water-shed to be ur-ban, while fertilized cr-ops and

for-ests take up 27.2 and 12.01, r~espectivelyv. In addition

to thc major- man-made flows mentioned above, Hlume Pond, which

collects runoff fr~om most of thie nor-theast par.t of the univer--

sity campus, ovler-flow.s into the northeasternn corner- of the

marsh (about 5.1 m /min dry~ weather- flow). Thie pond wans con-

str~ucted for recreational pur-poses and showJs occasional

natur-al level dr-ops due to sinkhole for-mations in the ar~ea.

There ar~e also sever-al smaller- str~eams and storm water








culverts which drain into the lake, particularly along the

northern shore.

Aerial photos support observers who recall Lake Alice

as being waterhyacinth-free until the early 1960s (Cas on ,

1970). The major hyacinth problem started with the diversion

of the heating plant and nutrient-laden sewage effluents into

the lake in 1964. Since then, many man-hours have been spent

to keep the western part of the lake open from hyacinths.

A dragline is employed several times a'year to keep the plants

in check and chemical spraying has been used periodically over

the years.

Despite its highly eutrophic condition (or possibly as a
result of it), Lake Alice has an abundance of wildlife includ-

ing large fish populations, an alligator population estimated

at 80 individuals, turtles, and many different species of

birds, including the osprey (Pandion haliaetus), the anhinga

(Anhinga anhinga), and the great blue heron (Ardea herodias).

The lake serves as an Audubon Society sanctuary, and hunting

and fishing are forbidden. At one time, the area was a

rookery for many varieties of herons (Jenni, 1969), but the

increased water input raised the water level and killed the

shoreline trees which served as nesting sites. Dead stumps

of many of these trees still remain.

Lake Alice can be summarized as a shallowJ, highly eutro-

phic lake with considerable wildlife diversity. The lake in

many ways resembles a slow-moving river because of its high

input-volume ratio (hence, low water retention time) and its









i n pu t- ouLt put a rra3n gemp~n t Th~e high nutrient levels in the

lake ar'e primar7il!' man-made, but natural sources are also

significant. The importance of the latter is suggested by

high nutrient concent rations in Hlume Streamn, relativlely high

or-thophosphate concentrations in natuural w~aters around Gaines-

i lle (Kauimaln, 1969), and high values of ph1osphoruLs measured

at Lake Alice in the early 1950s (0dum, 1953).


Cy re'ss Systemns

Sevral cyprless domnes are being studied uinder varyr-ing

degrees of management as par~t of thle R~ocke fel ler and NS1-RAHNlf

r~esear~ch project entitled "Cypress W~etlands for WaRter M~anage-

ment, Recycling, and Conservastion" (see Odumn, 1972b ; Odum

et al., 19741). The Ow~ens-111inois Research~ Site, located in

Figure S and showJn in more detail in Figure 17, contains the

cypr'ess domes that are under experimental manipulation. The

Sew~age Dome (0.53 ha) h~as received secondary! sewJage effluent

from the adjacenlt tr3ile~r park'sS package treatment plant

since Ma1rch 197-1. At peak uise, flowJ was approximastely 94.6

m3/day., maiking the application rate 1-'.5 cm/w~eek. A second

dome, the Groundwaster Dome, has received pumped groundwaster

at approximately' the same loading rate, also since ;arch 19741.

A fire swJept through the area on December 4 1973, creating

somre damage to these domtes, necessitating thes addition of a7

new ex:perimmental domne (0.9)9 ha) to the project design. SewJage

pumping to this dome began in December, 19741, after data for





















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this study w\ere collected, and the dome is therefore referred

to as the Ow~ens-Illinois Control Dome.

Figure 18 shows the location and access of the Austin

Cary Control Dome, located at the northwest corner of the

Austin Cary Memlor~ial Forest, owned, by the University of

Florida. This dome is much larger (5.4 ha) and has a more

mature stand, of cypress growing there. It has been used in

this study as the ultimate in natural conditions, complete

with surrounding pine forest. It also has a distinct central

pond whiich usually holds water throughout the year.

Figures 19 and 20 are aerial photos taken of the experi-

mental and control areas on November 23, 1974. Figure 19a

shows the W~hitney Trailer Park (155 trailers) which is supply-

ing secondary sewage to the Sewage Dome. Figure 19b shows

the Sew~age Dome (upper left), the Groundw(ater Dome (right

center) and another burned dome lowerr left). This last dome

has also been harvested since the fire, as indicated by the

spar-se canopy seen in the photo. Excess groundwater has

spilled over the edge of Groundwater Dome. The cleared areas

shown in light color surrounding the domes give an indication

of the extent of the fire. The Owens-Illinois Control Dome,

prior to sewage addition, is shown in Figure 20a. The darker

trees in the photo are pine which have invaded the dome and

managed to survive despite the presence of standing w~ater.

An aerial view of the Austin Cary Control Dome is shown in

Figure 20b.




















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F-igure 19!. Aeial'l photo0graphs of Owecns-Illinois Resear~ch
Site: (a) tr'ailer` park wiich~ contr~ibutes
secondariily-treated sewage to cy'pre~ss domecs
(to left of picture~). The sewage treatment
plant and its holding p~ond ar~e sh~own in th~e
upper center of th~e photograph. (b) Experi-
mental cypress domnes, including the Sewange
Dome (reivingg sewag3 e effluenlt as of Mar31ch,
194 -- uIpper left, Gr'oundwa1.ter Dome
(groundwater~ pum"ping~ as of ar11ch, 19l74) -
center right, and a third dome whiich hais
been str-essed by draina7go, fiIe, and3 h arve s t -
ing -- lower I left. Phiotos taken N~ov'embe r
3,19741.
















































(b)





























Figure 20. erciial photographs of (a3) OwJens-111inois
Control Dome receivingig sewagFe effluent as
of Decemnber, 197-1, hence a contr-ol in this
studyy, and l~b) Austin Cary\ Contr~ol Dome
(natural1 condi tions') Note di ffe rence in
surrounding p~inelands and in canopy) shade~s.
Phiotos taken N~ovemlber 23, 1974.
























(a)


r; ,.2









Wdithlacoochee State Forest

This additional site wans included early in the study,

due to the avlailability' there of cypress tr~ee growth data.

The W~ithlacoocheec State Forest is located in Pasco Hlernando,

Citrus and Sumpter Counties in central Florida, near Brooks-

ri lle. Par~ts of the forest ar~e located in the northwJest

corner of the Green Swamp, a vaRluable recharg~e ar-ea for the

Floridan Aqurifer-, and the headwJaters of the Wdithlacoochee

Rivr.The Rtichloam Tract (17,371 acr~es), the largest of

three traccts comprising the state forest, is wJithin the Green

Swamlp boundaryv and, because of its slowJ dr~ainage to the northi-

wJes t, it is dominated by cypress wJetlands inter~spersed among

the pine flatwJoods. Figure 21, wJhich1 outlines the Richloom

uni t, indicates that a consider-able franction of the area is

dominated by cypress. It is from this tr~act th-at tree growth

data havre been mnade available by the Florida Divrision of

Forestry! for 2041 circular plots of 0.2 acre each.
















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METHODS


MIathematical models and energy evaluations of ecosystems

have data requirements that can be satisfied only through a

judicious combination of field studies, literature searches,

discussion with knowledgeable persons, assumptions, and esti-

mations. This chapter presents methods used in data collec-

tion and in analyses of lake and cypress systems and then

describes the modeling effort and other mathematical tech-

niques used. Data collection involved field w\ork and data

reduction on the part of several investigators associated

with two research projects (s ee Ackn ow\le dgmen ts) .



Data Collection for Lake Alice


Hydrologic flows w\ere obtained through a combination of

field instrumentation and data gathering from knowledgeable

sources. Sewage flow and heating plant coolant flow into Lake

Alice were obtained from plant operators for the twJo facili-

ties. The combined flow of these two streams was measured on

several occasions with Gurley and Ott current meters with

good agreement between the given and measured values. The

base flow from H-umne Pond to Lake Alice (Figure 15) was also

measured on several occasions wJith a current meter. Rainfall

and evaporation data were obtained for the duration of the









stuldy per-iod fromn a meteorological station maintained by the

Agr-onomy Depar-tment of the Ulniversity of Florida 250 mn south

of the lake. Lake stage was monitored continuously with a

Stevecns water level recorder located adiacent to th~e board-

waslk dividing the miarsh and open lake. Ilypsographiic curves ,

relating the stage to area and thus to volume, wJere calculated

from existing bathymetric mnaps suich as the one shown in Figulre

15. Lake discharge wa~s calculated from the stage data, assum-

ing the ort flow~ to behavre as in a linear reser'oi r according

to the equastion

1.03
Q, = 12.21L 67.00)

wiher-e Qi = lake dischacrge cfs (cubic feet per second)

L = lake stage, ft above M~SL.

Constan~ts for the weir equation wer-e obtained through estimat-

tionn and analysis of thle water level data. A? general wecir-

exponent of 1.5 w:as found to caurse excessive ouitflows at high

stages. Trasnspiration by waterbyascinths was assumed to be

thr-ee times evapor~ation rates, based on the findings of Pen-

found and Earle (s1948), Timmer- and Wdeldon (1967), Knipling

et al. (1970), and Roger-s and Dav'is (1972). Runoff was8 then

calculated through a w~ater- budget approachl equlating the change

in stor-age of the lake to all the inflows and ouitilows as

showJn in the equation

R.+R. V(L) -V( L) I o

2 864100 7








wJhere Ri = runoff for day i, cfs (cubic feet per second)

V(L) = lake volume as a function of stage L, ft3

QI = net inflow, efs

=baseflow + direct rainfall evapotranspiration

Q, = lake discharge as described above.
The water budget data and a listing of the FORTRAN program

are available under separate cover at the Center for W~etlands,

University of Florida.

Waterhyacinth measurements included aerial surveys of

the hyacinth coverage and measurements of metabolism and bio-

mass. Aerial photos obtained by J. L. Fox on three occasions

during the study aided in determining the spatial coverage of

the hyacinths, especially on the open lake. Areas were

measured with a planimeter. WJate rhyacinth metabolism was

measured using an open system chamber with infrared CO2 gas

analysis. This effort was aided by K. Dugger, T. Center, and

S. Brown. A chamber made of clear polyacetate and buoyed on

a float enclosed the plants for an area of 0.49 m2. Air was

directed through the chamber from a blower-duct with the flow

rate determined periodically using a Hastings hot wire anemom-

eter. Slip streams of intake and exhaust gas were analyzed

with a Beckman infrared gas analyzer and CO2 concentrations
were calculated from calibration curves. The difference in

CO2 levels between the intake and the exhaust, when multiplied
by the flow rate, then represents the rate of carbon assimi-
lation in the chamber. A more detailed discussion of this

method is given by Carter et al. (1973). This experiment was








r-un for 241 hour-s for- twJo different sizes of hyacinths. Inte-

grationl of the resulting production curvle yields both gross

primary productivity anld r~espira~tion, assuming day and night

re~spira~tion ar-e equal. Solair radiation wa!s measured for this

study with a 24l-hour pyrobeliograph (Wdeathe~r-beasuret Co.) i n

thle wavetlength rangSe 0.36-2.5 um. Air temnperat3ure was

r-ecor~ded with a thermistor system (Yecllow Springs Instr-ument

Co.). The hyac3inths in the cha3mber wer-e har-vested after the

metabolism measurements, and both wett and dry! weights Jer~e

obtained.

Metabolism of open wa3ter- was deter-mined at several loca-

t ions in the open lake, onl three occasions by M. ;e irIn

(January,, Marcsh, and May)), and on two occaisionis by the auithor-

(A~pril anid July). Metabolism was determined by~ measul~rig thle

diur~nal change in dissolved oxyrgen and subseqluentlly calculat-

ing the r~atei of change of oxygeni. The method is outlined in

mor-e de ta il inl Odum (1956) and Odum and Hloskin (1958) iffu-

sion corrections w~er~e not u1sed inl this stuldy. D i ssolv~e d

oxygen was determined at thre~e-hour int~rv~als s on replicate

samples using the Azide modification of the Wdinkler method

(A.P. .A., 1971 ),

Chemical paramentters of water wer'e det~r~mined for- var-ious

sites throughout the lake dur-ing the sturdy period of January~

t through Sepiit emb er 1973, directed by P. L. B r~e on i k. P r iorI

to April a spot sampling progr-am was conducted, and afterl

that time automatic saimpler-s wer-e installed at Str-eam 1

(Station 1). by the boardwalk se~par~ating the mar-sh and lake








(Station 5), and in the open lake (Station 6). Station loca-

tions are shown in Figure 15. Each sampler was set to an

eight-hour frequency, producing 21 samples per week. Mercuric

chloride was added to each bottle prior to resetting thle

sampler each week. Analyses on each sample were done accord-

ing to the methods outlined in Table 1. Water temperature

was measured continuously with water temperature recorders

located at Stations 1 and 5. All data were entered on com-

puter cards and a program was written in FORTRAN to reduce

the data to monthly averages and standard deviations. In

addition, changes in water quality across the marsh were cal-

culated by the program for each parameter whenever data were

available concurrently at Stations 1 and 5. The program and

monthly output are available under separate cover at the

Center for Wetlands, University of Florida.

Sediment samples were taken in duplicate by a lake core

sampler along the boardwalk at Station 5 (see Figure 15).

Five cores (total area 114.5 cm2) were composite in a bucket

for each replication. Lengths of the cores were estimated

with a meter stick when samples were taken. Composite samples

were allowed to settle, after which overlying water was

siphoned off. Total weight was then determined. Subsamples

were dried for approximately 24 hours at 1000C to obtain dry

weights and fired in a muffle furnace at 5500C for 24 hours

to obtain volatile solids. Total nitrogen was determined

through Kjeldah1 digestion on 0.5 g (wet) of the original

comnposited samples. The ashed subsamples were extracted in



















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1.0 N nitric acid for phosphorus, calcium, magnesium, potas-

sium, and sodium determinations by the Soil Analytical Labo-

ratory at the University of Florida.



Data Collection for Cypress Wetlands


Hydrologic measurements were based on water level records

obtained from Stevens level recorders being maintained in eachi

experimental cypress dome. Rainfall data were obtained from a

rain gauge at the Owens-Illinois site. Rain records at the

Beef Research Unit of the University of Florida were used for

the Austin Cary Dome. Pumping schedules for the experimental

domes were measured by the project engineer while outflowJ from

the dome was estimated within a rectangular w~eir constructed at

the discharge from the dome. Data on pan evaporation were

used to estimate evapotranspiration at the Agronomy Depart-

ment's meteorological station located at the University of

Florida. Evapotranspiration measurements made by S. Cowles

and others in October, 1974 (unpublished data), in the sewage

dome matched the pan data. Runoff for the sewage dome was

then calculated according to the equation

V. -V.
1 1-1
1i t QI. t o


where Ri = net runoff into dome for day i

Vi = standing water volume for day i

QI = measured inflows for day i

sewagee flow + direct rainfall










Qo. = measured ouitflowJs for- day i
= veir flowJ + eva3potranspiration

t = timie interv'al

=1 day.

Gross runoff wras ca1lculated by' adding the net runoff to the

water loss r-ate determined for a period of no r'ainfall, w~ir-

floui, or sew~age purmpage. A listing of the FORTRAN~ pr-ogram

and thre water burdget data ar-e available ulnder- Se~parate covler

at the C~enter for IWetlands, University of Flor-ida7.

Cypress tree biomass wJas measured at a cypress dome inl

the Austin Cary' Fores~t. Diameter. at breast height (DE~H) vas

d~ter~mined wJith a diameter tape and total height was measured

with a clinometer- for- 16 trees repr~esenting a wide range of

DBH values. Fr-om these trees, ten were selected for- harvest

because they wrer most representatives of the DBHI and height

values foulndd for the trees at the ex~perimental site. The

diameter of each tree wJas measurred w~ith and without bark.

Each tree was curt at approximately' 2 ft above~ the gr-ound suir-

face with a chain saw, and the biomass wJas separated into

leaves, small br-anches (less than 1 cm in diameter:), large

branches, and main stem. We~t weights wrere measurred for- each

with a beam scale, and subsaimples wjere taken to determine

moisturre content. Total height and branch length v~ere also

mesusre~id on the felled tree. The stem was then subdivided

into S-ft sections, and cross-sections of 1 to 2 in weree

obtained at each S- ft interval up to -1 in in diameter. T'he

roots of seven trees were pulled out w~ith a tractor'; dynamite







was used on one occasion to loosen the roots. Moisture con-

tent was determined for each set of roots and for stem cross-

sections by drying in a kiln at 1000C for 72 hours. Seventy-

five percent recovery of roots was estimated and weights were

adj us ted according ly. The dry weight data for leaves, branches,

stem, and stump plus roots were used as the dependent variable

(y) in a regression analysis with the independent variable

chosen as x = /D~BH x Height with both DBH and height expressed

in centimete rs The form of the equation used was y = ax,

the form found most satisfactory for cypress by Carter et al.

(197 3) Leaf, branch, stem, and stump plus root biomass

values were then determined for the various experimental domes

using the regression relations and DBH and height data for

each cypress tree in the domes. The FORTRA~N program used for

these calculations and results of biomass determinations are

available under separate cover at the Center for W~etlands,

University of Florida.

Cypress net primary production was determined from the

above regressions. Measurements of cypress diameters at

breast height and of height over a six-year period were made

available for the Wiithlacoochee State Forest by the Florida

Division of Forestry. These data were from 204 circular

plots of 0.2 acre each, placed at fixed intervals throughout

the Richloam Tract of the forest in the early 1960's as part

of the Continuous Forest Inventory (CFI) data collection

effort. Twenty-three CFI plots dominated by cypress were

chosen from the 204 available for calculations of net









pr-oductivity. Plots w~ere selected to include a wJide range

of cy'pr-ess systems, the v;ariability being deter-mined pr-imlarily

by the tr-ees gr-owing in association w~ithl the cypress. The

D)1ll and mecrchantable height data wer-e entered onl computer-

cards, one card for' each cpr-ess tree. A com~puter- pr-ogram

was3~ then wr-itten in FORTRAN to deter-mine the pr~oductivity) of:

eachi cypress tr'ee accor-ding to the following r-elationship:

N~et Primary Productivity' = change in biomnass

+ litterf~all c root loss.

Biomass values f-or- each tr-ee at the beginning and end of

the mealsurementt per-iod wer-e deter-mined from r-egression equa-

tions discussed above which employed I'DBH1 x Heigiht as the

independent variable. It w~as fir-st necessary) to change mer--

chantable height to total height aiccor-ding to r-elationships

deter-mined from the cypr-ess hiarvest data. The avier3ge leaf

biomass for eachi tr-ee, deter-mined froml the above-mentionedd

r-egr-essions, when multiplied by' six years gave an estimate of

the litterfacll contr-ibution to net pr-oductiv;ity for- eachi tr-ee.

root loss wais estimated to be 27.70 of the total net pr~imary~!

pr-oduction based on data r-epor~ted by Woodwrell and W~hittaker`

(1968) for- a for-est at Br-ookhav;en Na~tionail Labora3tory. The

eq ua tion for- determination of net pr-oductivity on an annual

basis for each site is thus given as


NPP 1. 33 (B + t*L)
A-t

wher-e NPFP = cy~press net pr-imary! pr-oductiv;ity in g/m'/yr'I








A = area (809.4 m2)

t = time (6 years)

nB = biomass change for all cypress trees in plot (g)

L = average leaf biomass and thus approximate
litterfall for all cypress trees in plot
for one year (g/yr).

The program listing and complete output for the 23 plots

are available under separate cover at the Center for Wetlands,

University of Florida. Total plot productivity was determined

for comparative purposes from cypress productivity (NPP) by

dividing the cypress productivity by the fraction of trees

that are cypress.

Understory production and sunlight patterns were measured

at the control cypress dome at Austin Cary Forest because of

its well-developed central pond. The central pond generally

has a depth of at least 0.5 m, even in the dry season. Using

the same methods as in Lake Alice, measurements of underwater

metabolism were made four times: November, 1973; Mlarch, Mlay,

and August, 1974. Water samples for dissolved oxygen were

taken at approximately 3-hour intervals from an elevated plat-

form constructed near the center of the dome. The platform

was used to insure minimal disturbance of the water while

sampling. Oxygen was determined on replicate samples with

the Azide modification of the W~inkler method (A.P.H.A.,1971).

Calculations were corrected for oxygen diffusion by assuming

a value of 0.034 g-02 2L-yr at 0% saturation, a value

quoted by Odum (1956) for still water. Temperature of both
water and air were measured with a thermometer. Solar









radiation in the dome wars measured with a 24I-hour pyroblelio-

gr-aph (Bel fort Co.). Total solar radiation values w~ere

obtained from J. Steinberg for the November, ~ar~ch and Ma13Y

studies wilth an Eppley py'ranometer- at a ne~rby' research sta-

t ion at Lake Milze. A~ Weathe rreasure py'rohel iograph w~as used

for the August data. All solar gauges w~er-e calibrated against

each other- with thie Belfort instrument being used as the stan-

dard. Air temperature outside thle dome wacs obtained from

climatological data at the near-by Bee f Researchl Uni t operated

by th~e Univ'ersity of Florida?. Evaporation rates inside and

outside the dome w;er-e compared during th~e August experiment

w~ith replicate atmometers. The biomass of submerged aquatic

macr-ophytes wars deter-mined in February' w\ith four samples,

each taken at randomn locations w;ithin the central pond.

Standing water chemistry samples wecre taken in the four1

experimental cypress domes from the center- to th~e edge on a

monthly basis from A ril to October-, 19741 (see Br-e-onik et al.,

19;;4):. The samples were collected in one-liter- plastic

bottles and pr-eserved in mer-curic chlor-ide. pH w~as deter--

mined within a few hours of sampling and samples w~er-e refrig-

erated for- later- nutrient analysis (mainly nitrogen and phos-

phor-us) b\ the water- chlemistry~ group according to the methods
outlined in Table 1.

Sediment samples w\ere taken in November, 19:-1, wirth a

lake sediment sampler in orders to include the entire ortganic

layer of each dome. Five cores (total area. 1141.5 cm-) were

composite for three locations in each dome (~four locations








in the Sewage Dome). Total wet weight was recorded for each

location. Subsamples were treated in a manner similar to the

Lake Alice sediment analysis described above for dry matter,

volatile solids, nitrogen, phosphorus, calcium, potassium,

magnesium, and sodium.



Modeling Mlethods


Construction of models both for illustrative purposes

and for computer simulations incorporated the energy circuit

language developed by H. T. Odum (1971,1972a) A summary of

the symbols used in this dissertation is given in Figure 22

along with pertinent mathematical descriptions. The various

limiting factor modules already presented in Figure 13 were

also used.

Computer simulation involved the use of both digital and

analog facilities. The initial construction of a model and

the determination of the first order, ordinary nonlinear

differential equations associated with each state variable

are the same in both types of simulation. An example of a

differential equation is shown with Figure 22c. Constants

(k) are determined by assigning the best data values to every

flow (kQ) and storage (Q) and solving for the k values. From

this point, the methods for digital and analog computer simu-

lation diverge.















Figure 22. Energy language modules used for modellingg and
simnulation- in this dissertation (Odulln, 1971,
19728):

(a) Olutside SOUr.ce SUIPp~ling energyl to thle
systemr fromi on unrlimitedj storage.

(b) Hleat sink, outf~low~ of used energy with
entropy increase symibolic of th~e necessary
losses of energy~ due to the Second Law~ of:
Th~ermnodynamiics .

(c) Stora~ge of a quantity' of energy! in
the systemi. These are focus points for- t~e
formula7tion of diifferential eqluations for1
simrulationss and arle often rcefrerr to as
s tate var~i bles.C75

(d) Mlultiplicativ~e interaction in which
thle output is propjortionll~ to the products:
of the~ forces of the tw~o inp~uts.

(e) Interaction of tw~o flow~s in which the
output is somie unspecified function of the
tw~o forces dii~rivin the fos The multiplier
(J) is a7 special case of this more general
w:o rkgate.

(f) Composite symbol used to denote con-
sumer units such as5 fish or cities in- which~
the storage feeds back somie of its energv
to enhiance its uptake of evecn more energ;.

(g) A force (x) proportional1 to flow~ J
may) interact w~ithl other components in the
s'rs t e a.























































SELF MAINTAINING CONSUMER UNIT


HEAT SINK

(b)


Q= J-KO


SOURCE


PASSIVE STORAGE

(c)






Y CONTROL
FACTOR
INPUT\ OUTPUT


HEAT SINK


'1V FACTOR O


HEAT SINK


J = K XY


J = f (X,Y)


M1U LTIPLIER

(dj)


GENERALIZED WVORKGATE


(e)








J


FORCE FROM
A FLOWN

















Figure 22 continued

(h)j Cycling r~eceptor- module of chlor~o-
phyvll excitation ini green plants. A con-
t inualn flowi from excited (C*) t o de act ivare d
s t age s (C) creates a downstream energy) flow!.
This is similar to the Lumryv-Rieske model
presented in Figur 1c.

(i) Green plant or' plant community whiich
combines anablolismn of cycling r~eceptor (hI)
w~i th catabolismn of self-maintaining consumer-
un11it (f).

( ) Switch used whlen flow~s are recgulated
by on-off signals such as political decisions
an1d sudden firIe s.

(k) Constant gain amplifier` used w~hen a
vlery low~ flow~ (x) is being amplified b\
another source but without draining the
for~mer storag~e. Opera~tion is simiilar to
a Stereo record amplifier..

(1) Economic trannsactor' which shiows th~e
general r.elations~ip between energyv and
money, i.e., they flow~ in opposite dir~ec-
tions. Price is often expressed as
S= JZ/J.1

(m) Twlo-way w~orkgate in which~ flow~ can
go either way! depending onl back for~ces- The
negative sign indicates a linear decrease
in flow~ J withi an- increase in the driving
for~ce.

(n) Box: often used to lump linear ~r~o-
cesses. F~or example nutrients canl be
shown being r~ecyled fromn a respiratoryv
pathway.!'



































ECON\OMIIC TRANSACTOR


y DRIVING
'FORCE

C O



J= K (I-K Y)(C-0)

DIFFUSION MODULE WITH
NEGATIVE WVORKGATE


GREEN PLANT AND
OTHER PRODUCERS


CYCLING RECEPTOR
(h)


EN\ERIGY


GENERAL PURPOSE BOX


UNLIMITED
SOURCE


INPUT OUTPUT
X-t g g-~ x




CONSTANT GAIN
AMPCI FIR


INPUT~ OUTPUT




DIGITAL FUNCTIONS
j)




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