SY'STEPlS ANALYSIS OF NUITRIE~NT DISPOSAL IN\
CYIPR~ESS WEITLANVDS AN~D LAK;E E~COSYISTEM1S IN FLORIDiA
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
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-
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
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.
TABLE OF CONTENTS
AC KN OWLEDGMENT S ..........
LIST OF TABLES ..........
LIST OF FIGURES ...
. . ix
. . xv
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
. . 88
Data from Lake Alice .....
Lake Alice M~odel .......
D~ata from Cypr-ess W~etlands ..
Cypress Dome Mlodel ......
Cypress Pond M~ini-Mlodel ...
. . .
. . .
. . .
. . .
. . .
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
TABLE OjF CONTENTS continued
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
. 3 1
. . 40
LIST OF TABLES
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 . . . . . . . .
. . 105
LISTI OF: TABLES continued
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
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
. . 20
LIST OF FIGURES
F i gu re
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
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
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
LIST' OF FIGURES continued
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 ...
. . 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
W~illiam Joseph Miitsch
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.
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
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.
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-
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.
---- 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
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
Figure 3. General map of' research areas in Alach~ua
Count!', Florida, including Lake Alice
r~esearich si te and two cypress research
GENERAL MiAP OF RESEARCH
SITES IN ALACHUA COUN\TY,a
SCALE IN MILES
?\ ~~~Austin Cory Cypress~eerhSt
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
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.)
CONrT ROL DOME
EXPERIMIEN TA L CYPRESS
W'ETLAN~lDS Own~;S ILLINVOIS SITE
(FEET AtiOVE Mr.S.L.)
SI LO METERS
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
Nut- *-~----i x xy 1 `
Nutrients ttL II IHyocinths
///// ganicand Benthic
~ I ICpress
\Yater VOter C i
INlrtrients xi~~-_ NU~t-\ OrI Understory
W v (b)
or 0 0
o r-- c
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 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
Cypress, Alachua County
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 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,
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).
a I increasing
rr E~Nitrogen, etc.
"o I Nitrogen, etc.
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 -
Mi ts cher~lich (1909) presented one of the first mathie-
mlatical interpretations of the limiting factor' concept in the
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.
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
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)
V= K, I
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
p k kll
k I +k
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 = + '
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
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
P = KIN
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
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
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.
O [j -
vl '- "J '-O
C ~O Mu
U TI-H -~
~CI CE *
-O .0 'C 0~
l0e O ~
r "3 >
C U'u O 7t
---4 U 'i O
O r < '+< U).
O3 Z '- 01r
r0 . CO5:
-~r 2- 0 r
L M E ~- C -
r= 0 0 c. c.~
~SW 3~08~ IJ 'NOlltf~3~3
U ..- tMO
O v e-
cr 2 U vr
' va ,C
II 'O O
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
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,
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
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
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
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
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
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.
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.
r.r ;i' I:'~2.,,
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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
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
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
r0 U r
-1 +J Q U
0. IC '- E
UJ E O.1
r0O - C
3~~ (1 3 0
= or C r
*- *,-- O L r0 O
O U *0r -- >
E (3 X : 0
> c -
O -H O v
vi E 0. O '3
vs O0i E 0 M
*M '- O E O O
0z UH 0. < C, 1 2
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
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
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)
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.
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
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-
Figure 22. Energy language modules used for modellingg and
simnulation- in this dissertation (Odulln, 1971,
(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:
(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
(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
'1V FACTOR O
J = K XY
J = f (X,Y)
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-
( ) 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
(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
(n) Box: often used to lump linear ~r~o-
cesses. F~or example nutrients canl be
shown being r~ecyled fromn a respiratoryv
J= K (I-K Y)(C-0)
DIFFUSION MODULE WITH
GREEN PLANT AND
GENERAL PURPOSE BOX
X-t g g-~ x