A MODEL OF THE PHOSPHORUS CYCLE AND PHYTOPLANKTON GROWTH
IN SKAHA LAKE, BRITISH COLUMBIA
by
WILLIAM M. FLEMING
M.S.
A.B. Dartmouth College, 1963
Colorado State University, 1966
A THESIS SUBMITTED IN PARTIAL FULFILMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
i n the Department
of
C i v i l Engineering
We accept this thesis as conforming t o ^ h e
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June, 1974
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A B S T R A C T
Phosphorus i s recognized
phication of lakes.
as a key nutrient i n the c u l t u r a l eutro-
A simulation model of the phosphorus cycle i n eutro-
phic Skaha Lake shows t o t a l phosphorus to be a u s e f u l i n d i c a t o r f o r the
prediction of trophic s t a t e s .
Difference equations and a d a i l y time scale
are used i n a mass balance model which accounts f o r the dynamic s t r a t i f i c a tion regime of the lake.
Total phosphorus movement between epilimnion,
hypolimnion, and sediments i s d e t a i l e d i n a series of submodels.
An eddy
d i f f u s i o n submodel predicts loading from the hypolimnion to the epilimnion
which can equal external loading f o r short periods o f the summer.
phorus sedimentation
submodel predicts organic sedimentation
of primary production and inorganic sedimentation
ations.
A phos-
on the basis
from adsorption
consider-
A regeneration submodel considers the temperature-dependent decom-
p o s i t i o n rates of sedimented phosphorus.
A primary production submodel
accounts f o r temperature, l i g h t and phosphorus dependency, as w e l l as r e s p i r a t i o n , grazing, s i n k i n g and advection l o s s e s .
Based on known phosphorus
loading and three years of l i m n o l o g i c a l data, reasonable
between r e a l and simulated
agreement was found
t o t a l phosphorus concentration, phytoplankton b i o -
mass, and hypolimnetic dissolved oxygen.
Results show that three to four times more phosphorus apparently
returns to the lake from deep-water sediments than possible by b a c t e r i a l decomposition
probably
alone.
Improved simulation of phytoplankton production
could
be achieved with the i n c l u s i o n of a zooplankton submodel and extenii
iii
sion to include the s p e c i f i c growth dynamics of more than one a l g a l group.
The Michaelis-Menton
h a l f - s a t u r a t i o n constant appears to be the most
s e n s i t i v e c o e f f i c i e n t i n the primary production submodel.
The probable effects of four phosphorus management p o l i c i e s
are assessed using 20 years of hydrologic data (1949-69) and the eutrophic
conditions of 1970 as a s t a r t i n g point. While no attempt i s made to pred i c t the trophic status of the lake f o r the next 20 years, d e f i n i t e trends
are apparent.
With no phosphorus removal and no increase i n loading over
the hypothetical 20-year period, phytoplankton
blooms increase i n i n t e n s i t y
and hypolimnetic dissolved oxygen approaches zero.
With 60 per cent removal
of municipal phosphorus and conditions of e i t h e r low or high economic growth
i n the Penticton region, the eutrophic conditions o f 1970 are reached within
12 to 14 years.
A l g a l blooms and hypolimnetic dissolved oxygen d e f i c i t s are
p a r t i c u l a r l y serious during dry years.
With 100 per cent municipal phosphorus
removal, trophic conditions appear to improve s i g n i f i c a n t l y , with the p o s s i b i l i t y of minor a l g a l blooms during only dry years.
These r e s u l t s indicate
that complete removal of the phosphorus from municipal sources appears to
be the most r a t i o n a l long-range management p o l i c y .
These conclusions demonstrate that a t h e o r e t i c a l model to pred i c t trophic i n d i c a t o r s i n a lake can be useful as both a research tool and
a p r a c t i c a l planning aid f o r decision-making.
TABLE OF CONTENTS
Page
LIST OF TABLES
vii
LIST OF FIGURES
ix
CHAPTER
I.
INTRODUCTION
1
A.
PROBLEM DEFINITION.
1
1. The Eutrophication Problem
2. Phosphorus and Eutrophication
3. The Need For A Predictive Model
1
2
4
B.
II.
RESEARCH OBJECTIVES
'
7
THE OKANAGAN BASIN AND SKAHA LAKE
9
A.
9
THE OKANAGAN BASIN
1. Water Quantity and Quality Problems
9
2. Geographical Setting
10
3. Geological History
10
4. Hydrology.
12
5. Water Use
13
6. Cultural Development and Associated Phosphorus Loading. 13
B.
SKAHA LAKE
15
1.
15
15
16
16
16
19
21
21
21
24
24
25
25
27
2.
3.
4.
5.
Physical Limnology. . . . . . . . . . . . . . . . . . .
(a) The Lake Basin
(b) The Lake Sediments
Chemical Limnology
(a) Water Chemistry
(b) Sediment Chemistry
(c) Net Sedimentation Rates of Phosphorus Forms . . . .
Biological Limnology
(a) Phytoplankton and Periphyton
(b) Macrophytes . . . . .
(c) Zooplankton
(d) Fish
Trophic State
Paleolimnology. .
iv
V
CHAPTER
III.
Page
PHOSPHORUS CYCLING IN LAKES AND MODELLING APPROACH
29
A.
AND THE LIMITING NUTRIENT CONCEPT
29
The "Law o f t h e Minimum"
R e l a t i v e Importance o f Carbon, N i t r o g e n and P h o s p h o r u s .
(a) Carbon
(b) N i t r o g e n
(c) Phosphorus
29
30
30
31
32
EUTROPHICATION
1.
2.
B.
THE PHOSPHORUS CYCLE IN LAKES
34
1.
35
2.
3.
C.
35
36
36
37
38
44
MODELLING APPROACH
45
1.
45
46
47
48
48
50
2.
IV.
Phosphorus Compartments i n Lake Water
(a) Orthophosphate Phosphorus ( S o l u b l e R e a c t i v e
Phosphorus). . .
(b) S o l u b l e O r g a n i c Phosphorus
(c) P a r t i c u l a t e Phosphorus
(d) T o t a l Phosphorus
Turnover Rates o f Orthophosphate.
The Lake as a P r o d u c t i v i t y Chamber
Simulation Modelling
(a) Time S c a l e
(b) A p p r o a c h t o M a t h e m a t i c a l Statement o f R e l a t i o n s h i p s
S i m u l a t i o n Approaches to M o d e l l i n g t h e Phosphorus C y c l e
(a) The Compartment Approach
(b) The Mass Budget Approach
DEVELOPMENT OF A MODEL FOR SKAHA LAKE
53
A.
FUNDAMENTAL INPUT-OUTPUT EQUATION
53
1.
53
53
54
54
55
55
55
55
56
2.
3.
B.
Form o f t h e E q u a t i o n f o r t h e E p i l i m n i o n
(a) I n p u t Terms
(b) Output Terms
( c ) Combined Mass B a l a n c e
Form o f t h e E q u a t i o n f o r the H y p o l i m n i o n
(a) I n p u t Terms.
(b) Output Terms
(c) Combined Mass B a l a n c e
.
M o d i f i c a t i o n o f Mass B a l a n c e D u r i n g M i x i n g P e r i o d s . . .
MIXING BEHAVIOR OF SKAHA LAKE AND VOLUME CHANGES
OF EPILIMNION AND HYPOLIMNION
56
vi
CHAPTER
Page
C.
DEVELOPMENT OF SUBMODELS
58
1.
58
59
59
60
61
61
61
61
63
63
67
67
69
2.
3.
4.
5.
V.
Eddy D i f f u s i o n Submodel
(a) Simplifying Assumptions for Eddy D i f f u s i o n
(b) Equation for Eddy D i f f u s i o n Transport
(c) C o e f f i c i e n t of Eddy D i f f u s i o n
Sedimentation Submodel
(a) Sedimentation from the Epilimnion
(1) Sedimentation of Inorganic Phosphorus
a. P r e c i p i t a t i o n of Phosphorus Minerals. . . .
b. Adsorption of Phosphate
(2) Sedimentation of Organic Phosphorus
(b) Sedimentation from the Hypolimnion
(1) Sedimentation of Inorganic Phosphorus
(2) Sedimentation of Organic Phosphorus
(3) Resulting Expression f o r Sedimentation
from the Hypolimnion
Internal Loading Submodel..
(a) Mechanisms C o n t r o l l i n g Phosphorus Transport
at the Sediment-Water Interface
(1) Physical Disturbance and Mixing
(2) Physical D i f f u s i o n
(3) B i o l o g i c a l Uptake
(4) Anaerobic Chemical Regeneration
(5) Decomposition Regeneration
(b) Formulation of Internal Loading Submodel
(1) L i t t o r a l Zone Regeneration
(2) Deep Water Sediment Regeneration
Primary Production Submodel
.
(a) Other Phytoplankton Models
(b) Basic Phytoplankton Equation
(c) Phytoplankton Growth
(1) Temperature Dependency
(2) Light Dependency
(3) Nutrient Dependency
(4) F i n a l Growth Rate Expression
(d) Phytoplankton Losses
(1) Respiration Losses
(2) Grazing by Zooplankton
(3) Sinking of Phytoplankton Cells
(4) Advection Losses
Hypolimnetic Dissolved Oxygen Submodel. . . .
71
72
73
73
74
75
76
77
79
79
80
81
82
84
84
85
85
91
94
95
95
96
97
98
98
RESULTS
101
A.
101
VERIFICATION OF THE MODEL FOR SKAHA LAKE.
vii
CHAPTER
Page
1.
2.
3.
4.
5.
B.
C.
VI.
101
101
107
Ill
I l l
115
115
SENSITIVITY ANALYSES
117
1.
2.
117
120
S e n s i t i v i t y of Phosphorus Loading and Hydrology . . .
S e n s i t i v i t y of Physical and B i o l o g i c a l Coefficients .
EDDY DIFFUSION
123
DISCUSSION
125
A.
INTERPRETATIONS AND LIMITATIONS
125
1.
2.
3.
126
126
127
B.
C.
VII.
Total Phosphorus Concentration
(a) Upper Mixed Layer
(b) Hypolimnion Phosphorus
.
Phytoplankton Production
Dissolved Oxygen i n the Hypolimnion
Simulation of the South Basin of Skaha Lake . . . . .
V e r i f i c a t i o n for 1970-71 and 1972-73
Sedimentation from the Epilimnion
Regeneration of Phosphorus from Deep-Water Sediments.
Phytoplankton Production
APPLICATION TO MANAGEMENT OF THE EUTROPHICATION PROBLEMS
OF SKAHA LAKE
130
SUITABILITY OF THE MODEL FOR OTHER LAKES
134
SUMMARY AND CONCLUSIONS
LITERATURE CITED
137
140
APPENDIX
A.
INPUT DATA FOR SKAHA LAKE
152
B.
COLLECTION AND ANALYSES OF LIMNOLOGICAL DATA
159
1.
2.
3.
159
160
161
Total Phosphorus
Phytoplankton
Dissolved Oxygen
LIST OF TABLES
Table
Page
I.
PHYSICAL CHARACTERISTICS OF SKAHA LAKE
15
II.
CHEMICAL CHARACTERISTICS OF SKAHA LAKE
18
III.
ALGAL ABUNDANCE IN SKAHA LAKE, 1969-70
22
PHYTOPLANKTON IN SKAHA LAKE,. 1971
22
PERIPHYTON
23
IV.
V.
VI.
IN SKAHA LAKE, 1971
TURNOVER TIMES OF PHOSPHORUS FLUX BETWEEN COMPARTMENTS
40
VII.
SENSITIVITY OF COEFFICIENTS ON PHOSPHORUS CONCENTRATION . . . . 121
VIII.
SENSITIVITY OF COEFFICIENTS ON PHYTOPLANKTON PRODUCTION . . . . 122
A-l.
MIXING AND EDDY DIFFUSION DATA.
153
A-2.
RADIATION AND EPILIMNION TEMPERATURE
155
A-3.
ESTIMATED PERCENTAGES
OF TOTAL PHOSPHORUS ENTERING SKAHA LAKE
FROM KNOWN SOURCES, 1969-71
156
A-4.
MONTHLY OUTFLOW HYDROLOGY FROM SKAHA LAKE, 1969-70
157
A-5.
YEARLY OUTFLOW HYDROLOGY FROM SKAHA LAKE, 1949-73
158
viii
LIST OF FIGURES
Figure
Page
1.
Location and watershed boundary of the Okanagan Basin
2.
Bathymetry of Skaha Lake
11
3.
Hypsometric curves of the north and south basins of Skaha Lake . .
17
4.
Eutrophication of lakes i n the Okanagan Basin compared
to other lakes i n Europe and North America
26
Phosphorus transformations i n s t r a t i f i e d lakes during summer;
expressed i n turnover times .
41
6.
Adsorption of phosphorus on an oxidized calcerous sediment. . . .
70
7.
Growth rate of phytoplankton as a function of temperature . . . .
86
8.
Relative photosynthesis rate as a function of l i g h t i n t e n s i t y . .
88
9.
Growth rate of a phytoplankton population as a function of
phosphorus concentration
92
5.
6
10.
A l g a l r e s p i r a t i o n rate as a function of temperature
95
11.
Loading rate of phosphorus to Skaha Lake, 1969-70,
and phosphorus outflow rate
102
Phosphorus concentration i n surface water of Skaha Lake, 1969-70,
with no modification of o r i g i n a l assumptions
103
Phosphorus concentration i n surface water of Skaha Lake, 1969-70,
with the sedimentation rate from the epilimnion doubled
105
Simulated sedimentation rate of phosphorus from the epilimnion of
Skaha Lake, 1969-70, and regeneration rate from l i t t o r a l s e d i ments
.
106
Phosphorus concentration i n surface water of Skaha Lake, 1969-70,
with the sedimentation rate from epilimnion doubled and the r e generation rate from deep-water sediments X 3.5
108
Simulated sedimentation rate of phosphorus from the hypolimnion
of Skaha Lake, 1969-70, and the regeneration rate from deep-water
sediments
109
12.
13.
14.
15.
16.
ix
X
LIST OF. FIGURES (Continued)
Figure
17.
18.
19.
20.
21.
22.
23.
24.
25.
Page
Simulated sedimentation rates of organic phosphorus and
inorganic phosphorus from the hypolimnion of Skaha Lake,
1969-70
110
Simulated phosphorus concentration i n the hypolimnion of
Skaha Lake, 1969-70
112
Phytoplankton biomass i n the trophogenic layer of
Skaha Lake, 1969-70
113
Dissolved oxygen concentration i n the hypolimnion of
Skaha Lake, 1969-70
114
Simulated phosphorus, phytoplankton and hypolimnetic dissolved
oxygen with varying phosphorus loading and hydrologic discharge,
Skaha Lake, 1969-70
118
Loading rate of phosphorus from external sources to Skaha Lake,
1969-70, and simulated " i n t e r n a l loading" to the epilimnion by
eddy d i f f u s i o n
124
Simulated phytoplankton growth rates showing the l i m i t i n g e f f e c t s
of temperature, l i g h t and phosphorus, Skaha Lake, 1969-70. . . . .
129
Hypothetical e f f e c t s of four d i f f e r e n t phosphorus management
p o l i c i e s on the long-range eutrophication of Skaha Lake.
133
Predictions of the trophic status of Skaha Lake with present
phosphorus loading p o l i c i e s , t e r t i a r y treatment f o r phosphorus
removal, and land disposal of sewage (Stockner and Pinsent 1974) . 135
CHAPTER I
INTRODUCTION
A.
PROBLEM DEFINITION
1.
The
Eutrophication
Most l a k e s b e g i n
scarce
Problem
their existence
in a relatively nutrient-
s t a t e , as many N o r t h American l a k e s d i d t e n t o f i f t e e n
y e a r s ago
f o l l o w i n g the P l e i s t o c e n e g l a c i a t i o n .
surrounding
thousand
As n u t r i e n t s l e a c h from
r o c k s o v e r g e o l o g i c time, t h e y accumulate i n the water
and
sediments, r e s u l t i n g i n the growth o f p r i m a r y p r o d u c t i o n
(mainly
and
stimulates
other photosynthetic
ary production
organisms).
Primary production
(or p r i m a r y consumption) by
of i n c r e a s i n g n u t r i e n t content
and
production
g e n e r a l l y r e f e r r e d t o as e u t r o p h i c a t i o n , and may
comes a swamp, then a bog,
and
and
i t i s usually a
t o become e u t r o p h i c .
take
(Some deep l a k e s
However, the p r o c e s s
can be
short geologic
time span.
many N o r t h American l a k e s , such as Lake E r i e , has
s e v e r a l decades.
(mesotrophy) may
The
be d e s i r a b l e to enhance such v a l u e s
1
amounts
eutrophication of
increased
While moderate l e v e l s of
will
acceler-
ated by t h e c u l t u r a l impact o f man's a c t i v i t i e s which can add v a s t
over the l a s t
be-
f i n a l l y a meadow.
never become e u t r o p h i c ) .
of n u t r i e n t s o v e r a v e r y
This
one,
u n t i l a lake
a deep l a k e i n a n u t r i e n t - s c a r c e watershed may
tens o f thousands of y e a r s
probably
(fish).
i s a natural
continue
While e u t r o p h i c a t i o n i s a n a t u r a l p r o c e s s ,
v e r y slow one,
second-
s m a l l a q u a t i c a n i m a l s , which i n
t u r n enhances secondary consumption by l a r g e r a q u a t i c a n i m a l s
process
algae
exponentially
eutrophication
as f i s h
production,
2
advanced l e v e l s have s e v e r e d e t r i m e n t a l e f f e c t s .
Highly eutrophic lakes,
w h i c h t e n d t o be p l a g u e d b y a l g a l blooms and g r e a t l y r e d u c e d r e c r e a t i o n a l v a l u e s , may become a n a e r o b i c
i n deeper w a t e r s .
Furthermore,
these
w a t e r s may d e v e l o p t a s t e , o d o u r , c o l o u r and f i l t e r c l o g g i n g problems
which reduce water supply
I t i s important
values.
t o d i s t i n g u i s h between " n a t u r a l e u t r o p h i c a t i o n " ,
a g r a d u a l p r o c e s s o v e r thousands o f y e a r s , and " c u l t u r a l e u t r o p h i c a t i o n " ,
an a c c e l e r a t e d p r o c e s s o f n u t r i e n t e n r i c h m e n t t a k i n g p l a c e i n t e n s o f
years o r l e s s .
S t i m u l a t o r y n u t r i e n t s , e s p e c i a l l y phosphorus and n i t r o -
gen, have b o t h n a t u r a l and c u l t u r a l o r i g i n s .
R a i n f a l l , r u n o f f and ground
water from n a t u r a l o r w i l d e r n e s s watersheds normally c o n t r i b u t e only s m a l l
percentages of n u t r i e n t s required f o r accelerated e u t r o p h i c a t i o n .
f r o m a g r i c u l t u r a l , d o m e s t i c and i n d u s t r i a l s o u r c e s
Nutrients
a r e g e n e r a l l y the major
causes o f c u l t u r a l l y e u t r o p h i c l a k e s .
The
e f f e c t of a drainage
w i t h i n i t i s of prime importance.
b a s i n on t h e t r o p h i c s t a t u s o f l a k e s
As s u g g e s t e d by H u t c h i n s o n (1969), i t
i s u n r e a l i s t i c t o conceive o f o l i g o t r o p h i c or e u t r o p h i c water types, but
r a t h e r o f l a k e s and t h e i r d r a i n a g e
t r o p h i c o r e u t r o p h i c systems.
b a s i n s and s e d i m e n t s as f o r m i n g
oligo-
F o r i n s t a n c e , t h e c o e x i s t e n c e i n t h e same
watershed o f a h i g h l y p r o d u c t i v e a g r i c u l t u r a l i n d u s t r y , together w i t h a
nonproductive
surface water i s incompatible
(Stumm and S t u m m - Z o l l i n g e r
1972).
2.
Phosphorus and E u t r o p h i c a t i o n
The key r o l e p l a y e d by p h o s p h o r u s , e i t h e r as a s t i m u l a t o r y
n u t r i e n t o r a s an i n d i c a t o r o f t h e p r e s e n c e o f s t i m u l a t o r y n u t r i e n t s , has
been g e n e r a l l y a c c e p t e d
by most s c i e n t i s t s .
The p r e s e n c e a n d . r a t e
of increase
3
o f phosphorus c o n c e n t r a t i o n s i n l a k e w a t e r s i s c o n s i d e r e d
t o be an
impor-
t a n t i n d i c a t i o n of the t r o p h i c s t a t e of l a k e s and o f the r a t e a t w h i c h
eutrophication i s progressing.
Consider
the f o l l o w i n g o b s e r v a t i o n s :
" C o n t r o l of phosphorus i n p u t t o w a t e r s i s the key
to the c o n t r o l o f e u t r o p h i c a t i o n i n a m a j o r i t y of c a s e s . "
(O.E.C.D. 1973).
"A r e l a t i o n s h i p between phosphorus l e v e l s and a l g a l
p r o d u c t i v i t y has been demonstrated f o r many n a t u r a l w a t e r s . "
(Kramer et al. 1972) .
"For most i n l a n d w a t e r s phosphorus appears t o p l a y a
major r o l e i n i n f l u e n c i n g p r o d u c t i v i t y . Under a l m o s t a l l
c i r c u m s t a n c e s phosphorus i s a key element i n the f e r t i l i z a t i o n of n a t u r a l bodies of water."
(Stumm.and StummZollinger
1972).
"These, and many o t h e r o b s e r v a t i o n s have f o s t e r e d the
widespread b e l i e f t h a t the r a p i d e u t r o p h i c a t i o n of l a k e s
t h r o u g h o u t the w o r l d i s l a r g e l y b e i n g caused by i n c r e a s e d
i n p u t o f phosphorus r e s u l t i n g f r o m human a c t i v i t i e s . "
(Rigler
1973).
"Of a l l the elements p r e s e n t i n l i v i n g o r g a n i s m s , phosphorus i s l i k e l y t o be the most i m p o r t a n t e c o l o g i c a l l y , because the r a t i o o f phosphorus t o o t h e r elements i n o r g a n i s m s
tends t o be c o n s i d e r a b l y g r e a t e r t h a n the r a t i o i n the p r i mary s o u r c e s o f the b i o l o g i c a l e l e m e n t s . A d e f i c i e n c y i n
phosphorus i s t h e r e f o r e more l i k e l y t o l i m i t the e a r t h ' s
p r o d u c t i v i t y o f any r e g i o n o f the e a r t h ' s s u r f a c e t h a n i s a
d e f i c i e n c y of any o t h e r m a t e r i a l e x c e p t w a t e r . "
(Hutchinson
1957).
". . .mass b a l a n c e c a l c u l a t i o n s show t h a t i n Lake E r i e
as a w h o l e , phosphorus i s g e n e r a l l y t h e l i m i t i n g growth f a c t o r , and work on many o t h e r l a k e s i n N o r t h A m e r i c a and Europe
r e v e a l s t h a t the same i s t r u e f o r a l a r g e number of l a k e s i n
the w o r l d . "
( P r i n c e and B r u c e 1972).
"Phosphorus i s u s u a l l y the i n i t i a t i n g f a c t o r [ i n e u t r o p h i c a t i o n ] w h i l e other substances. . .together w i t h organic
growth f a c t o r s , p r o b a b l y a l s o p l a y a p a r t . "
(Vollenweider
1968).
4
3.
The Need F o r A P r e d i c t i v e Model
As V o l l e n w e i d e r
(1969) has n o t e d , n u t r i e n t budgets o f l a k e s
a r e a f u n d a m e n t a l p r o b l e m o f t h e o r e t i c a l and a p p l i e d l i m n o l o g y .
known about t h e g e n e r a l
the supply
t h e o r y o f n u t r i e n t c y c l i n g i n l a k e s ; t h a t i s , about
o f n u t r i e n t s , l o s s e s t h r o u g h v a r i o u s mechanisms, and
t i o n o v e r time.
Much i s
concentra-
Much i s a l s o known about t h e q u a l i t a t i v e r e l a t i o n s h i p be-
tween n u t r i e n t c o n c e n t r a t i o n
and b i o l o g i c a l production
i n lakes.
Quanti-
t a t i v e l y , much l e s s i s known about n u t r i e n t b u d g e t s , as v e r y few d e t a i l e d
budget s t u d i e s have been p e r f o r m e d on l a k e s .
phorus budget i s no
In t h i s regard,
t h e phos-
exception.
The c o n c e n t r a t i o n
four basic f a c t o r s :
l a k e from a l l sources;
o f phosphorus i n a l a k e i s d e t e r m i n e d by
(a) t h e r a t e o f i n p u t o f t o t a l phosphorus t o t h e
(b) t h e s e d i m e n t a t i o n
o f phosphorus, or the r a t e
a t w h i c h e x c h a n g i n g phosphorus i s l o s t f r o m f u r t h e r m e t a b o l i s m by i n c o r p o r a t i o n i n t o i n o r g a n i c i n s o l u b l e p r e c i p i t a t e s and undecayed
organic
m a t t e r i n t h e l a k e b o t t o m (Hayes and P h i l l i p s 1958); (c) t h e morphometric
p r o p e r t i e s o f t h e l a k e , w h i c h i n f l u e n c e t h e r m a l s t r a t i f i c a t i o n and r e l a t i v e s i z e of the photosynthetic
l a y e r (Hayes and P h i l l i p s 1958); and (d)
h y d r o l o g i c i n p u t w h i c h d e t e r m i n e s how q u i c k l y phosphorus i s d i l u t e d and
flushed through the l a k e .
Because o f t h e i m p o r t a n c e o f phosphorus i n t h e e u t r o p h i c a t i o n
process,
i t i s o f g r e a t p r a c t i c a l i m p o r t a n c e t o be a b l e t o p r e d i c t from
known l o a d i n g (phosphorus i n p u t ) t h e f o l l o w i n g :
(1) t h e c o n c e n t r a t i o n o f
phosphorus i n t h e e p i l i m n i o n and h y p o l i m n i o n ; (2) t h e amount o f phosphorus
l o s t t o t h e s e d i m e n t s ; (3) t h e amount o f phosphorus r e g e n e r a t e d by t h e
5
sediments to the water;
flow-through;
of reducing
(4) the amount of phosphorus l o s t by
(5) the. amount of r e s u l t i n g a l g a l growth;
(or i n c r e a s i n g ) the phosphorus s u p p l y .
e n a b l e p r e d i c t i o n o f the time n e c e s s a r y
levels.
Q u a n t i f i c a t i o n o f these
(6)
hydrologic
the
effects
T h i s i n f o r m a t i o n would
to r e a c h s p e c i f i e d
eutrophication
f a c t o r s f o r p r e d i c t i o n purposes i s p o s s i b l e
through the f o r m u l a t i o n o f a s i m u l a t i o n model o f the phosphorus-phytoplankton system.
There i s a need f o r a model which accounts f o r the dynamic
stratification
regime o f temperate l a k e s and which d e t a i l s phosphorus move-
ment between e p i l i m n i o n , h y p o l i m n i o n and
be
initially
developed by e i t h e r of two
model f o r a s t r a t i f i e d
cycle i n a s p e c i f i c
Is
the one
l a k e ; or
b a s i c approaches:
(a) a
lake.
after
Skaha Lake, one
The
second apporach
particularly
o f a c h a i n o f l a k e s i n the Okanagan B a s i n
the l a k e has
i n the form o f a l g a l blooms.
been s e r i o u s l y degraded
f i v e - y e a r study was
of
of t h i s type
(Figure
shown s i g n s o f i n c r e a s i n g e u t r o p h i c a t i o n ,
During
(Coulthard
of the i n c r e a s i n g r e c r e a t i o n a l , a g r i c u l t u r a l and
an e x h a u s t i v e
temperate
verification.
w i t h i n the l a k e has been l e s s than a meter, and
the l a k e has
the model w i t h
G e n e r a l i z a t i o n o f the model to o t h e r
B r i t i s h Columbia, i s i d e a l l y s u i t e d f o r a study
In recent years,
general
(b) a s p e c i f i c model d e t a i l i n g the phosphorus
chosen i n t h i s study because o f the need to v e r i f y
lakes i s considered
1).
Such a model c o u l d
l a k e w i t h e u t r o p h i c a t i o n problems.
d a t a from a s p e c i f i c
southern
sediments.
these blooms
visibility
the r e c r e a t i o n a l v a l u e
and
Stein
1967).
i n d u s t r i a l use
r e c e n t l y completed
of
Because
o f the
area,
to d e t e r m i n e , i n p a r t ,
Figure 1. Location and watershed boundary of the Okanag
Basin. Drainage divides between lake basins shown by
dotted l i n e s .
7
present l e v e l s
and causes o f e u t r o p h i c a t i o n i n the Okanagan l a k e s
B r i t i s h Columbia Okanagan Agreement
1969).
p l a c e d on Skaha Lake, and p a r t i c u l a r l y
(Canada-
Major l i m n o l o g i c a l emphasis
complete d a t a was
collected
was
on the
m i x i n g regime, phosphorus l o a d i n g , s e d i m e n t a t i o n , phosphorus i n the water
mass, and a l g a l b i o m a s s .
These d a t a form the base from which
this
model i s developed and v e r i f i e d .
B.
RESEARCH OBJECTIVES
The o b j e c t i v e s o f t h i s r e s e a r c h a r e f o u r f o l d :
(1) t o d e s c r i b e
the p h y s i c a l , c h e m i c a l and b i o l o g i c a l p r o c e s s e s c o n t r o l l i n g the phosphorus
c y c l e i n Skaha Lake; (2) to f o r m u l a t e a s i m u l a t i o n model which p r e d i c t s
s e a s o n a l v a r i a t i o n s of t o t a l phosphorus i n the w a t e r mass; (3) to formul a t e a model which p r e d i c t s s e a s o n a l v a r i a t i o n s i n p h y t o p l a n k t o n
mass; (4) t o f o r m u l a t e a model which p r e d i c t s
d i s s o l v e d oxygen
bio-
depletion
r a t e s i n the h y p o l i m n i o n .
These o b j e c t i v e s a r e pursued i n t h e f o l l o w i n g s i x c h a p t e r s .
Chapter I I d e s c r i b e s t h e water q u a n t i t y and q u a l i t y problems o f t h e Okanagan B a s i n , and the l i m n o l o g y o f Skaha Lake.
Emphasis
i s p l a c e d on n u t r i e n t
l o a d i n g and b i o l o g y .
Chapter I I I d i s c u s s e s t h e r e l a t i o n s h i p between n u t r i e n t s
and
e u t r o p h i c a t i o n , and d e t a i l s the c o m p l e x i t y o f the phosphorus c y c l e i n
lakes.
M o d e l l i n g approaches are e v a l u a t e d and the mass b a l a n c e method
is described.
I n Chapter IV the fundamental i n p u t - o u t p u t e q u a t i o n s f o r
the e p i l i m n i o n and h y p o l i m n i o n o f Skaha Lake a r e p r e s e n t e d .
of each submodel
The
details
(eddy d i f f u s i o n , s e d i m e n t a t i o n , i n t e r n a l l o a d i n g , p r i m a r y
8
production, and hypolimnetic dissolved oxygen) are then discussed.
The
assumption of a strong r e l a t i o n s h i p between primary production and phosphorus sedimentation i n Skaha Lake i s stressed.
In Chapter V the results of the model are presented and v e r i f i e d with Skaha Lake data on phosphorus concentration, a l g a l biomass,
and hypolimnetic dissolved oxygen.
S e n s i t i v i t i e s of the major "forcing
functions" (phosphorus loading and hydrologic discharge) and of the physic a l - b i o l o g i c a l c o e f f i c i e n t s used i n submodels are analyzed.
Chapter VI
i s a discussion of i n t e r p r e t a t i o n s and l i m i t a t i o n s of the model; included
i s an a p p l i c a t i o n of the r e s u l t s to the management of the eutrophication
problems of Skaha Lake.
Chapter VII summarizes the major conclusions of
the study, and assesses the value of the model as a research tool and
planning a i d .
CHAPTER I I
THE OKANAGAN BASIN AND SKAHA LAKE
A.
THE OKANAGAN BASIN
1.
Water Q u a n t i t y and Q u a l i t y Problems
The Okanagan B a s i n i n B r i t i s h Columbia i s p l a g u e d by w a t e r
problems o f b o t h q u a n t i t y and q u a l i t y .
The b a s i n l i e s i n t h e r a i n s h a -
dow o f an o r o g r a p h i c p r e c i p i t a t i o n system, r e s u l t i n g i n a n n u a l p r e c i p i t a t i o n as l o w as 25 cm a t O l i v e r ( K e l l e y and S p i l s b u r y 1 9 4 9 ) .
While the
3
2
average a n n u a l r u n o f f f o r B r i t i s h Columbia i s 118 m /hr/km , t h e n e t i n 3
2
f l o w t o Okanagan Lake i s 9.8 m /hr/km
(Marr 1970).
Even w i t h t h e l a r g e
s t o r a g e c a p a c i t y o f t h e l a k e s , a w a t e r s h o r t a g e i n t h e v a l l e y h a s a 10
p e r c e n t chance o f o c c u r r e n c e i n any y e a r because o f i r r i g a t i o n
ments f o r 25,000 h e c t a r e s o f l a n d (Marr 1 9 7 0 ) .
require-
Great f l u c t u a t i o n s i n run-
o f f from one y e a r t o t h e n e x t have c r e a t e d a need f o r f l o o d c o n t r o l dams
on t h e r i v e r s c o n n e c t i n g t h e l a k e s , e n a b l i n g c a r e f u l l y c o n t r o l l e d w a t e r
l e v e l s t o be m a i n t a i n e d .
The w a t e r q u a l i t y problems f o c u s m a i n l y around s i g n s o f i n c r e a s i n g e u t r o p h i c a t i o n , p a r t i c u l a r l y a l g a l blooms.
Skaha Lake has i n
r e c e n t y e a r s (1968-71) e x h i b i t e d two blooms.per y e a r —
a minor one i n
l a t e s p r i n g and a more s e r i o u s one i n l a t e summer o r autumn.
Although
Osoyoos Lake has n o t e x h i b i t e d a l g a l blooms, s i g n s o f i n c r e a s i n g
p h i c a t i o n a r e evident (Booth 1969).
eutro-
Okanagan L a k e , much l o n g e r and
deeper t h a n e i t h e r Skaha o r Osoyoos L a k e s , s t i l l appears t o be i n an
oligotrophic
state.
9
10
2.
Geographical
Setting
The Okanagan B a s i n o c c u p i e s a 8100
P l a t e a u o f s o u t h e r n B r i t i s h Columbia
km
2
(Figure 1).
a r e a i n the
The
Interior
central valley
w i t h i n the b a s i n i s a U-shaped t r o u g h w i t h a c h a i n of narrow, n o r t h south trending g l a c i a l l a k e s —
ure 1).
Okanagan, Skaha, Vaseux and
Osoyoos
(Fig-
The v a l l e y bottom v a r i e s i n w i d t h from 2 to 13 km and r i s e s
from
a v a l l e y bottom e l e v a t i o n o f 275 m t o 2440 m i n the s u r r o u n d i n g mountains
(Marr 1970).
3.
Geological History
A c c o r d i n g t o S t . John (1973), t h e Okanagan V a l l e y i s a
t u r a l t r e n c h o v e r l y i n g a system
o f l i n k e d f a u l t s which s e p a r a t e
of l a t e P a l e o z o i c o r e a r l y M e s o z o i c
age.
strucbedrock
The e a s t s i d e o f Skaha Lake
i s u n d e r l a i n by Monashee metamorphic r o c k s and
later intrusives,
while
bedrock on the west s i d e c o n s i s t s o f a n d e s i t e and t r a c h y t e f l o w s and
agglomerates
o f Eocene o r O l i g o c e n e age.
c o n t a c t between t h e s e bedrock
The
fault
t r a c e forming
the
t y p e s runs a l o n g the course o f McLean
Creek, an e a s t e r n t r i b u t a r y t o Skaha Lake ( S t . John 1973).
The bedrock base of the Okanagan t r e n c h i s o v e r l a i n by
i d a t e d sediments
unconsol-
p r i m a r i l y of g l a c i a l o r i g i n , which r e a c h a t h i c k n e s s o f
600 m i n the m i d d l e o f Okanagan Lake ( S t . John 1973).
i n t h i c k n e s s under Skaha Lake from about
The
sediments
370 m n o r t h o f Kaleden
vary
( F i g u r e 2)
to l e s s than 30 m a t the narrow p o i n t s e p a r a t i n g the l a k e ' s n o r t h and
s o u t h b a s i n s . A c c o r d i n g t o S t . John,
cene (one m i l l i o n y e a r s ago
i t i s p r o b a b l e t h a t d u r i n g the P l e i s t o -
to the p r e s e n t ) the v a l l e y was
a sedimentation
t r a p f o r m o r r a i n a l m a t e r i a l , g l a c i a l outwash, and l a c u s t r i n e and
sediments.
fluvial
inflow
F i g u r e 2. Bathymetry o f Skaha Lake; c o n t o u r i n t e r v a l 25 f t
(from S t . John 1973). C i r c l e d numbers i n d i c a t e p e r i p h y t o n s t a t i o n s .
12
The g l a c i e r s began to recede somewhat before 10,000 years
and Fulton (cited i n St. John 1973)
advanced by 9750 B.P.
ago,
reports the recession to be well
(before present).
By 8900 B.P.
a l l of the i c e had
melted and the g l a c i a l lakes had been drained to the l e v e l of the e x i s t i n g
lakes.
The clay and s i l t g l a c i o l a c u s t r i n e c l i f f s bordering southern Okana-
gan and Skaha Lakes were probably formed during the period of g l a c i a l recession when g l a c i a l downwasting processes were shaping the basin's present
topography (St. John 1973).
St. John estimates that a very large per-
centage of the sediments are of g l a c i a l o r i g i n , while only a few tens of
meters of sediment can be attributed to sedimentation
stem lakes.
from the modem main-
The mass wastage that has occurred from the c l i f f s bordering
Skaha Lake i s v i s i b l e as l a n d s l i d e scars, and deposits on the lake bottom
from these landslides are present
4.
(St. John 1973).
Hydrology
The annual runoff into Okanagan Lake has been estimated to
vary between 0.099 km
3
i n 1929
to 0.918
km
3
i n 1948
(with a mean value
3
of
0.450 km
(Marr 1970).
To emphasize the a r i d condition of the area,
2
Marr has noted that the average net inflow from the 6060 km
watershed amounts to a y i e l d of only 8.26
cm.
Okanagan Lake
The great v a r i a t i o n i n nat-
u r a l runoff has prompted the construction of dams at or below the o u t l e t s
of a l l the mainstem lakes to c o n t r o l flow-through
have a controlled l e v e l f l u c t u a t i o n of 1.3
for
rates.
The lakes
m or l e s s (Marr 1970).
now
Except
6.4 km of natural channel below Vaseux Lake, s t i l l used as a spawning
area f o r sockeye salmon, a l l of the streambanks connecting the lakes have
been a r t i f i c i a l l y
channelized.
13
The contribution of water from the higher elevations of the
basin i s e s s e n t i a l to the water supply of the lakes.
Marr (1970) has
estimated that no runoff i s contributed from areas up to 900 m i n e l e vation, 25 cm i s contributed from areas at 1200 m, and 60 cm comes from
areas at 1800 m.
3
The average annual inflow to Skaha Lake i s 0.474 km , r e s u l t i n g
i n a t h e o r e t i c a l hydrologic turnover of 0.89/year (inflow/lake volume =
0.474/0.54).
Therefore, the t h e o r e t i c a l retention time of water i n the
lake (the r e c i p r o c a l of the turnover) i s 1.1 years.
Okanagan Lake has a
greater retention time (nearly 60 years) because of i t s much greater v o l ume.
Osoyoos Lake has a retention time of about 0.4 years.
5.
Water Use
Marr reports that in.1966 i r r i g a t i o n accounted f o r the use of
3
0.178 km
of water.
Three-quarters of the i r r i g a t i o n water comes from
over 100 storage reservoirs located i n the uplands of the watershed (Russell
and McNeil 1974, Marr 1970).
Marr (1970) indicates that the p o s s i b i l i t y of
further upland storage i s l i m i t e d and the source of large future demands
must come i n the form of pumping from the mainstem lakes.
This i s one
important economic reason f o r concern about the water quality of the
lakes.
3
Domestic use of water accounts f o r about 0.01 km , or l e s s
than 10 per cent of a g r i c u l t u r a l consumption (Marr 1970).
6. C u l t u r a l Development and Associated Phosphorus Loading
The Okanagan V a l l e y i s one of the fastest growing regions i n
14
B r i t i s h Columbia.
From 1961
to 1971
the population increased from 75,000
to 113,000, an increase of 51 per cent (the province as a whole increased
34 per cent) (Okanagan Study Commission 1971).
estimated
By 1980
to reach 160,000, a 41 per cent increase from
Using estimates from Vollenweider
(1973) have calculated that about 1.7
•now enters the lake system.
the population i s
1971.
(1968), Patalas and
kg/capita/year
Salki
of t o t a l phosphorus
Unless measures are taken to remove phos-
phorus from water before i t enters the lakes, the loading can be expected
to increase approximately
proportionately to the population growth.
The
e f f e c t on the water q u a l i t y of the lakes would, by most r a t i o n a l estimates,
be extremely undesirable.
Patalas and S a l k i (1973) estimate that 88 to 90
per cent of the t o t a l phosphorus load to Skaha Lake i s associated with c u l t u r a l sources
(municipal sewage, a g r i c u l t u r e and i n d u s t r y ) .
If no measures were taken to remove phosphorus from effluent
be-
fore i t reached Skaha Lake, Patalas and S a l k i (1973) estimate that loading
2
w i l l nearly double between now
year).
and 1990
(from 2.3 g/m
2
/year to 4.0 g/m
/
However, i f 80 per cent of the c u l t u r a l or c o n t r o l l a b l e phosphorus
load were removed, the 1990
loading (even with the projected population
growth) would decrease to about 1.0 g/m
/year, or be cut by more than h a l f .
Patalas and S a l k i speculate that i f s i m i l a r phosphorus removal took place
throughout the basin, the trend of trophic changes i n Okanagan Lake could
be reversed from high oligotrophy or low mesotrophy to the middle range
of oligotrophy, and Skaha and Osoyoos Lakes would change from high to moderate eutrophy.
15
B.
SKAHA LAKE
1.
Physical Limnology
(a) The Lake Basin.
S i g n i f i c a n t physical c h a r a c t e r i s t i c s of the
lake basin are shown i n Table 1.
TABLE I
PHYSICAL CHARACTERISTICS OF SKAHA LAKE*
Volume
.558 km"
3
2
Surface Area
20.1 km
Mean Depth
28 m
Maximum Depth
57 m
Maximum Length
11.9 km
Maximum Width
2.4 km
Perimeter
29.5 km
Maximum Surface Temperature
25°C
Warming Rate of Hypolimnion
.37°C/month
Maximum Transparency (Secchi d i s k ) , 1939
12 m
Maximum Transparency, 1971
Data from Blanton and Ng 1972
7m
16
A hypometric curve showing the r e l a t i o n s h i p between area and
depth i s shown i n Figure 3.
The bathymetry of the lake basin (Figure 2) shows that the lake
i s divided into two basins separated by a bedrock s i l l at a depth of about
24 m (St. John 1973).
A well-defined bench at a depth of 15 m e x i s t s
near the mouth of McLean Creek.
The f a c t that the southern basin i s
smaller i n surface area than the northern one
and much shallower
(3.0 km 2 compared to 17.1 km 2 )
(mean depth of 15 m compared to 28 m) has important
p l i c a t i o n s for the r e l a t i v e b i o l o g i c a l p r o d u c t i v i t y of each basin.
im-
St.
John observes that the dual basin morphology provides a terrigenous s e d i ment trap s i t u a t i o n , with the northern basin accumulating
more terrigenous
material and the southern one more organic carbon. The phosphorus c y c l i n g
model described i n Chapter IV considers each basin separately.
(b) The Lake Sediments.
Core samples taken from the sediments i n -
dicate that t y p i c a l deep muds consist of 58.5
clay and 0.5 per cent sand (St. John 1973).
per cent s i l t , 41 per cent
Some of the surface sediments
contain a predominance of sand, i n d i c a t i n g recent l a n d s l i d e s from lakeside
cliffs.
St. John reports an average sedimentation
with an average annual net accumulation
rate of about 0.21
cm/year,
i n the past 100 years of 1.5 x 10^ kg
of m a t e r i a l .
2.
Chemical Limnology
(a) Water Chemistry.
Table II shows representative v a r i a t i o n s i n
chemical c h a r a c t e r i s t i c s during the years 1968-71.
It i s important
that although hypolimnetic dissolved oxygen values l e s s than 2 mg/1
to note
have been
recorded, the hypolimnion of Skaha Lake has not, at least during the four
years for which data are a v a i l a b l e , become anaerobic.
Figure 3. Hypsometric curves of the north and south basins
of Skaha Lake showing the relationship between area and depth.
18
TABLE I I
CHEMICAL CHARACTERISTICS, SKAHA LAKE*
**
Hypolimnetic
D i s s o l v e d Oxygen
<2 mg/1 t o s a t u r a t i o n
Hypolimnetic
Oxygen D e f i c i t
0.076 mg/cm /day 0
2
pH
8.1 t o 9.2
T o t a l Residue
102
Bicarbonate
38 to 115 mg/1
Silicate
0.4 t o 6.4 mg/1
2
t o 159 mg/1
Orthophosphate,
epilimnion
<0.002 t o 0.095 mg/1 (P)
Orthophosphate,
hypolimnion
0.006 t o 0.085 mg/1 (P)
Orthophosphate,
S p r i n g M i x i n g 1971
0.015 mg/1 (P)
T o t a l Phosphorus,
Epilimnion
0.007 t o 0.124 mg/1 (P)
T o t a l Phosphorus,
Hypolimnion
0.008 t o 0.104 mg/1 (P)
T o t a l Phosphorus,
Spring Mixing
1971
0.060 mg/1 (P)
Nitrate,
Epilimnion
<0.01 t o 0.02 mg/1
Nitrate,
Hypolimnion
<0.01 to 0.17 mg/1
Total Kjeldahl nitrogen,
Epilimnion
Total Kjeldahl nitrogen,
Hypolimnion
<0.01 t o 0.75 mg/1
0.08 t o 0.69 mg/1
*
Data from S t e i n and C o u l t h a r d 1971 , P a t a l a s and S a l k i 1973,
and W i l l i a m s 1972.
Seasonal v a r i a t i o n s i n d i s s o l v e d oxygen and t o t a l phosphorus
w i l l be d i s c u s s e d i n d e t a i l i n Chapter V.
19
(b) Sediment Chemistry.
S t . John (1973) r e p o r t s t h a t deep
sedi-
ments from t h e south b a s i n c o n t a i n 1.69 times g r e a t e r c o n c e n t r a t i o n s o f
o r g a n i c c a r b o n than deep sediments f rom
the south b a s i n i s p r o b a b l y
the north basin.
due t o two f a c t o r s :
The i n c r e a s e i n
(1) " d i l u t i o n " o f o r g a n i c
m a t t e r i n the n o r t h b a s i n by more t e r r i g e n o u s m a t e r i a l , and (2) g r e a t e r
production
o f o r g a n i c m a t t e r by t h e s h a l l o w e r
south b a s i n .
show a sharp i n c r e a s e i n o r g a n i c c a r b o n i n the upper f i v e
According
t o S t . John, t h i s f i v e c e n t i m e t e r s
of s e d i m e n t a t i o n ,
represents
Core p r o f i l e s
centimeters.
about 23 y e a r s
which i s about the l e n g t h o f time sewage has been d i s -
charged i n s i g n i f i c a n t q u a n t i t y i n t o t h e l a k e .
A p a t i t e , m a i n l y i n the form Ca^Q (PO^)^ ( O H ^ ,
l a r g e p a r t i n Skaha sediment c o m p o s i t i o n ,
appears t o p l a y a
b o t h s u r f i c i a l l y and a t depth.
In t h e s u r f i c i a l sediments, an average of 70 p e r cent o f the phosphorus
(by w e i g h t ) i s i n the form o f a p a t i t e ( W i l l i a m s 1973).
t i t e probably
e n t e r s t h e l a k e when r a i n s erode t h e c l i f f s s u r r o u n d i n g t h e
l a k e , and t h i s p r o c e s s would proceed w i t h o r w i t h o u t
John, p e r s o n a l
has
Most o f t h e apa-
communication).
Williams
man's i n f l u e n c e ( S t .
a l s o assumes t h a t t h e a p a t i t e
a t e r r i g e n o u s o r i g i n from t h e watershed, and does n o t form as a r e s u l t
of c h e m i c a l
precipitation within the lake.
He f u r t h e r assumes t h a t a p a t i t e
p l a y s l i t t l e o r no r o l e i n t h e phosphorus c y c l e o f t h e l a k e because o f
i t s v e r y low s o l u b i l i t y and s i g n i f i c a n c e as a n u t r i e n t source
organisms.
The f a c t t h a t a p a t i t e i s c o n c e n t r a t e d
near the s h o r e l i n e and i n -
l e t s i s further indication of terrigenous o r i g i n .
Apatite increases
depth i n the sediment column, i n d i c a t i n g c o n v e r s i o n
to a p a t i t e w i t h i n the sediment
( W i l l i a m s 1973).
f o r aquatic
from o r g a n i c
William's
with
phosphorus
conclusion i s
20
supported by results showing that the increase i n apatite with depth
i s matched by an approximately equal decline i n organic phosphorus.
Adsorbed phosphorus
(inorganic phosphate ions associated
with sediment components having a high capacity to take up orthophosphate
from s o l u t i o n by exchange with hydroxyl groups)
average of 18 per cent of the phosphorus
sediments (Williams 1973).
constitutes an
(by weight) i n the s u r f i c i a l
Williams concludes that i t i s l i k e l y
that
phosphorus adsorbed onto sediments remains e s s e n t i a l l y unaltered, and
i s not involved i n conversion to apatite or regeneration to overlying
waters.
The concentration of adsorbed phosphorus increases with
increasing water depth and distance from shore.
A decrease i n adsorbed
phosphorus concentration with depth i n the sediment i s probably due
to loading increases i n recent years (Williams 1973).
Organic phosphorus makes up an average of 12 per cent of
the
phosphorus
(by weight) i n the s u r f i c i a l sediments (Williams 1973).
Williams concludes that approximately 20 per cent of the sedimented
organic phosphorus i s converted into orthophosphate or soluble organic
phosphorus and returns to the overlying water;
this amount, however,
i s small compared with loading of phosphorus from external sources.
Within the sediments further breakdown of organic phosphorus to
orthophosphate occurs, but the orthophosphate i s converted to apatite
within the sediments and does not regenerate to overlying waters
(Williams.19 73).
21
(c) Net Sedimentation Rates of Phosphorus Forms.
St. John (1973)
estimates a t o t a l net sedimentation rate of 1.15 x lo7 kg/yr.
mate
This e s t i -
i s a single one, and does not account f o r d i f f e r e n t sedimentation
rates i n d i f f e r e n t parts of the lake.
age s u r f i c i a l concentrations
Combining t h i s estimate with aver-
of apatite, sorbed phosphorus and organic
phosphorus of 635 ppm, 177 ppm and 109 ppm respectively, Williams estimates
the following annual sedimentation rates:
3.
apatite
7600 kg
sorbed phosphorus
2000 kg
organic phosphorus
1300 kg
Total
10900 kg
B i o l o g i c a l Limnology
(a) Phytoplankton and Periphyton.
Phytoplankton have been measured i n
two ways, both of which are "standing stock" measurements and do not r e f l e c t
p r o d u c t i v i t y (rate of growth). Table I I I shows a l g a l abundance during selected
months i n 1969-70 i n c e l l s / m l (Stein and Coulthard 1971), with percentages of
four a l g a l types.
The figures represent the average of samples taken from
four depths (surface to 18 m) i n the north basin.
The table shows that during 1969-70 a spring bloom (April) occurred,
dominated by diatoms and phytoflagellates; and a summer (July) bloom occurred,
dominated by blue-green algae.
Blue-green algae dominated during l a t e
summer and autumn.
These concentrations are averages of 36 s u r f i c i a l samples taken
in shallow and deep sections i n both basins of the lake.
22
TABLE I I I
ALGAL ABUNDANCE
(algal
•k
counts i n c e l l s / m l )
A p r i l 1970
T o t a l Phytoplankton
%
%
%
%
IN SKAHA LAKE, 1969-70
June 1969
3100 **
Blue-Green A l g a e
Green A l g a e
Diatoms
Phytoflagellates
2.3
4.1
40.3
42.2
J u l y 1969
Sept. :
**
76
2120
446
19.4
0
69.8
10.8
59.2
3.2
18.5
18.6
91.0
0.8
3.8
4.2
*
For greens and b l u e - g r e e n s , a c h a i n o f 12-15 c e l l s = 1 a l g a l
" c e l l " as shown i n T a b l e III.
**
a l g a l bloom
D u r i n g 1971 c h l o r o p h y l l a was m o n i t o r e d
d i c a t e p h y t o p l a n k t o n biomass.
Monthly
i n s u r f a c e waters to i n -
sampling shows the f o l l o w i n g
vari-
a t i o n i n t h e n o r t h and south b a s i n s from May t o September ( W i l l i a m s 1972),
indicated
i n T a b l e IV.
TABLE IV
PHYTOPLANKTON IN SKAHA LAKE, 1971
( v a l u e s i n ug/1 c h l o r o p h y l l d)
MAY
JUNE
JULY
AUGUST
SEPT.
LATE SEPT.
North
8
6
12
29
26
290
South
5
10
19
10
25
140
23
The
o r d e r - o f - m a g n i t u d e i n c r e a s e i n l a t e September i n d i c a t e s a
l a r g e bloom, but
the dominant s p e c i e s r e s p o n s i b l e was
t a i l e d phytoplankton
Periphyton
Table V
data
i s presented
not
determined.
i n Chapter V.
( a t t a c h e d a l g a e ) abundance d u r i n g 1971
f o r t h r e e s e c t i o n s o f the l a k e
(Stockner et al.
i s shown i n
1972a).
i s a t the extreme n o r t h and near the Okanagan R i v e r i n f l o w .
on the e a s t e r n shore about midway i n the n o r t h b a s i n , and
the south b a s i n near the o u t f l o w
De-
Station 1
Station 2 i s
station 3 is in
(Figure 2).
TABLE V
PERIPHYTON IN SKAHA LAKE,
( v a l u e s i n ug/1
1971
c h l o r o p h y l l a)
APRIL
MAY
JUNE
JULY
AUGUST
SEPTEMBER
0.5
1.0
1.5
38.5
49.5
5.0
Station 2
0.5
1.5
1.0
1.5
1.0
Station 3
0.1
0.5
1.7
2.0
1.5
Station 1
While s t a t i o n s 2 and
3 show low p e r i p h y t o n growth, s t a t i o n 1
c a t e s v e r y pronounced growth d u r i n g J u l y and August.
hypothesize
t h a t t h e low biomass a t s t a t i o n s 2 and
u t i l i z a t i o n o f n u t r i e n t s by p h y t o p l a n k t o n
biomass a t s t a t i o n 1 may
3 may
populations.
et al.
(1972a)
be because o f
High
i n d i c a t e t h a t p e r i p h y t o n p o p u l a t i o n s use a v a i l a b l e
n u t r i e n t s from the Okanagan R i v e r b e f o r e
plankton.
Stockner
indi-
they can be taken up by the
phyto-
24
(b) Macrophytes.
Macrophytes grow i n the l i t t o r a l , or shallow
shoreline region of Skaha Lake.
The l i t t o r a l can be defined as the zone
extending from the shoreline to a depth where v i s i b l e plant growth occurs,
or the area above the compensation depth
al.
1972b).
for photosynthesis (Stockner et
I
The l i t t o r a l zone comprises about 3.2 km
cent of the surface area i n Skaha Lake.
2
or
17 per
Submergent macrophytes predomi-
nate i n the north end, whereas extensive beds of both emergent and submergent vegetation grow on the l i t t o r a l bench of the east and west shorel i n e s (Stockner et al. 1972b).
F l o a t i n g leafed plants and emergent vege-
t a t i o n occurs i n the south end of the lake.
Macrophytes and associated epiphytic periphyton have the a b i l i t y
to trap considerable quantities of nutrients before they can be u t i l i z e d
by phytoplankton (Stockner et al. 1972b).
Because Skaha Lake contains s i g -
n i f i c a n t l y less l i t t o r a l area than the other mainstem lakes (about 25 per
cent of the surface area of Okanagan Lake and the north basin of Osoyoos
Lake i s l i t t o r a l ) , nutrients may be more a v a i l a b l e f o r phytoplankton
growth i n Skaha (Stockner et al. 1972b).
This may be an important factor
in explaining the r e l a t i v e l y high trophic l e v e l of Skaha Lake.
(c) Zooplankton. The crustacean plankton (copepods and cladocerans)
were sampled i n 1969 by Patalas and S a l k i (1973).
Four species of copepods
and eight species of cladocerans were found, with Cyclops bicuspidatus
Diaptomus ashlandi
dominant i n a l l three lakes.
and
Relative volumes of s e t t l e d
3
net
plankton i n Okanagan, Skaha and Osoyoos Lakes were 13, 19 and 26 mm
respectively.
The average number of crustacean zooplankton i n Okanagan
2
2
Lake was 188 individuals/cm , in' Skaha Lake 238 individuals/cm and i n
2
Osoyoos Lake 161 individuals/cm .
2
/cm
25
(d) F i s h .
of salmonid
in 1971
According to Northcote et al.
species to the f i s h stock of Skaha Lake was
than 1948
(4.6 per cent from 14.8
whitefish were much lower i n 1971
1948,
(1972), the contribution
than i n 1948;
only f i v e were netted in 1971.
17 were c o l l e c t e d i n 1971.
per cent).
considerably lower
Numbers of mountain
whereas 60 were netted i n
No carp were netted i n 1948, whereas
The apparent s h i f t i n species composition
from
salmonid and coregonine species to coarse f i s h i s an i n d i c a t i o n of increasing eutrophy (Larkin and Northcote 1969).
The low average age of salmonids i n Skaha, Vaseux
may
and Wood Lakes
be i n d i c a t i v e of advanced eutrophication (Northcote et al. 1972).
Lar-
kin and Northcote (1969) c i t e research i n Europe showing that the average
age of coregonids gradually decreased
as eutrophication increased.
Four
f i s h a t t r i b u t e s used as eutrophication indices f o r the mainstem Okanagan
lakes
( r e l a t i v e abundance, average length, weight-length
lead Northcote et al.
and growth rate)
(1972) to conclude that Skaha Lake i s the most eutro-
phic, followed by Osoyoos and Vaseux.
4.
Trophic State
The word "trophic" has been defined as "the rate and ways of
o
supplying a lake with organic matter" (Aberg and Rodhe 1942).
The
adjec-
t i v e s o l i g o t r o p h i c , mesotrophic and eutrophic were used by Naumann (1932)
and Thienemann (1931) to describe increasing l e v e l s of organic production
i n lakes.
Figure 4 shows the trophic state (as described by annual phos-
phorus loading) of the Okanagan lakes compared with other lakes i n the
world
(from Vollenweider
1968,
Patalas and S a l k i 1973).
Skaha Lake f a l l s
family of f i s h containing the whitefish and cisco (when these
are not included i n the Salmonidae)
-
10.o-i
Eutrophic
Lakes
<
^ Lake Norrviken
(Sweden)
O
OSOYOOS
SKAHA
U.
o
*3a.
c-
<
o
<
Z>
z
z
<
•
I.OH
Greifensee —
(Switzerland )
Pf dff ikersee — •
( Switzerland)
..
• Moses ,Lake
Mesotrophic
Lakes
(I)
Baldeggersee (Switzerland)
O Zurichsee
( Switzerland)
Lake Washington
(U.S.A.)
Lake Ontario
( U.S.A.)
^(Canada)* Lake Geneva
Lake Malare
(France'^witzerland )
.(Sweden)
Lake MendotaQ
Hallwillersee
Lake Constance
( U.S.A.)
(Switzerland)
(Austria, Germany, Switzerland)
Lake F u r e s r f ^ ' "
(Denmark )||JJ Lake Annecy,
• . . r T f l l l ! ^ t r a n c e -'
,Tiirlersee
|( Switzerland )
L
a
(
k
C
e
a
E
n
o
d
r
i
a
e
)
1
yOligotrophic
Lakes
11
50
100
500
MEAN D E P T H ( m )
Figure 4. Eutrophication of lakes i n the Okanagan Basin compared to other lakes
i n Europe and North America (Patalas and Salki 1973). C r i t e r i a of annual phosphorus loading and mean depth from Vollenweider (1968, 1969) . Open c i r c l e s indicate
loading estimates from Haughton et a l . 1974; black c i r c l e s indicate loading c a l culated by Patalas and Salki (1973) according to Vollenweider (1968) c r i t e r i a ;
squares indicate 1990 loading estimates with no phosphorus removal; triangles
indicate 1990 loading with 80% removal of municipal phosphorus.
%
1
l
27
w e l l w i t h i n t h e c l a s s i f i c a t i o n o f a e u t r o p h i c l a k e f o r the f o l l o w i n g r e a sons :
1. The t o t a l phosphorus c o n c e n t r a t i o n (at o v e r t u r n ) has
been (1970) g r e a t e r than 0.03 mg/1 ( c r i t e r i a from V o l l e n w e i d e r
1968).
2
2.
Phosphorus l o a d i n g i s g r e a t e r t h a n 0.5 g/m / y e a r ,
w h i c h i s c o n s i d e r e d t o be i n t h e "dangerous" l o a d i n g c a t e g o r y
f o r a l a k e of Skaha's mean depth by V o l l e n w e i d e r (1968).
3.
The h y g o l i m n e t i c oxygen d e p l e t i o n r a t e i s g r e a t e r
t h a n 0.05 mg/cm /day ( c r i t e r i a from H u t c h i n s o n 1957).
4.
The minimum t r a n s p a r e n c y i s l e s s t h a n 2 m
f r o m Beeton 1 9 6 5 ) .
(criteria
5.
Salmonid f i s h s p e c i e s have d e c r e a s e d i n r e l a t i v e
abundance s i n c e 1948 and have a low a v e r a g e age ( c r i t e r i a
f r o m L a r k i n and N o r t h c o t e 1969).
6.
C h l o r o p h y l l a v a l u e s i n d i c a t i n g p h y t o p l a n k t o n biomass
have been g r e a t e r t h a n a s e a s o n a l range o f 5 - 140 mg/m
(crit e r i a f r o m Sakamoto, c i t e d i n V o l l e n w e i d e r 1968).
7. Dominance of b l u e - g r e e n a l g a e and d i a t o m s i s e v i d e n t
d u r i n g much o f t h e growing s e a s o n ( c r i t e r i a f r o m Sawyer 1973).
The
c o n c l u s i o n s of
S t e i n and C o u l t h a r d (1971), S t o c k n e r
(1972),
and P a t a l a s and S a l k i (1971) f u r t h e r support t h e c l a s s i f i c a t i o n o f Skaha
L a k e as m o d e r a t e l y
5.
eutrophic.
Paleolimnology
According to Stockner
(1972),
c o r e s t a k e n i n the sediments of
Skaha Lake i n d i c a t e g e n e r a l l y o l i g o t r o p h i c c o n d i t i o n s p r i o r t o 1940.
The
most s i g n i f i c a n t change i n d i a t o m assemblages has o c c u r r e d i n t h e l a s t
25
y e a r s ( t h e u p p e r 7-8 cm of s e d i m e n t ) , w i t h diatoms i n d i c a t i v e o f e u t r o p h i c
c o n d i t i o n s showing marked i n c r e a s e s i n r e l a t i v e abundance.
cm
In t h e upper 8
of sediment t h e r e i s a s i g n i f i c a n t i n c r e a s e i n t h e d i a t o m
crotonensis
Fragilaria
( i n d i c a t i v e of e n r i c h e d c o n d i t i o n s ) and a c o r r e s p o n d i n g
decrease
28
in the diatoms C y c l o t e l l a o c e l l a t a and Melosira
oligotrophic
conditions).
Stockner a t t r i b u t e s
italica
( i n d i c a t i v e of
t h i s recent change i n
dominant diatom assemblages to sewage enrichment, mainly from the
Penticton sewage treatment plant.
Stockner notes that in Lake Washington
(Seattle) the peak abundance of F r a g i l a r i a cvotonensis
the f i r s t occurrence of blue-green a l g a l blooms.
corresponded with
CHAPTER I I I
PHOSPHORUS CYCLING IN LAKES AND
A.
EUTROPHICATION AND
1.
The
"Law
THE
MODELLING APPROACH
LIMITING NUTRIENT CONCEPT
o f t h e Minimum"
L i e b i g ' s "law o f the minimum" ( f i r s t s t a t e d by J u s t u s
1840)
Liebig in
e x p r e s s e s the i d e a t h a t the growth of a p l a n t i s dependent on
amount o f e s s e n t i a l n u t r i e n t p r e s e n t e d t o i t i n minimum q u a n t i t y .
e v e r , work s i n c e L i e b i g ' s t i m e has
shown t h a t two
s a t i s f i e d bef ore t h e p r i n c i p l e can be a p p l i e d
The
conditions
the
How-
should
be
(Odum 1 9 7 1 ) .
f i r s t c o n d i t i o n i s t h a t the "law"
i s o n l y a p p l i c a b l e under
s t e a d y s t a t e c o n d i t i o n s when n u t r i e n t i n f l o w e q u a l s n u t r i e n t
outflow.
Odum (1971) o b s e r v e s t h a t c u l t u r a l e u t r o p h i c a t i o n u s u a l l y produces a v e r y
"unsteady s t a t e " i n w h i c h p r o d u c t i o n
die-offs.
may
R e l e a s e of d i s s o l v e d n u t r i e n t s upon d e c o m p o s i t i o n o f the
i n i t i a t e a n o t h e r bloom.
most l a k e s e x h i b i t a n u t r i e n t g a i n o v e r t i m e (Sawyer
(Vallentyne
1970;
the
phosphorus, n i t r o g e n , and
be o f o n l y academic i n t e r e s t .
element i n c u l -
A c c o r d i n g t o Odum
n o t be r e l e v a n t because c a r b o n d i o x i d e ,
o t h e r elements may
29
"carbon-
K u e n z e l 1969), w h i c h a t t e m p t s
t o d e c i d e w h i c h n u t r i e n t , c a r b o n o r p h o s p h o r u s , i s t h e key
(1972), t h e " e i t h e r / o r " argument may
nutrients,
1966).
I n v i e w o f t h i s i n t e r p r e t a t i o n of L i e b i g ' s law,
t u r a l e u t r o p h i c a t i o n , may
algae
i n p u t o f n u t r i e n t s seldom e q u a l s o u t -
Because l a k e s a c t as n a t u r a l t r a p s f o r b o t h sediments and
phosphorus c o n t r o v e r s y "
and
The n u t r i e n t budget of a l a k e i s seldom, i f
ever, i n a steady s t a t e c o n d i t i o n —
put.
o s c i l l a t e s between a l g a l blooms
r a p i d l y replace
each o t h e r
as
30
l i m i t i n g factors during the o s c i l l a t i o n .
For example, Goldman (1968)
found potassium, s u l f u r , and molybdenum to be most l i m i t i n g to growth
in Castle Lake, C a l i f o r n i a .
The second constraint which should be applied to Liebig's law
i s that of "factor i n t e r a c t i o n . " The a v a i l a b i l i t y of a substance other
than the minimum one may
(Odum 1971).
modify the rate of u t i l i z a t i o n of the minimum one
Rodhe (1948) found that Asterionella
in a
phosphorus-limiting
3
culture medium showed no growth with an addition of 10 mg P/m
phosphorus-limiting
, whereas i n
Lake Erken water the algae grew s i g n i f i c a n t l y with the
addition of only one mg P/m
(cited i n Hutchinson 1957).
Hutchinson specu-
lates that some material, possibly a peptide Influencing the rate with
which phosphorus i s assimilated, i s lacking i n the culture media but i s
present
i n the lake water.
A complicating aspect of the concept i s that d i f f e r e n t phyto-
plankton populations
have d i f f e r e n t nutrient requirements.
maximum growth of Botryococcus
braunii
of 0.089 mg/1,
palea
while Nitzschia
For example,
occurs at a phosphorus concentration
grows f a s t e s t at 0.018
mg/1
(Odum 1971).
Green f l a g e l l a t e s grow w e l l when nitrogen i s i n the form of urea, u r i c a c i d ,
and ammonia, while the diatom Nitschia
requires inorganic n i t r a t e for maximum
growth (Odum 1971).
2.
Relative Importance of Carbon, Nitrogen and Phosphorus
(a) Carbon.
Carbon has several natural sources:
epilimnion waters
are u s u a l l y saturated with carbon dioxide from the atmosphere, and
ates come from erosion material ubiquitous
(Prince and Bruce 1972).
bicarbon-
i n v i r t u a l l y a l l drainage basins
In most lakes these natural sources alone are
cient to support the observed biomass.
suffi-
31
In a study of growth rates of Chlorella,
with respect to carbon a v a i l a b i l i t y , Morton et al.
Microcystis
t
and Anabaena
(1972) conclude that
" i t i s very d i f f i c u l t to control growth by carbon dioxide c o n t r o l i n systems open to the atmosphere."
They report that the atmosphere i s an ade-
quate source of carbon dioxide (even i n the "absence of wind mixing) f o r
depths to at l e a s t 1.7 m, permitting substantial a l g a l production.
Morton
et al. further report that n a t u r a l l y present bicarbonate can be u t i l i z e d
by algae as a source of carbon, and can provide enough carbon f o r large
a l g a l blooms.
Mass balance carbon budget r e s u l t s from Lake E r i e indicate that
the carbon supply from natural sources i s at l e a s t 25 times as much as
the carbon from c u l t u r a l sources (Prince and Bruce 1972).
I t i s concluded
that the carbon from sewage would be completely i n s u f f i c i e n t to account
for the observed biomass In Lake E r i e .
(b) Nitrogen.
Nitrogen enters lakes from a v a r i e t y of n a t u r a l and
c u l t u r a l sources, and has been shown i n a number of cases to be one of the
important l i m i t i n g nutrients.
If s u f f i c i e n t phosphorus i s i n the water at
the time of spring overturn before growth begins, i t has been shown that
nitrogen can become a l i m i t i n g f a c t o r l a t e r i n the summer (Prince and Bruce
1972).
Based on a study of 17 lakes i n Wisconsin, Sawyer (1967) concludes
that at l e a s t 0.3 mg/1
inorganic nitrogen plus at l e a s t 0.015 mg/1
phosphate are necessary at the time of spring mixing to stimulate
inorganic
algal
blooms l a t e r i n the season.
Goldman (1968) reports that a sequence of l i m i t i n g nutrients ranged
from magnesium i n the spring to nitrogen i n the summer to phosphorus i n the
autumn In Brooks Lake, Alaska.
In Lake Tahoe iron and nitrogen limited
32
phytoplankton growth. Goldman concludes that ". . .some component of the
phytoplankton w i l l respond p o s i t i v e l y to almost any a d d i t i o n of nutrients,
but the community as a whole w i l l tend to share some common d e f i c i e n c i e s . "
Nitrogen has s p e c i a l c h a r a c t e r i s t i c s (compared to phosphorus)
which l i m i t i t s usefulness as a c o n t r o l l i n g nutrient i n c u l t u r a l eutrophication.
The fact that some nuisance blue-green species have the a b i l i t y
to f i x their own nitrogen from elemental ^
the control of t h i s source d i f f i c u l t .
blue-green alga Anabaena azolla
small Danish lakes.
Olsen (1970) reports that the
can f i x up to 95 kg N/ha i n one summer i n
B i l l a u d (1966) reports that some species of Anabaena
i n Alaskan lakes f i x nitrogen accounting
at the peak of the growing season.
dium can also f i x nitogen i n lakes.
denitrifioans)
dissolved i n lake water makes
f o r 50 per cent of the a s s i m i l a t i o n
Bacteria such as Azotobaater
and
Clostri-
D e n i t r i f y i n g bacteria (e.g., Pseudomonas
can convert n i t r a t e s to n i t r i t e s and molecular nitrogen under
anaerobic conditions, adding further d i f f i c u l t y to the q u a n t i f i c a t i o n of the
nitrogen c y c l e .
The high s o l u b i l i t y of n i t r a t e i n ground water causes leaching of
n i t r a t e into lakes.
This input comes from a g r i c u l t u r a l sources and septic
tanks i n aerobic s o i l , and i s d i f f i c u l t to quantify as well as to eliminate.
(c) Phosphorus.
Much evidence i s a v a i l a b l e showing a d i r e c t relation-r
ship between phosphorus (usually accompanied by nitrogen as well) and a l g a l
growth (Stockner 1972).
The Lake Washington case (Edmondson 1970) i s a
s t r i k i n g example of an extremely high c o r r e l a t i o n between phosphate concent r a t i o n at spring mixing and summer a l g a l biomass for 30 years of observations.
Edmondson's r e s u l t s show c l e a r l y that the c o n t r o l l i n g factor
in eliminating the lake's eutrophication problems was the reduction (by
33
about 50 per cent) of phosphorus loading.
The e f f e c t s of removal of phosphorus from sewage show that phosphorus can be the most important nutrient l i m i t i n g a l g a l growth.
reports (using Selenastmm
Maloney
as a test organism) that re-addition of phosphate
to " t e r t i a r y e f f l u e n t " (secondary e f f l u e n t with the phosphorus removed) at
l e v e l s of 0.02, 0.04 and 0.06 mg P / l resulted i n c e l l counts of 213,000/ml,
314,000/ml and 644,000/ml,respectively, a f t e r 14 days of growth (cited i n
Vallentyne 1970).
The t e r t i a r y e f f l u e n t without any added phosphorus showed
a growth of only 3,700 c e l l s / m l .
Vallentyne concludes that "there i s . . .
no question about the effectiveness of sewage treatment f o r phosphate r e moval i n terms of reducing a l g a l growth."
Phosphorus was shown to be the most important l i m i t i n g f a c t o r i n
the production of the green alga Cladophora
i n the Great Lakes (Neil and
Owen 1964).
Decreases i n carbon, nitrogen and phosphorus i n 46 Swiss lakes
during the growing season are related to i n i t i a l concentrations of the
same elements i n the spring (data published by Thomas 1970 and analyzed
by Vollenweider 1970, cited i n Prince and Bruce 1972).
Significant corre-
l a t i o n i s reported between spring concentration and subsequent per cent
decrease during the summer (as dissolved nutrients were taken up by plants)
for each nutrient, but the highest c o r r e l a t i o n i s reported f o r phosphorus
a v a i l a b i l i t y and phosphorus decrease.
Cross-correlation analyses show high
c o r r e l a t i o n between phosphorus a v a i l a b i l i t y and nitrogen and carbon decreases
during the growing season; but they indicate i n s i g n i f i c a n t or very low correl a t i o n between carbon or nitrogen a v a i l a b i l i t y and phosphorus decrease (Prince
and Bruce 1972),
Prince and Bruce conclude, on the basis of Vollenweider s
1
34
analysis, that phosphorus a v a i l a b i l i t y appears to be the dominant factor
in the metabolism of the 46 Swiss lakes
(which range from o l i g o t r o p h i c to
highly eutrophic), and that phosphorus i s the key nutrient governing the
production of algae i n these lakes.
In the lakes of the world i n which nutrients have been related
to production,
i t can be concluded that "phosphorus i s most frequently the
l i m i t i n g element, followed
i n order of decreasing
importance by nitrogen
and carbon" (Prince and Bruce 1972).
B.
THE PHOSPHORUS.CYCLE IN LAKES
Ponds and lakes are e s p e c i a l l y u s e f u l f o r the quantitative study
of nutrient c y c l i n g because the i n t e r a c t i o n s are r e l a t i v e l y self-contained
over short periods of time.
Although he exaggerated the "closed system"
properties of lakes, Forbes i n 1887
appreciated
". . .forms a l i t t l e world within i t s e l f —
the idea that a lake
a microcosm within which a l l
the elemental forces are at work and the play of l i f e goes on i n f u l l ,
but on so small a scale as to bring i t e a s i l y within the mental grasp."
The exponential
increase i n knowledge of the phosphorus cycle i n the l a s t
25 years i s summarized by Hutchinson (1969):
"It became apparent (Hutchinson 1941) that i n many
small lakes the nutrient elements were undergoing very
rapid c y c l i c a l changes, passing from the sediments into
the free water and back, i n dying plankton or l i t t o r a l
vegetation, over and over again. The easy a v a i l a b i l i t y
of a r t i f i c i a l radioisotopes a f t e r 1945 made the d e t a i l e d
i n v e s t i g a t i o n of t h i s kind of cycle possible (Hutchinson
and Bowen 1947, 1950; C o f f i n et al. 1949; Hayes et al.
1952) and culminated i n R i g l e r ' s extraordinary discovery
(1956, 1964) that the turnover time of i o n i c phosphorus
i n the epilimnion of a lake i n summer can be of the
order of 1 minute."
35
1.
Phosphorus
The
phosphorus:
" t o t a l phosphorus" d e t e r m i n a t i o n c o n s i s t s o f t h r e e types o f
s o l u b l e orthophosphate
o r g a n i c phosphorus
phorus.
Compartments i n Lake Water
( s o l u b l e r e a c t i v e phosphorus);
( s o l u b l e u n r e a c t i v e phosphorus); and p a r t i c u l a t e
D e f i n i t i o n s o f t h e s e types and t h e i r s i g n i f i c a n c e
cycle are discussed
i n this
(a) Orthophosphate
form o f phosphorus
soluble
i n t h e phosphorus
section.
Phosphorus
( S o l u b l e R e a c t i v e Phosphorus).
i s assumed t o be t h e s o l u b l e , i n o r g a n i c p o r t i o n
and i s t h e form i n which
phos-
32
P occur.
isotopes such as
Experiments
the c y c l i n g o f r a d i o a c t i v e phosphorus measure t h i s compartment
This
(PO^, ) ,
involving
(Rigler
1973).
-3
Orthophosphate,
o r PO^ , i s g e n e r a l l y assumed t o be the q u a n t i t y measured
when m e m b r a n e - f i l t e r e d water
(0.45 u f i l t e r )
i s a n a l y s e d by one o f the molyb-
denum b l u e t e c h n i q u e s . .
However, R i g l e r p o i n t s o u t t h a t o r t h o p h o s p h a t e i s p r o b a b l y g r o s s l y
o v e r e s t i m a t e d by u n i v e r s a l l y - u s e d a n a l y t i c a l t e c h n i q u e s f o r the f o l l o w i n g
reasons:
(1) f i l t r a t i o n might
phosphates-phosphorus
filtrate;
o r r e a d i l y h y d r o l y s e d phosphate
(2) a c i d i f i c a t i o n
l y s e f r e e phosphate
damage d e l i c a t e a l g a l c e l l s and r e l e a s e
esters into the
o f the sample w i t h s u l f u r i c
_3
e s t e r s and r e l e a s e PO^
phates o r from c o l l o i d a l i r o n phosphate;
a c i d c o u l d hydro-
from f u l v i c a c i d - m e t a l phos-
(3) a r s e n i c i s one o f the elements
_3
t h a t can i n t e r f e r e s e r i o u s l y w i t h t h e c o l o r i m e t r i c d e t e r m i n a t i o n o f PO^
the molybdenum b l u e t e c h n i q u e .
R i g l e r concludes that
in
there i s considerable
e v i d e n c e s u g g e s t i n g t h a t c h e m i c a l l y d e t e r m i n e d orthophosphate i s much
-3
-3
g r e a t e r than a c t u a l PO^ and assumes t h a t " t h e PO^, compartment i s v e r y
s m a l l and cannot be measured c h e m i c a l l y . "
This unfortunate f a c t leads
36
Rigler to conclude that severe l i m i t a t i o n s must be imposed on the i n t e r -3
pretation of tracer r e s u l t s because rate constants of.PO^
uptake cannot
be converted to phosphorus fluxes (flux implies a rate constant multiplied
by an amount) because the chemically determined amount i s i n question.
The s i z e of the orthophosphate compartment
i s quite small, even
by conventional estimates which are assumed to be overestimated.
In a
study of nine Ontario lakes which ranged from oligotrophic to eutrophic,
Rigler (1964) found that only f i v e to eight per cent of the t o t a l phosphorus
was orthophosphate.
(b) Soluble Organic Phosphorus.
This portion of the phosphorus
content of water has, by most i n v e s t i g a t o r s , been assumed to be the d i f f e r ence between the "soluble phosphorus" portion and the orthophosphate portion.
Soluble phosphorus i s the measure obtained when membrane-filtered (0.45 microns) water i s analyzed a f t e r being digested with an o x i d i z i n g acid s o l u t i o n
(Rigler 1973).
In 1964 R i g l e r found that nine lakes In Ontario presumably
had 12 to 32 per cent of the t o t a l phosphorus i n the form of soluble organic
phosphorus.
However, more recent evidence demonstrates that current a n a l y t i c a l
methods do not adequately separate organic and p a r t i c u l a r phosphorus (Rigler
1973).
R i g l e r prefers to refer to this compartment
as "soluble unreactive
phosphorus," arguing that a n a l y t i c a l techniques cannot s u f f i c i e n t l y d i s t i n g u i s h
between soluble organic and p a r t i c u l a t e phosphorus.
(c) P a r t i c u l a t e Phosphorus.
This compartment
i s equal to the
t o t a l phosphorus value minus the soluble phosphous determination.
Accord-
ing to Rigler (1973) , the o r i g i n a l assumption by early workers that a l l
p a r t i c u l a t e phosphorus i s associated with large plankton and trypton ( i n -
37
organic p a r t i c u l a t e phosphorus) must be rejected.
P a r t i c u l a t e phosphorus
i s associated with p a r t i c l e s ranging i n size from large zooplankton (and
f i s h ) down to c o l l o i d s , and the choice of a 0.45 micron f i l t e r to separate
p a r t i c u l a t e and "soluble unreactive" phosphorus i s quite a r b i t r a r y .
Rigler
maintains that much of the "soluble unreactive" part i s i n p a r t i c l e s less
than 0.1 micron and much i s c o l l o i d a l , but perhaps only a small f r a c t i o n
i s i n solution.
In 1964 Rigler found that nine Ontario lakes had 62 to 83 per cent
of the t o t a l phosphorus i n the form of p a r t i c u l a t e phosphorus.
(d)
Total Phosphorus.
This compartment i s measured when an un-
f i l t e r e d water sample i s treated by persulfate acid digestion and analyzed.
It should include a representative sampling of the phosphorus associated
with the bacteria and plankton (both phyto- and zoo-) from the depth at
which the sample i s c o l l e c t e d .
While the assumption that the measurement
includes phosphorus i n phytoplankton i s r e l a t i v e l y v a l i d , a s i m i l a r assumpt i o n f o r zooplankton i s questionable.
At times, a s i g n i f i c a n t f r a c t i o n
epilimnetic phosphorus may be i n the form of zooplankton (Riger 1973).
Because zooplankton exhibit pronounced horizontal d i s t r i b u t i o n
patterns ("patchiness") as well as d a i l y v e r t i c a l migration, an adequate
sample at a given depth would have to be an average of several locations a t
d i f f e r e n t times of the day (Rigler 1973).
I t i s not surprising that t o t a l
phosphorus i n the trophogenic layer can f l u c t u a t e greatly from day to day,
as 50 or 100 ml samples are normally taken (Rigler 1973).
For example,
Chamberlain (1968) showed that one extra Daphnia i n a 50 ml water sample
would increase the t o t a l phosphorus of the sample by 4 Mg/1, very s i g n i f i cant when the t o t a l phosphorus averaged 14 yg/1 (cited i n R i g l e r 1973).
38
In summary, i t can be concluded
that while a l l the compartments
of phosphorus have measurement d i f f i c u l t i e s , orthophosphate i s perhaps the
least r e l i a b l e and t o t a l phosphorus perhaps the most.
2.
Turnover Rates of Orthophosphate
Measurement of the phosphorus f l u x rate i n lakes i s the best
method a v a i l a b l e f o r study of the c y c l i n g a c t i v i t y of phosphorus.
qy (1960) states the argument i n t h i s
Pomer-
way:
"Measurement of the concentration of dissolved phosphate i n natural waters gives a very l i m i t e d i n d i c a t i o n of
phosphate a v a i l a b i l i t y . Much or v i r t u a l l y a l l of the phosphate i n the system may be i n s i d e l i v i n g organisms at any
given time, yet i t may be overturning every hour with the
r e s u l t that there w i l l be a constant supply of phosphate
f o r organisms able to concentrate i t from a very d i l u t e
solution. Such systems may remain stable b i o l o g i c a l l y
for considerable periods i n the apparent absence of
a v a i l a b l e phosphate. The observations presented here
suggest that a rapid f l u x of phosphate i s t y p i c a l of
highly productive systems, and that the f l u x rate i s
more important than the concentration i n maintaining
high rates of organic production."
The concept of "turnover" i s a useful one f o r comparing exchange
rates of phosphorus between d i f f e r e n t compartments of an ecosystem such as
a lake.
A f t e r equilibrium has been reached, the "turnover r a t e " i s the
f r a c t i o n of the t o t a l amount of phosphorus i n a component which i s released
(or which enters) i n a given time period.
"Turnover time" i s the r e c i p r o -
c a l of the turnover rate, or the time required to remove the phosphorus
content of the considered compartment i n the absence of other t r a n s f e r r a l
mechanisms.
A hypothetical exchange between two compartments i n a lake
w i l l i l l u s t r a t e the
concept:
39
dissolved
°4
i n water
P
10
Ug/1
5 yg/1
• day
4 yg/1
• day
P in
phytoplankton
20
yg/1
I n t h i s example the " t u r n o v e r r a t e " between the d i s s o l v e d P0~^
and p h y t o p l a n k t o n
compartment (due
i s 5 yg/1 • day exchange * 10 yg/1
t o u p t a k e by a l g a e and
compartment
consequent growth)
i n the water compartment = 0.5/day.
" t u r n o v e r t i m e " i s the r e c i p r o c a l of 0.5,
The
or two d a y s , w h i c h i s e q u a l t o the
-3
time necessary
f o r a c o m p l e t e t u r n o v e r o f t h e PO^
i n the water.
Now,
if
we l o o k a t t h e o p p o s i t e pathway i n w h i c h the p a r t i c u l a t e phosphorus i n the
phytoplankton
i s decomposed by b a c t e r i a and r e - e n t e r s the d i s s o l v e d
compartment, t h e t u r n o v e r r a t e i s 4/20
PO.
4
= 0.2/day, w i t h a t u r n o v e r t i m e o f
f i v e days.
Turnover t i m e s between v a r i o u s phosphorus compartments a r e
c i t e d i n T a b l e VT> . and a s i m p l i f i e d s c h e m a t i c o f t r a n s f o r m a t i o n s i s
_3
shown i n F i g u r e 5.
The t u r n o v e r t i m e o f e p i l i m n e t i c PO^
from water to
o r g a n i c compartments has been measured i n a v a r i e t y o f temperate l a k e s
from o l i g o t r o p h i c t o e u t r o p h i c , and
l a i n 1968,
ing
i n d y s t r o p h i c and bog l a k e s (Chamber-
R i g l e r 1964); i t i s g e n e r a l l y between one and e i g h t m i n u t e s
summer s t r a t i f i c a t i o n
( R i g l e r 1973).
dur-
This f l u x i s indicated i n Figure
-3
5 as b e i n g between the s o l u b l e i n o r g a n i c PO^
compartments.
and
phytoplankton-bacteria
R i g l e r n o t e s t h a t s i m i l a r t u r n o v e r t i m e s can be
expected
d u r i n g the p r o d u c t i v e p e r i o d i n l a k e s t h a t have a h i g h r a t i o o f p a r t i c u l a t e phosphorus:orthophosphate.
winter
The
considerably longer turnover
time i n
(around one day) can be a t t r i b u t e d to d e c r e a s e d t e m p e r a t u r e , i n c r e a s e d
40
TABLE
VI
TURNOVER TIMES OF PHOSPHORUS FLUX BETWEEN COMPARTMENTS
ORIGINAL
COMPARTMENT
Soluble
Soluble
RECEIVING
COMPARTMENT
inorganic P
(summer)
(winter)
phytoplankton
inorganic
soluble
P
bacteria
littoral
TURNOVER
TIME
and
0.9
-
REFERENCE
7.3 minutes
Rigler
1964
<30 u
7 minutes 0 . 2 days
organic P
vegetation
0.09
days
(Sphagnum)
l i t t o r a l vegetation
0.34
days
7 days
R i g l e r 1964
Hayes and
P h i l l i p s 1958
(Eriaaulon)
l i t t o r a l vegetation
and s e d i m e n t s
l i t t o r a l sediments
Soluble organic P
Particulate P
soluble inorganic
l i t t o r a l fauna
P
(mussels)
deep-water sediments
H
II
P h y t o p l a n k t o n <30 u
Zooplankton
(excretion)
L i t t o r a l vegetation
soluble
II
II
inorganic P
5.4 2.7
1 7 . 0 days
days
0.2
days
2.5
days
C o f f i n et al.
1949
H a y e s et al.
1952
Hayes and
P h i l l i p s 1958
it
Kuenzler
H
1961
50 d a y s
100 d a y s
40 - 7 1 d a y s
2.2 days
2 . 1 days
Hutchinson 1941
R i g l e r 1956
G a c h t e r 1968
R i g l e r 1973
Haney 1970
3
Hayes and
P h i l l i p s 1958
days
(Erioaulon)
Littoral
vegetation
3.5
(Sphagnum)
Sediments i n u n s t r a - '
t i f i e d lake
"
" (no b a c t e r i a )
"
" (with b a c t e r i a )
39 - 176 d a y s
1 5 . 5 days
3.6 days
days
C o f f i n et al.
1949
Hayes and
P h i l l i p s 1958
41
0.2
days-
3-8daysPhytoplankton
and bacteria
EPILIMNION
2 days
JL
Zooplankton
(herbivores and
carnivores)
3-7 weeks
HYPOLIMNION
Particulate
P
3-7weeks
weeks
or
longer
Figure 5. Phosphorus transformations in stratified lakes
during summer; expressed in turnover times. Dashed lines
indicate no data available on rates.
42
c o n c e n t r a t i o n of orthophosphate and
to the reduced
biomass o f
plankton
( R i g l e r 1973).
-3
The
r e t u r n o f PO^
form i n water i s m a i n l y due
phytoplankton;
from the b i o t i c p o o l to the d i s s o l v e d o r t h o t o t h r e e mechanisms:
(2) e x c r e t i o n by z o o p l a n k t o n :
and
(1) d i r e c t
r e l e a s e by
(3) enzymatic h y d r o l y s i s
of o r g a n i c phosphorus compounds e x c r e t e d by organisms o r produced by decompo s i t i o n o f dead p l a n k t o n
( R i g l e r 1973).
n o t been measured w i t h s u f f i c i e n t
d i r e c t r e l e a s e by
While the t h i r d mechanism
s o p h i s t i c a t i o n to determine a
s m a l l p l a n k t o n has been e s t i m a t e d
has
flux,
from t h e r a t e of r e -
32
lease of
hr
P from s e s t o n
(suspended p a r t i c u l a t e m a t t e r ) as a v e r a g i n g
( t u r n o v e r time o f 53 hours or 2.2
zooplankton
tude (0.02
has been e s t i m a t e d
hr
- 1
)
d a y s j R i g l e r 1973).
0.019
E x c r e t i o n by
from g r a z i n g r a t e s t o be of s i m i l a r magni-
to the r e l e a s e by
small plankton
(Haney 1970,
R i g l e r 1973).
R i g l e r f e e l s t h a t most of the phosphorus e x c r e t e d by z o o p l a n k t o n i s u l t i -3
m a t e l y r e g e n e r a t e d as PO^ , a l t h o u g h a p a r t o f i t may be e x c r e t e d i n o r g a n i c
phosphorus compounds.
The
s o l u b l e o r g a n i c compartment
(referred
u n r e a c t i v e phosphorus") a c t u a l l y c o n s i s t s of two
the r e l a t i o n s h i p of the l a r g e r subcompartment
subcompartments, but
(particle
the c y c l e i s u n c l e a r , F i g u r e 5 shows i t t o be one
o r g a n i c and
to by R i g l e r as " s o l u b l e
s i z e 0.1
compartment.
because
- 0.45u) to
The
soluble
i n o r g a n i c compartments appear t o exchange phosphorus about
two
-3
o r d e r s of magnitude slower
ments, and
Hayes and
R i g l e r notes
than
Phillips
the PO^
and
phytoplankton-bacteria
(1958) r e p o r t a t u r n o v e r
time of f i v e
comparthours.
t h a t the p h y s i c a l - c h e m i c a l n a t u r e o f t h i s compartment i s
l a r g e l y unknown, as i s i t s f u n c t i o n i n the phosphorus economy of the
still
tropho-
g e n i c l a y e r . While some of the s o l u b l e o r g a n i c f r a c t i o n i s u n d o u b t e d l y
utilized
43
d i r e c t l y f o r b i o l o g i c growth, the quantity and rate have not been ascertained.
Phytoplankton of a size greater than 30y are pictured by R i g ler
(1973) as comprising a large compartment through which phosphorus
cycles r e l a t i v e l y slowly (no rates are given) and from which phosphorus
i s l a r g e l y regenerated by decomposition.
-3
Movement between the PO^ compartment and l i t t o r a l vegetation i s
r e l a t i v e l y rapid (two to eight hours, Hayes and P h i l l i p s 1958), while
movement from vegetation back to the water i s much slower (three to
eight days; Hayes and P h i l l i p s 1958, Confer 1969).
P a r t i c u l a t e organic phosphorus i n the form of dead plankton
c e l l s sediments to the bottom of lakes at rates
of between 1.0 and
2.5
per cent/day, r e s u l t i n g i n turnover times of between 40 and 100 days
(Hutchinson 1941, R i g l e r 1956, Gachter
1968).
The return of phosphorus from the sediments
(or " i n t e r n a l load-
ing") i s an extremely important key to understanding the eutrophication
process, and w i l l be dealt with i n considerable d e t a i l i n the section on
i n t e r n a l loading.
It w i l l simply be noted here that the turnover time of
t h i s f l u x can vary from days to weeks or longer.
of the f l u x between sediment mud
Laboratory measurement
-3
(with bacteria) and P0^
i s reported by
Hayes and P h i l l i p s (1958) to be about three days i n both d i r e c t i o n s .
With
no bacteria present, the exchange between the sediment and the water was
slowed to 15 days.
_3
The importance of bacteria i n determining rates of PO^
i n aquatic ecosystems should not be underestimated.
exchange
Rigler (195 6) surmised
that bacteria might be the primary cause f o r rapid turnover times between
44
plankton and water and noted that they compete very e f f e c t i v e l y with algae
_3
for PO^
.
Rhee (1972) studied the competition for phosphates between a
bacterium species (Pseudomonas)
found that a l g a l growth was
and an a l g a l species (Scenedesmus),
He
severely limited i n the presence of b a c t e r i a ,
but the growth of bacteria was hardly affected by algae.
growth rate of bacteria accounted for the suppressed
The
faster
growth of algae i n
mixed cultures.
3.
The Lake as a P r o d u c t i v i t y Chamber
The contrast between biomass and p r o d u c t i v i t y (rate of growth)
i s a very important one for aquatic ecosystems, and stresses the importance
of turnover rate i n determining organic growth.
Ketchum (1967) states the
contrast i n t h i s way f o r the marine environment:
" I t has been estimated by Ryther (1960) that the plant
biomass i n the oceans i s only 0.1% of the t o t a l plant b i o mass on earth, but that t h i s small population contributes
40% of the annual world production of organic matter. The
large production which r e s u l t s from such a small standing
crop i n the marine environment i s an i n d i c a t i o n of the
r a p i d i t y of the turnover of the population. P r a c t i c a l l y
a l l of the photosynthesis of the sea i s carried on by
microscopic plants which can, under i d e a l conditions,
double their population size d a i l y . In contrast to t h i s
i t takes 50 years or more to develop a f o r e s t (90.5% of
the earth's biomass) and the rate of annual production
(25% of the t o t a l ) i s a small f r a c t i o n of the standing
crop at any one time."
The t o t a l reserve of phosphorus i n a body of water ( i . e . , the
quantity of soluble, p a r t i c u l a t e , sestonic, and accessible sedimented phosphorus), i s a pertinent gross parameter because i t indicates the ultimate
capacity for biomass synthesis (Stumm and Stumm-Zollinger 1972).
authors note that s t o i c h i o m e t r i c a l l y 1 mg of phosphorus w i l l y i e l d
The
(on the
45
average) about 100 mg o f a l g a l biomass, which e x e r t s a b i o c h e m i c a l
demand o f a p p r o x i m a t e l y 140 mg.
T h i s means t h a t secondary sewage e f f l u e n t
which c o n t a i n s 3-8 mg phosphorus/1 c a n y i e l d 300-800 mg/1 o r g a n i c
i n the p r o d u c t i v e
C.
oxygen
environment of a e u t r o p h i c
matter
l a k e such as Skaha.
MODELLING APPROACH
Modelling
t h e phosphorus budget and p h y t o p l a n k t o n growth i n a
l a k e i s a s i m u l a t i o n problem.
processes
Simulation
o f the p h y s i c a l and b i o l o g i c a l
i n a l a k e has two major g o a l s , one t h e o r e t i c a l and one p r a c t i c a l :
(1) t h e model i n c r e a s e s u n d e r s t a n d i n g of how the l a k e f u n c t i o n s , and (2)
the model e n a b l e s p r e d i c t i o n o f e u t r o p h i c a t i o n problems as a response t o
varying nutrient inputs.
aim
M a t h e m a t i c a l programming, which has the s p e c i f i c
o f maximizing or minimizing
an o b j e c t i v e f u n c t i o n s u b j e c t
i s n o t a p p l i c a b l e t o t h i s problem.
made on a minimum s t a n d a r d
techniques
1.
At a l a t e r
to c o n s t r a i n t s ,
stage when a d e c i s i o n must be
o f water q u a l i t y w i t h minimum c o s t ,
optimization
may be q u i t e u s e f u l .
Simulation
Modelling
In the s i m u l a t i o n o f a complex system such as a l a k e , i t i s n e c e s s a r y t o make a r e a s o n a b l e
model i s too simple,
compromise between s i m p l i c i t y and r e a l i t y .
i t may n o t be a u s e f u l a b s t r a c t i o n o f n a t u r e .
I f the
If i t
i s t o o complex and i n c l u d e s too many v a r i a b l e s , more d a t a a r e r e q u i r e d
are
a v a i l a b l e . Excessive
complexity
burdens c o m p u t a t i o n a l f a c i l i t i e s as w e l l
as t h e human mind i n the i n t e r p r e t a t i o n o f c a u s a l
and M c N e i l
accuracy
than
interactions.
As R u s s e l l
(1974) s t a t e , ". . .the aim i s t o produce r e s u l t s o f a c c e p t a b l e
w i t h models o f minimum, c o m p l e x i t y . "
46
C o n s i d e r i n g the
e n t s , sediments and
and
immense c o m p l e x i t y o f i n t e r a c t i o n s between n u t r i -
b i o t a i n a l a k e , and
the
measuring these i n t e r a c t i o n s , i t i s not
amount of r e a l i s m must be
applied
sacrificed.
d i f f i c u l t y of i d e n t i f y i n g
s u r p r i s i n g that a c e r t a i n
Walters
(1971) o b s e r v e s t h a t
e c o l o g i c a l problems i n which p r e d i c t i o n i s the g o a l ,
g e n e r a l i t y are
often
sacrificed for precision.
some degree of p r e c i s i o n the n u t r i e n t
f y i n g assumptions must be made.
The
in
realism
In o r d e r to p r e d i c t
relationships within
detailed discussion
a lake,
o f the
and
with
simpli-
submodels
a m p l i f i e s t h e n a t u r e o f the assumptions made i n t h i s model.
(a) Time S c a l e .
The
next s t e p i n model b u i l d i n g
the
time s c a l e t o be
For
i n i t i a l modelling of phosphorus c o n c e n t r a t i o n
it
c o n s i d e r e d , and
r e s o l u t i o n of
i s u s e f u l t o l o o k a t a time span of one
model.
a l g a e i n the
and
predicted
lake,
and
alization
(a l o n g
time s c a l e
r e s u l t i n g a l g a l growth,
the
phosphorus
refined u n t i l
actual
time i n t e r v a l ) .
t h i s i n t e r v a l i s too
(and
too
cycle
short
(a s h o r t
While i t has
time i n t e r v a l ) and
been shown i n the
are
gener-
previous
i n minutes between some compartments i n
f o r p r a c t i c a l use
e x p e n s i v e i n computer t i m e ) .
a month) i n t e r v a l would be
of a l g a l m e t a b o l i s m
(or time i n t e r v a l ) i s another com-
between d e t a i l
s e c t i o n t h a t phosphorus can
f o r years
scale.
y e a r i n o r d e r to v e r i f y
the model p r o g r e s s i v e l y
of the
promise, i n t h i s i n s t a n c e
(twice
time
v a l u e s agree r e a s o n a b l y w e l l .
Resolution
a lake,
and
the
Model r e s u l t s are compared w i t h a c t u a l measurements of
and
run
the
i s to d e c i d e
i n a model which w i l l
A weekly or
bi-weekly
s a t i s f a c t o r y , except t h a t most c o e f f i c i e n t s
e x p r e s s e d i n the
T h e r e f o r e , a compromise i n t e r v a l of one
l i t e r a t u r e i n u n i t s per
day
i s chosen.
day.
47
(b) Approach
to Mathematical Statement of Relationships.
Two
basic mathematical approaches have been used i n modelling e c o l o g i c a l systems:
(1) continuous form, with the use of d i f f e r e n t i a l equations; and
(2) discrete form, with the use of difference equations.
The continuous
form describes changes that occur continuously over time, and while they
are the most powerful way of representing general flow processes i n ecolog i c a l systems, they are often d i f f i c u l t to solve (Walters 1971).
Further-
more, Watt (1968) points out that many b i o l o g i c a l processes have v a r i a b l e s
which do not have continuous, but rather d i s c r e t e values.
The only p r a c t i c a l approach i n modelling the volume changes
associated with lake s t r a t i f i c a t i o n i s the use of a f i n i t e time period
(difference equation).
The d a i l y changes i n volume occurring during the
spring s t r a t i f i c a t i o n and autumn d e - s t r a t i f i c a t i o n processes cannot be
p r a c t i c a l l y described by a d i f f e r e n t i a l equation, and are more accurately
represented by a difference equation.
Difference equations have the advant-
age of being clearer to understand, making the p o s s i b i l i t y of errors hidden
in the complexity of d i f f e r e n t i a l equations less l i k e l y .
For these reasons the discrete form (difference equations) was
chosen f o r the equations i n t h i s model.
With t h i s form computations are
performed f o r each time i n t e r v a l according to the following r e l a t i o n s h i p
(adapted from Walters 1971):
value of
variables
now
statement of
relationships
or rules f o r
change
value of variables
a f t e r one time period
48
The e s s e n c e o f t h i s t y p e o f systems model i s t h e " s t a t e m e n t of r e l a t i o n s h i p s "
or
" r u l e s f o r change" w h i c h d e f i n e t h e way v a r i a b l e s w i l l change
1971).
(Walters
W i t h t h e s e r u l e s i n c o r p o r a t e d i n t h e i n p u t s and o u t p u t s , t h e way
i n w h i c h e a c h v a r i a b l e w i l l change e a c h day can be shown as f o l l o w s
(adapted
from W a l t e r s 1971):
new v a l u e
of v a r i.a b, l,e
c
=
o l d value
o f v a r .i aib_ l, e
+
c
inputs
- o u t p*u t s
With the use o f t h i s input-output format, the problem o f d e v e l o p i n g a
systems model i s reduced t o c h o o s i n g r e a s o n a b l e ways t o e x p r e s s t h e
change o f t h e i n f l o w s and o u t f l o w s o f t h e system o v e r t i m e ( W a l t e r s 1 9 7 1 ) .
Other s e c t i o n s o f t h i s c h a p t e r d i s c u s s t h e d e t a i l s o f t h e s e t r a n s f o r m a t i o n s .
2.
S i m u l a t i o n Approaches t o M o d e l l i n g t h e Phosphorus C y c l e
Two b a s i c approaches have been used i n m o d e l l i n g t h e phosphorus
c y c l e i n a q u a t i c systems: (a) t h e "compartment" a p p r o a c h ; and (b) t h e "mass
balance" approach.
(a)
The Compartment A p p r o a c h .
T h i s a p p r o a c h uses r a d i o p h o s p h o r u s
32
t r a c i n g data (
P) as i t s b a s i s , and emphasizes t h e r a t e o f movement o f
phosphorus between t h e compartments, as d i s c u s s e d i n t h e s e c t i o n on phosphorus c y c l i n g and shown i n F i g u r e 5.
the
M o d e l l i n g s e v e r a l compartments and
i n t e r a c t i o n s between each one can be enormously complex.
F o r example,
a phosphorus model w i t h 15 compartments can have as many as 55 pathways o f
f l u x between compartments ( K l u e s e h e r 1970).
S i m p l e r compartment models
have been c o n c e i v e d , b u t even a s i x compartment phosphorus model has a t
l e a s t 23 I m p o r t a n t f l u x pathways ( F l e m i n g 1971).
49
Rigler
(1973) d i s c u s s e s t h e problems i m p l i c i t i n t h e f o r m u l a t i o n
of a compartment model f o r phosphorus c i r c u l a t i o n i n a l a k e .
Firstly,
this
method assumes t h e system i s i n a s t e a d y s t a t e , and t h i s c o n d i t i o n i s r a r e l y , i f e v e r , met i n a q u a t i c ecosystems (except t h a t d u r i n g summer s t a g n a t i o n
a pseudo s t e a d y - s t a t e i s sometimes a c h i e v e d i n some temperate l a k e s ) .
32
Secondly,
P i s i n t r o d u c e d o n l y i n t h e o r t h o p h o s p h a t e compartment, and
w h i l e measurement o f t h e r a t e of movement o f t h e t r a c e r i s c o n s i d e r e d v a l i d ,
measurement o f t h e q u a n t i t y o f o r t h o p h o s p h a t e i n e a c h compartment i s i n s e r i o u s q u e s t i o n (see p r e v i o u s s e c t i o n ) .
Thirdly,
t h e c h e m i c a l and p h y s i c a l
n a t u r e o f s o l u b l e o r g a n i c ( o r s o l u b l e u n r e a c t i v e ) phosphorus i s s t i l l
largely
unknown, a s i s i t s r o l e i n t h e phosphorus economy o f the t r o p h o g e n i c zone.
F o u r t h l y , e x i s t i n g data a r e inadequate t o provide t r u e r a t e constants of
phosphorus movement out o f t h e e p i l i m n i o n t o t h e l i t t o r a l and h y p o l i m n i o n .
Rigler
( p e r s o n a l communication) c a u t i o n s a g a i n s t t h e compartment a p p r o a c h
f o r a n a l y s i s o f phosphorus c i r c u l a t i o n between e p i l i m n i o n , h y p o l i m n i o n
and
s e d i m e n t s because t h e s e k i n d s o f f l u x d a t a have n o t been q u a n t i f i e d .
W h i l e no a t t e m p t s have been made t o f o r m u l a t e even a s i m p l i f i e d
compartment model o f phosphorus f l u x i n a f r e s h w a t e r system, a t l e a s t one
a t t e m p t (Pomeroy et al. 1969) has been made i n a s a l t w a t e r marsh.
This
model i n c l u d e s seven compartments (some o f w h i c h a r e d i v i d e d i n t o subcompartments) and a t l e a s t 14 f l u x e s ( r a d i o p h o s p h o r u s t r a c i n g ) between compartments.
Because o f t i d a l f l u s h i n g , r o u t e s o f e x p o r t f r o m t h e system c o u l d n o t be
evaluated.
In summary, i t c a n be c o n c l u d e d t h a t t e c h n i q u e s o f t r a c i n g phosphorus i n a q u a t i c ecosystems have n o t y e t r e a c h e d t h e l e v e l o f s o p h i s t i c a t i o n
n e c e s s a r y t o e n a b l e m o d e l l i n g o f t h e phosphorus c y c l e by the compartment
approach.
50
(b)
The Mass Eudget Approach.
A more f r u i t f u l approach to the
problem of nutrient budgets i n lakes i s proposed by Vollenweider
Extending the e a r l i e r work of B i f f i
(1963) and P i o n t e l l i and T o n o l l i (1964)
Vollenweider begins with the basic mass balance assumption
of
(1969).
that the amount
a substance i n a lake i s e s s e n t i a l l y a function of the supply and loss
(brought about by sedimentation and outflow) of the substance.
B i f f i con-
siders the hydrologic flow-through an e s s e n t i a l f a c t o r , while P i o n t e l l i
and T o n o l l i emphasize the l o s s through sedimentation.
Vollenweider ex-
tends these concepts i n an analysis of the t o t a l phosphorus budgets of
eight Swiss lakes, and formulates the following r e l a t i o n s h i p .
General form:
change in mass of phosphorus = loading - sedimentation - outflow
S p e c i f i c form:
dm
W
-TT—
dt
for
=
T
J
-
am
w
pm
w
which a steady-state solution i n terms of phosphorus concentration and
s p e c i f i c loading i s :
[m_J
w'
where
=
z
" (a+p)
L
i s the mass of phosphorus i n the lake (kg); J i s the loading (kg);
a i s an empirically determined
sedimentation c o e f f i c i e n t (years ^~); p i s
the c o e f f i c i e n t of hydrologic flow-through (years ^ ; equal to Q/V, where
3
3
Q i s the outflow discharge (m /year) and V i s the lake volume, m ); [m ] i s
w
o
_
the mean concentration of phosphorus i n the lake (g/m ); z i s the mean depth
of
the lake (m); and L i s the s p e c i f i c loading of phosphorus to the lake
(g/m ).
2
51
Vollenweider accounts f o r the fact that during s t r a t i f i c a t i o n
only a part of the e n t i r e lake volume i s involved i n mixing and hydrologic
flow-through, and has developed an expression for the "mean exchange e p i l i m nion" during t h i s period.
Vollenweider assumes that the loading r a t e i s
constant and that the concentration of phosphorus i n the outflow i s the
same as the average concentration i n the lake.
The most d i f f i c u l t part of the analysis i s the formulation of
an expression which accurately describes the sedimentation of phosphorus.
Vollenweider decided that h i s o r i g i n a l assumption
that phosphorus
sedimenta-
t i o n Was a l i n e a r function of the amount of phosphorus i n the water (c* ^)
11
did not adequately f i t experimental data.
He therefore introduced a co-
e f f i c i e n t , T, which made sedimentation a function of loading as well as
the amount of phosphorus i n the water.
The r e s u l t i n g equation produced a
s a t i s f a c t o r y f i t with experimental data when a mean value of 0.39 for T was
used:
d [m ]
—~—
dt
w
L
=
t
—
—
z
loading
L
-
a[m ] - — ( 1 - p )
w
—
z
-
P[m]
w
-
sedimentation
-
outflow
Vollenweider suggests that further development of this model should include
a set of simultaneous reaction equations
to describe the complexities of
the sediment-water exchanges (1968 and personal communication).
O'Melia
(1972) extends Vollenweider's model with the d i v i s i o n of
a lake into an epilimnion and hypolimnion, and the introduction of a term
to describe the eddy d i f f u s i o n of phosphorus from hypolimnion to epilimnion.
52
O'Melia's mass balance formulation for the epilimnion i s :
dP
dt"
d[P ]
g
=
W
+
inflow
k
z e-^T
A
"
+ eddy diffusion
s V
e
"
[ P P ]
- sedimentation
^ T
[ P
-
]
outflow
With the exception of the eddy d i f f u s i o n term (the second term i n the equat i o n ) , t h i s formulation i s almost i d e n t i c a l to Vollenweider's.
Here P
is
the amount of t o t a l phosphorus i n the epilimnion (kg); W i s the rate of i n put of t o t a l phosphorus from the land (kg/year), a l l of which i s assumed to
enter the epilimnion; the term k A d[P ]/dz describes the input of phosphate
Z
6
S
to the epilimnion by d i f f u s i o n from the hypolimnion, where
i s the co-
2
e f f i c i e n t of eddy d i f f u s i o n or v e r t i c a l mixing (m /year), A i s the area
2
of the thermocline (m ),.d[P ]/dz i s the gradient of soluble phosphate
s
across the thermocline
(mg/1); the term sV [PP] i s the sedimentation
where s i s the sedimentation c o e f f i c i e n t
epilimnion (m ), and
e
loss,
(years ^ ) , V^ i s volume of the
[PP] i s the concentration of p a r t i c u l a t e phosphorus
in the epilimnion (mg/1); the l a s t term i s the outflow
( a l l considered to
3
be from the epilimnion) i n which Q lake discharge (m /year) and
[P^] i s
o
the concentration of t o t a l phosphorus in the epilimnion (g/m
).
O'Melia
does not include a model f o r the mass balance of phosphorus i n the hypolimnion, which i s e s s e n t i a l for the determination of the concentration
gradient across the thermocline.
CHAPTER IV
DEVELOPMENT OF A MODEL FOR SKAHA LAKE
The work o f V o l l e n w e i d e r and O'Melia forms t h e e s s e n t i a l base
from w h i c h a mass b a l a n c e model f o r an e p i l i m n i o n - h y p o l i m n i o n - s e d i m e n t
system c a n be f o r m u l a t e d .
I n t h i s model " t o t a l phosphorus"
t h e b a s i c measure f o r t h e element.
i s considered
The n o r t h and s o u t h b a s i n s o f Skaha
Lake a r e c o n s i d e r e d s e p a r a t e l y , and h o r i z o n t a l homogeneity i s assumed I n
each b a s i n .
S e p a r a t e e q u a t i o n s a r e f o r m u l a t e d f o r t h e e p i l i m n i o n and
hypolimnion.
The b a s i c form o f t h e s e e q u a t i o n s i s d e s c r i b e d i n t h i s
s e c t i o n , w h i l e t h e d e t a i l s o f submodels a r e d e s c r i b e d i n a l a t e r
A.
section.
FUNDAMENTAL INPUT-OUTPUT EQUATION
1.
Form o f t h e E q u a t i o n f o r t h e E p i l i m n i o n
I f s t e a d y s t a t e c o n d i t i o n s p r e v a i l e d i n t h e n u t r i e n t budget o f
a l a k e , t h e f o l l o w i n g r e l a t i o n s h i p would be t r u e :
I n p u t - Output = 0
or
Input = Output
However, most l a k e s a c t a s n a t u r a l t r a p s f o r sediments
and e x h i b i t a n u t r i e n t g a i n over t i m e .
( i n c l u d i n g phosphorus)
I n order t o understand
t h e dynamics
o f t h i s n u t r i e n t i n c r e a s e , i n p u t s and o u t p u t s must be d e s c r i b e d i n d e t a i l .
A l l terms a r e r a t e s i n kg/day.
(a) Input Terms.
Input o f phosphorus c a n be d e s c r i b e d by t h e
following equation:
53
54
input = P
where P
L E
+ P
+ P
E
v
+
P
R E
i s external loading from a l l sources (kg/day), P
i s eddy
d i f f u s i o n from the hypolimnion (kg/day), P^ i s a volume gain of phosphorus
(kg/day) as the epilimnion forms and develops following spring mixing, and
P
R E
i s regeneration of organic phosphorus from b a c t e r i a l decomposition i n
the l i t t o r a l zone (kg/day).
The loading term, P _, i s the summation of natural and c u l t u r a l
T
sources of phosphorus.
Natural sources come from d u s t f a l l and p r e c i p i t a t i o n
on the lake surface, streamflow from v i r g i n watersheds, and ground water i n f l u x from natural sources.
C u l t u r a l sources include municipal waste, storm
sewer flows, i n d u s t r i a l waste, a g r i c u l t u r a l return flow, a g r i c u l t u r a l ground
water, septic tank ground water, and inputs from disturbed watersheds
logging and mining).
(e.g.
The c o l l e c t i o n and r e l i a b i l i t y of these data are d i s -
cussed i n Appendix B.
(b) Output Terms.
Output of phosphorus from the epilimnion i s
described by the following equation:
Output = P
where P^
E
S E
+ P
Q
i s the sedimentation to the hypolimnion (kg/day) and P^ i s the
outflow (kg/day).
(c) Combined Mass Balance.
for
The combined mass balance equation
the epilimnion becomes:
P
TE
=P
IE
+P
LE
+ P + P + P
-P
E
V
RE
SE
-P
0
where P^g i s the r e s u l t i n g amount of t o t a l phosphorus (kg) i n the e p i l i m nion at the end of each time period (day) and P
i s the i n i t i a l amount of
55
phosphorus (kg) a t t h e b e g i n n i n g o f each p e r i o d .
The o u t f l o w o f phosphorus from the l a k e , P_,
0
i s e q u a l t o QC
,
e
3
where Q i s t h e d i s c h a r g e o f water from the l a k e (m /day) and C
c o n c e n t r a t i o n of phosphorus i n t h e e p i l i m n i o n (kg/m
2.
Form o f the E q u a t i o n f o r t h e
3
e
i s the
).
Hypolimnion
As i n t h e e p i l i m n i o n , a mass b a l a n c e f o r t h e h y p o l i m n i o n c o n s i s t s
of
i n p u t and o u t p u t terms e x p r e s s e d as r a t e s i n kg/day.
(a) Input Terms.
Input t o t h e h y p o l i m n i o n can be d e s c r i b e d by
the f o l l o w i n g equation:
Input - P
where P
+
L R
P r h
i s l o a d i n g by s e d i m e n t a t i o n from t h e e p i l i m n i o n (kg/day) and
P
LH
RH
i s r e g e n e r a t i o n from the sediments
(b) Output Terms.
(kg/day), or " i n t e r n a l
loading."
Output f r o m the h y p o l i m n i o n can be d e s c r i b e d
by t h e f o l l o w i n g e q u a t i o n :
Output = P
where P
on
S
H
+
P
E
+ P
v
+
P
Q
i s t h e s e d i m e n t a t i o n l o s s ( k g / d a y ) , P_ i s t h e eddy d i f f u s i o n
h
t o t h e e p i l i m n i o n ( k g / d a y ) , P^ i s a l o s s t o t h e e p i l i m n i o n a s
loss
stratification
o c c u r s a f t e r s p r i n g m i x i n g ( k g / d a y ) , and P^ i s an o u t f l o w l o s s w h i c h
occurs
d u r i n g c o m p l e t e m i x i n g when t h e e n t i r e l a k e i s t r e a t e d as a h y p o l i m n i o n i n
t h e model ( k g / d a y ) .
(c) Combined Mass B a l a n c e .
for
The combined mass b a l a n c e e q u a t i o n
t h e h y p o l i m n i o n becomes:
P
TH
= P
IH
+ P
LH
+P
RH
-P
SH
- P
E
- P
V
- P
0
where P_
i s the r e s u l t i n g amount o f t o t a l phosphorus (kg/day) i n the hypoIn
56
limnion at the end of each day and P
/
i s the i n i t i a l amount (kg/day) at
the beginning of the d a i l y period (equal to P
f o r the previous day).
TH
3.
Modification of Mass Balance During Mixing Periods
During months when the lake i s completely mixed (mid-November to
mid-April) the hypolimnion model w i l l be used to describe the balance of phosphorus i n the entire lake.
The fact that s l i g h t inverse s t r a t i f i c a t i o n
occurs i n winter when an i c e cover forms on at least part of the lake i s
not taken into account, except by adjustment of c o e f f i c i e n t s as described
in another section.
With the advent of autumn mixing phosphorus i s brought from the
hypolimnion (where i t has been accumulating during summer stagnation) to
the trophogenic layer. This phosphorus increase may
stimulate an autumn
phytoplankton bloom.
B.
MIXING BEHAVIOR OF SKAHA LAKE AND VOLUME CHANGES OF EPILIMNION AND
HYPOLIMNION
No attempt i s made to predict the thermal regime
l y the mixing behavior) of the lake.
(and
consequent-
Instead, thermal data describing the
mixing behavior of the lake i n 1969-70 are used to c a l c u l a t e volumetric
changes of the epilimnion, metalimnion
(thermocline) and hypolimnion i n
each basin (Table A - l i n Appendix A).
Area-depth relationships from the
hypsometric curve (Figure 2) and thermal data are used f o r the c a l c u l a t i o n s .
The end of the complete mixing period occurs in mid-April when
the formation of the epilimnion begins.
As the t o t a l volume of the lake r e -
mains constant, growth of the volume of the epilimnion i s at the expense of
the hypolimnion.
Therefore, as the epilimnion increases In volume, the
57
hypolimnion correspondingly decreases i n volume.
Computation
of these
volume changes takes into account changes i n volume of the metalimnion
(thermocline).
As the volume of the epilimnion grows with increasing
s t r a t i f i c a t i o n , phosphorus within such volume i s l o s t from the hypolimnion and added to the epilimnion (W. K. Oldham, personal
communication).
This phosphorus exchange i s included i n the mass budget as
and i s
calculated according to the following equation:
V
where P
v
x h
i s the mass of phosphorus l o s t from the hypolimnion and added
to the epilimnion (kg),
i s the volume of water l o s t from the hypolim-
3
nion and added to the epilimnion (m ) and C^ i s the concentration of t o t a l
3
phosphorus i n the hypolimnion (kg/m ).
Thermal records show that the inverse s t r a t i f i c a t i o n of winter
i s completely absent by mid-March, and vigorous mixing takes place from
mid-March to mid-April.
The s t a r t i n g point chosen f o r the model i s mid-
March which could be termed the beginning of the "spring overturn."
The
period of complete mixing i n the autumn ("autumn overturn") begins i n midNovember and l a s t s u n t i l mid-December when the inverse s t r a t i f i c a t i o n of
winter begins.
ber,
During some years an ice cover begins to form i n mid-Decem-
and can remain on at l e a s t part of the lake u n t i l March.
Dissolved
s o l i d s data c o l l e c t e d during two winters (Stein and Coulthard 1971)
indi-
cate l i t t l e v e r t i c a l v a r i a t i o n and r e l a t i v e l y complete mixing during the
period of i c e cover.
For v a l i d a t i o n purposes mixing data f o r 1969-70 i s used, and
for prediction purposes an "average mixing year" i s developed by
computing
58
mean mixing volume v a r i a t i o n s for the years 1967-71.
These are shown i n
Table A - l of Appendix A.
C.
DEVELOPMENT OF SUBMODELS
The detailed development of f i v e submodels i s described i n t h i s
section:
eddy d i f f u s i o n , sedimentation,
i n t e r n a l loading, primary
production, and dissolved oxygen.
1.
Eddy D i f f u s i o n Submodel
Eddy d i f f u s i o n i s commonly regarded as the main mechanism of
v e r t i c a l heat transport through the water column of a thermally s t r a t i f i e d lake (Mortimer 1942, Hutchinson
sidered by Lerman and S t i l l e r
1957).
The same mechanism i s con-
(1969) and O'Melia (1972) to be responsible
for the transport of dissolved substances,
including phosphorus, through
the water column.
Upward transport of soluble phosphorus from hypolimnion
to e p i -
limnion can produce high concentrations of phosphorus i n the euphotic
zone (O'Melia 1972).
O'Melia c a l c u l a t e s that the v e r t i c a l f l u x of phos-
phate to the epilimnion of the Vierwaldstatersee (Switzerland) can exceed
inputs of phosphorus from land runoff during summer stagnation.
For t h i s
2
c a l c u l a t i o n O'Melia assumes an eddy d i f f u s i o n c o e f f i c i e n t of 0.05 cm /sec
i n a thermocline 5 m thick with a concentration gradient of 0.02 mg/1 of
2
inorganic phosphorus across the thermocline.
The r e s u l t
(0.6g/m »year) i s
equal to the estimated t o t a l phosphorus loading from the land to the lake,
and exceeds the "permissible loading" l e v e l proposed by Vollenweider
for a lake of the Vierwaldstatersee's mean depth (104 m).
(1968)
59
(a) Simplifying Assumptions f o r Eddy D i f f u s i o n .
Three major
processes are considered to dominate the eddy d i f f u s i o n process in s t r a t i f i e d lakes: (1) turbulence i s the d r i v i n g force which determines
tensity and r a t e of eddy d i f f u s i o n ;
(2) temperature
the i n -
differences between
epilimnion and hypolimnion cause thermal s t r a t i f i c a t i o n which i n h i b i t s
eddy d i f f u s i o n ; (3) the concentration gradient of dissolved
substances
between s t r a t i f i e d layers determines the net transport between the l a y e r s .
Turbulence i s caused mainly by wind which mixes the epilimnion to varying
degrees.
Attempts to model thermocline development from wind data have
not been very s a t i s f a c t o r y
(Hutchinson 1957), making turbulence a d i f f i -
c u l t process to quantify i n lakes.
Furthermore,
i n order to v e r i f y a
model f o r turbulence e f f e c t s , d e t a i l e d temperature
Unfortunately, v e r t i c a l temperature
only twice a month.
records are necessary.
p r o f i l e s from Skaha Lake are a v a i l a b l e
For these reasons, turbulence i s assumed to be con-
stant i n the eddy d i f f u s i o n model, and the epilimnion i s considered to be
continually mixed to the thermocline.
Thermal s t r a t i f i c a t i o n and the phos-
phorus concentration gradient are the processes considered i n t h i s submodel.
(b) Equation for Eddy D i f f u s i o n Transport.
An expression d e s c r i b -
ing transport of soluble phosphorus between hypolimnion and epilimnion i s :
P
where P
E
= k C A
e g t
i s the rate of phosphorus movement by eddy d i f f u s i o n (kg/day); k
i s the c o e f f i c i e n t of eddy d i f f u s i o n (a function
C
2
of temperature, m /day);
i s the concentration gradient of soluble and c o l l o i d a l phosphorus across
the thermocline (kg/m
3
*m);
and A
2
i s the area of the thermocline (m ).
The
60
simplifying assumption i s made that turbulence caused by wind mixing i s constant during the s t r a t i f i e d period, and that complete mixing occurs within
the
epilimnion.
C o l l o i d a l and soluble phosphorus involved i n eddy d i f f u -
sion amount to approximately 30% of the t o t a l phosphorus content i n Skaha
Lake (calculated from Stein and Coulthard 1971 and Williams 1972).
(c) C o e f f i c i e n t of Eddy D i f f u s i o n .
Estimation of this c o e f f i c i e n t
i s the major t h e o r e t i c a l consideration of t h i s submodel.
Lerman and
Stiller
(1969) review three methods f o r the estimation of the c o e f f i c i e n t , of which
the
f i n i t e difference method i s the most applicable f o r modelling on a sea-
sonal basis.
The method i s used extensively i n studies of d i f f u s i o n and heat
movement, and i s based on replacing the d i f f e r e n t i a l s by differences between
the
temperature values i n two p r o f i l e s recorded at times t and t+1 (Lerman and
S t i l l e r 1969).
six
The following equation expresses the r e l a t i o n s h i p i n terms of
temperatures:
three at time t at depths z-1, z, and z+1, and three at
time t+1 at the same depths (Lerman and S t i l l e r 1969):
k
where M
X
= x K /x D
l2
t
2
i s the thickness of the metalimnion (thermocline) (m);
D
x
e
i s the time period chosen (day);
= T
1
2
=
( T
- T
z,t
z,t+l
z-l,t
+
T
«-l t+l
)
i
=
2 ( T
z,t
+
+
(
Vl,t
+
Vu.t+l*
where T i s temperature (°C).
C o e f f i c i e n t s f o r the s t r a t i f i c a t i o n period of 1969-70 are calculated from temperature p r o f i l e s and presented i n Table A - l i n Appendix A.
The
values are i n the same range of magnitude and v a r i a t i o n as those calculated by
61
O'Melia f o r the Vierwaldstattersee (1972) and by Lerman and S t i l l e r f o r Lake
Tiberias (1969).
2.
Sedimentation Submodel
This submodel considers only the downward movement of p a r t i c u l a t e
phosphorus by sedimentation.
Regeneration back from lake sediments i s con-
sidered i n the succeeding submodel (internal loading). Sedimentation processes
from the epilimnion and hypolimnion are considered to be d i f f e r e n t , and are
dealt with separately.
(a) Sedimentation from the Epilimnion.
Sedimentation of phosphorus
from the epilimnion occurs i n both inorganic and organic forms.
mechanisms predominate
Different
i n the sedimentation of each form.
(1) Sedimentation of Inorganic Phosphorus.
There are two
major mechanisms responsible for the sedimentation of inorganic phosphorus
in lakes:
(1) chemical p r e c i p i t a t i o n of phosphorus minerals; and (2) adsorp-
tion of phosphate onto the surface of the lake sediment.
a. P r e c i p i t a t i o n of Phosphorus Minerals.
There are three
phosphorus mineral groups which may be involved i n inorganic p r e c i p i t a t i o n :
the calcium phosphates, the iron phosphates, and the aluminum phosphates.
The
mineralogy and stoichiometry of a l l these groups are complicated (Kramer et
al. 1972).
It i s possible to calculate the equilibrium s t a b i l i t y r e l a t i o n s h i p s
of the apatites, v a r i s c i t e , and strengite using pK values, assuming average concentrations of the cations (Ca, Fe, A l ) , and knowing the pH of the water and
concentration of soluble phosphate
(Kramer et al. (1972).
Modelling the sea-
sonal v a r i a t i o n of these variables Is beyond the scope of t h i s i n v e s t i g a t i o n .
Furthermore,
i n eutrophic lakes such as Skaha, the sedimentation of organic
phosphorus i s considered q u a n t i t a t i v e l y more important than inorganic
62
phosphorus.
However, an u n d e r s t a n d i n g
o f t h e pathways o f c h e m i c a l
precipi-
t a t i o n o f phosphates i n l a k e s i s p e r t i n e n t t o t h i s d i s c u s s i o n .
Stumm (1964) c o n c l u d e s t h a t h y d r o x y a p a t i t e
may l i m i t phosphate
_3
(PO^
) concentrations
i n l a k e s t o 0.03 mg/1; he computes from t h e o r e t i c a l
e q u i l i b r i u m r e l a t i o n s h i p s t h a t t h e e q u i l i b r i u m c o n c e n t r a t i o n o f phosphate
i n contact with hydroxyapatite
i s 0.03 mg/1 a t a pH o f 7, and t h a t a d d i -
t i o n s o f phosphate beyond t h i s l e v e l would cause p r e c i p i t a t i o n o f h y d r o x y a p a t i t e i n the sediments.
and
f i e l d observations
p l a y s an i m p o r t a n t
waters."
However, Lee (1970) p o i n t s o u t t h a t l a b o r a t o r y
i n d i c a t e t h a t ". . . i t i s d o u b t f u l t h a t
hydroxyapatite
r o l e i n t h e e n v i r o n m e n t a l c h e m i s t r y o f phosphate i n n a t u r a l
Lee o b s e r v e s t h a t t h e r e a r e many e u t r o p h i c l a k e s where t h e c o n c e n -
t r a t i o n o f phosphate g r e a t l y exceeds 0.03 mg/1 (the M a d i s o n , W i s c o n s i n l a k e s
t y p i c a l l y have 10 t o 50 t i m e s t h i s amount), and h y d r o x y a p a t i t e
nant f o r m o f sediment phosphorus.
i s n o t a domi-
P o r c e l l a et al. (1971) c o n c l u d e t h a t w h i l e
Stumm's h y p o t h e s i s may be a p p l i c a b l e t o o l i g o t r o p h i c l a k e s , i t i s i n c o n s i s t e n t
with the observation
i n e u t r o p h i c l a k e s t h a t phosphate c o n c e n t r a t i o n s
d u r i n g a l g a l a c t i v i t y and do n o t i n c r e a s e a g a i n u n t i l autumn m i x i n g
decrease
occurs.
They n o t e t h a t b i o l o g i c a l g r o w t h and d e c o m p o s i t i o n , as w e l l as t h e s e c o n d a r y
e f f e c t s o f m i c r o b i a l r e a c t i o n s on pH, b e t t e r e x p l a i n t h e o b s e r v e d c y c l i n g o f
nutrients i n eutrophic
lakes.
E x p e r i m e n t s i n a h e t e r o t r o p h i c b i o l o g i c a l r e a c t o r (a t a n k s i m u l a t i n g
a e u t r o p h i c l a k e ) i n d i c a t e t h a t removal o f phosphorus by t h e s e d i m e n t a t i o n o f
dead a l g a l c e l l s i s q u a n t i t a t i v e l y more i m p o r t a n t
t a t i o n o f p h o s p h a t e s (Tenney et at. (1972).
removal occurs
than the chemical
precipi-
I t was found t h a t no phosphate
i f t h e biomass i s removed from the s u s p e n s i o n and c o n t i n u e d
63
aeration proceeds, even at r e l a t i v e l y high pH values.
It i s concluded that
chemical conditions i n Skaha Lake (maximum recorded pH of 9.2) are not conducive to s i g n i f i c a n t chemical p r e c i p i t a t i o n of insoluble
phosphates.
While Williams (1973) reports that the majority of the phosphorus
i n the s u r f i c i a l sediments of Skaha Lake i s i n the form of hydroxyapatite
(70%), he concludes that the apatite comes d i r e c t l y from the s o i l and rocks
of the watershed, not from chemical p r e c i p i t a t i o n within the lake.
e r a l o g i c a l composition of the bedrock supports this hypothesis.
The
min-
The depofii-
t i o n a l pattern of apatite sedimentation shows that the highest concentrations
occur i n the northern basin near the inflow of the Okanagan River.
Locally
high apatite concentrations exist near areas of probable erosion and transport from the watershed.
Williams concludes that the hydroxyapatite plays
l i t t l e or no r o l e i n the phosphorus cycle of the lake waters, either before
or a f t e r deposition.
Personal communication with Williams confirms that
stream input estimates of phosphorus probably do not include apatite, as i t
i s a r e l a t i v e l y heavy mineral not normally sampled with conventional stream
sampling techniques.
These findings support the hypothesis that chemical
p r e c i p i t a t i o n of hydroxyapatite has l i t t l e ,
i f any, e f f e c t on the phosphorus
budget of Skaha Lake water.
b. Adsorption of Phosphate.
Since t h i s sedimentation
mechanism i s assumed to be s i g n i f i c a n t only during the mixing period (November to March) when the epilimnion does not e x i s t , i t w i l l be discussed i n
the section on sedimentation from the hypolimnion.
(2) Sedimentation of Organic Phosphorus.
Seasonal v a r i a t i o n i n
the sedimentation of organic phosphorus i s assumed to be a function of p r i -
64
mary production i n the epilimnion, which r e s u l t s i n the sedimentation of
organic matter.
Evidence supporting t h i s assumption
comes from many inves-
tigators.
In a study of oxygen-nutrient relationships i n the central basin
of Lake E r i e , Eurns and Ross (1972) report that high rates of oxygen depletion occur i n the same areas as profuse primary productivity.
They conclude
that since approximately 88 per cent of the hypolimnetic oxygen was consumed
i n the decay of organic materials during the summer of 1970,
i t i s probable
that a massive a l g a l bloom was the major cause of anaerobic conditions that
subsequently developed i n the hypolimnion.
(the
The bloom caused " a l g a l r a i n s "
sedimentation of dead a l g a l c e l l s from the epilimnion to the hypolimnion,
and then to the sediment) which formed a f l u f f y green layer on the bottom, 2
to 3 cm thick.
Much phosphorus accompanied the sedimentation of these a l g a l
c e l l s , a portion of which was regenerated back to the hypolimnion following
decomposition
(details of t h i s process are discussed i n the next section on
i n t e r n a l loading).
Williams and Mayer (1972) summarize the s i g n i f i c a n c e of
t h i s elegant study:
"We now know that the summer months have been
marked by a tremendous increase i n the deposition of phosphorus on the sediment-water interface, i n the form of a l gal remains, and that a high proportion of t h i s algal-derived
phosphorus i s retained by the sediments during [the aerobic
portion of] t h i s period."
Hutchinson
(1957) describes an experiment by Elnsele
(1941) i n
which phosphatewas a r t i f i c i a l l y added to the eutrophic Schleinsee to study
the uptake of soluble orthophosphate by organisms and subsequent
sedimentation.
The t o t a l organic (soluble and p a r t i c u l a t e ) phosphorus increased almost as
much as the inorganic phosphorus decreased, and i t was evident that phosphate
65
was being taken up very r a p i d l y and sedimented
as p a r t i c u l a t e organic
phosphorus.
Sedimentation rates of phosphorus have been measured i n eutrophic
lakes during extreme summer s t r a t i f i c a t i o n i n two ways:
tracing; and
(2) actual measurement with sediment traps.
method, Hutchinson
(1)
radiophosphorus
Using the former
(1950) found that about two per cent of the t o t a l phos-
phorus i n the trophogenic layersedimented d a i l y , while Rigler (1964) reports
a d a i l y loss of about one per cent.
These values are similar to those ob-
tained by Bosch f o r the Vierwaldstattersee from analyses of the phosphorus
content of sediment traps (Gachter 1968).
Bosch found that 1.4
to 2.5 per
cent of the phosphorus i n the trophogenic layer ended up i n the sediments
daily.
Seasonal v a r i a t i o n , and e s p e c i a l l y the response to a l g a l blooms, i s
not reported i n these investigations.
Rigler (1973) observes that these
rates of phosphorus loss are consistent with Hutchinson' s r e s u l t s (1938)
showing the hypolimnetic oxygen d e f i c i t i n four lakes to be d i r e c t l y prop o r t i o n a l to the amount of p a r t i c u l a t e organic matter i n the water.
The following expression describes sedimentation of organic phosphorus from the epilimnion to l i t t o r a l sediments and the hypolimnion:
POT. = B
c
where P
SE
SE
sk pb k re
i s the rate of organic phosphorus sedimentation from the e p i l i m -
nion (kg/day), B
s
i s the rate of sedimentation of phytoplankton c e l l s (bio-
mass) from the epilimnion (kg/day), k ^ Is the c o e f f i c i e n t of phosphorus i n
phytoplankton biomass (kg phosphorus/kg dry weight phytoplankton), and k
is
the c o e f f i c i e n t of phosphorus r e c y c l i n g within the epilimnion (dimensionless).
66
T h i s i s a c o n s e r v a t i v e e s t i m a t e o f o r g a n i c phosphorus s e d i m e n t a t i o n , as i t
i s o u t s i d e o f t h e scope o f t h i s r e s e a r c h t o a c c o u n t f o r s e d i m e n t a t i o n l o s s e s
of
z o o p l a n k t o n and h i g h e r t r o p h i c l e v e l s .
While t h i s e x p r e s s i o n d e s c r i b e s
t h e amount l o s t from t h e e p i l i m n i o n , i t i s i m p o r t a n t t o n o t e t h a t about 17
per c e n t o f t h i s amount ends up i n l i t t o r a l
to
sediments and 83 p e r c e n t goes
t h e h y p o l i m n i o n (based on a s u r v e y o f t h e l i t t o r a l a r e a o f Skaha Lake,
S t o c k n e r et al. 1972b).
T h i s I n f o r m a t i o n i s used
i n the f o l l o w i n g
section
on i n t e r n a l l o a d i n g , o r r e g e n e r a t i o n from t h e sediments.
The biomass o f p h y t o p l a n k t o n s i n k i n g f r o m t h e e p i l i m n i o n each
day
(B ) i s e s t i m a t e d by t h e f o l l o w i n g r e l a t i o n s h i p :
BS
p
where B i s t h e biomass o f p h y t o p l a n k t o n i n t h e t r o p h o g e n i c l a y e r ( k g ) and Sp
i s t h e r a t e o f s i n k i n g a s c e l l s sediment
o u t o f t h e t r o p h o g e n i c l a y e r (day "*").
Both B and Sp a r e e s t i m a t e d by t h e p r i m a r y p r o d u c t i o n submodel i n a f o l l o w i n g
section of t h i s chapter.
The c o e f f i c i e n t o f phosphorus i n p h y t o p l a n k t o n biomass ( k ^ ^ ) I s
c a l c u l a t e d f r o m t h e a s s u m p t i o n t h a t p h y t o p l a n k t o n have, on the a v e r a g e , a
f i x e d c o m p o s i t i o n o f the major elements.
f i n e d an average organism
R e d f i e l d et at. (1963) have de-
s t o i c h i o m e t r y o f ^^06^16^1^263^110
t
*
ie
o c e a n s
«
T h i s r a t i o i s v e r y s i m i l a r t o a C:N:P r a t i o i n t h e p a r t i c u l a t e o r g a n i c m a t t e r
i n t h e w a t e r above t h e t h e r m o c l i n e i n Lake E r i e o f 122:18:1 (Burns and Ross
1972).
A l t h o u g h a n a l y s e s o f organisms do n o t always agree w i t h t h i s
composi-
t i o n and c a n v a r y due t o " l u x u r y " uptake o f a v a i l a b l e phosphorus (Kramer et
al.
1972) i t i s a r e a s o n a b l e a p p r o x i m a t i o n f o r m o d e l l i n g p u r p o s e s .
c u l a r weight o f t h i s average m o l e c u l e
The mole-
( d r y w e i g h t ) o f o r g a n i c m a t t e r i s 3551
67
g-atoms, and the phosphorus portion weighs 31 g-atoms; the resultant f r a c t i o n of phosphorus i n a mass of organic matter i s 31/3551, or 0.0090.
There-
fore, the c o e f f i c i e n t of phosphorus i n plankton (by weight) i s approximated
as 0.009 mg P/mg
dry weight of phytoplankton.
s l i g h t l y higher figure of 0.011
Strickland (1965) reports a
for diatoms i n the ocean.
The c o e f f i c i e n t of r e c y c l i n g , k
» I
s
estimated according to the
quantity of organic matter decomposed within the epilimnion, thereby r e l e a s ing soluble phosphate f o r reuse by plankton and preventing t h i s portion of
epilimnion phosphorus from sedimenting to the hypolimnion.
Kajak et al. (1970)
found that 63 per cent of t o t a l primary production i n several P o l i s h lakes
was decomposed i n the epilimnion, therefore never sedimenting to the hypolimnion.
Of the remaining 37 per cent which reached the hypolimnion as seston,
19 per cent was decomposed i n the hypolimnion and 18 per cent was decomposed
in the sediments.
It i s estimated from these r e s u l t s that approximately 60
per cent of the phosphorus i n organic matter remains and i s decomposed i n
the epilimnion, and that the c o e f f i c i e n t of r e c y c l i n g (which indicates that
percentage reaching the hypolimnion) i s approximately
(b) Sedimentation From the Hypolimnion.
from the hypolimnion result from two major mechanisms:
0.4.
Sedimentation losses
(1) inorganic s e d i -
mentation by adsorption on the bottom sediments; and (2) organic sedimentation
of a l g a l c e l l s .
(1) Sedimentation of Inorganic Phosphorus.
phorus sedimentation during the growing season i s assumed to be
While phosdominated
by organic forms, the assumption i s not v a l i d during the period of complete
mixing when low water temperatures and decreased solar r a d i a t i o n cause organic
68
production to be minimal.
During t h i s period (mid-November to mid-April)
soluble inorganic forms of phosphorus are not r a p i d l y taken up by organisms
and the concentration of dissolved orthophosphate
phorus) increases.
(or soluble reactive phos-
It i s suggested that during t h i s six-month period the
dominant mechanism of phosphorus
phate by the sediments.
sedimentation i s adsorption of orthophos-
R e l a t i v e l y complete mixing takes place during t h i s
period (except f o r s l i g h t inverse s t r a t i f i c a t i o n i n mid-winter), r e s u l t i n g i n
a reasonably uniform d i s t r i b u t i o n of soluble phosphorus
column and enabling sediment-water
throughout the water
contact at a higher rate than possible dur-
ing s t r a t i f i c a t i o n .
Adsorption reactions are important i n c o n t r o l l i n g the exchange of
phosphorus between sediments and the overlying water, and many studies i n dicate that
phosphate tends to be r e a d i l y adsorbed to lake sediments (Lee
1970, Golterman 1973, Williams and Mayer 1972).
Williams and Mayer (1972)
report that sorbed phosphorus accounts f o r up to 50 per cent of the t o t a l phosphorus i n the s u r f i c i a l sediments of Lake E r i e .
Eighteen per cent of the
phosphorus i n the s u r f i c i a l sediments of Skaha Lake i s composed o f sorbed
phosphorus, which i s the most abundant form after apatite (which accounts
f o r 70 per cent)(Williams 1973).
The adsorption of phosphorus by lake muds has been quantified with
radiophosphorus experiments by Olsen (1958).
For oxidized sediments, Olsen
found that phosphate equilibrium between sediments and water i s described
as the d i f f e r e n c e between gross adsorption (a) and release back to the water
(r).
The gross adsorbed amount follows the Freundlich adsorption isotherm,
v
expressed as k C
where k and v are constants for the p a r t i c u l a r type of
a
a
a
69
sediment and C i s the concentration of orthophosphate i n the water.
Arm-
strong and Gloyna (1967) used a s i m i l a r form of the Fr.eundlich adsorption
isotherm to describe the adsorption of radionuclindes to aquatic sediments.
Olsen (1958) found that release back to the water i s expressed as
-v
k C
r
where k and v are constants f o r the sediment and C i s the concentrar
r
t i o n of orthophosphate i n the water (mg/1).
The expression f o r net adsorp-
tion (loss from the water to the sediment) i s :
net adsorption = gross adsorption - release (a-r)
v
= k C
a
a
where adsorption i s i n mg P/kg of sediment
-
-v
k C
r
r
(dry weight) (Figure 6)«
It i s
assumed that approximately the upper one mm of sediment i s involved i n the
adsorption process (Olsen 1958), which means that 1.7 x 10^ kg of sediment
2
are involved (assuming the area of the north basin to be 17 km
and the speci-
f i c g r a v i t y of the sediment i s 0.1). For a calcerous lake sediment, Olsen found
the constants to be:
k = 171, k = 13.5, v =0.17, and v =0.5.
a
' r
' a
'
r
(2) Sedimentation of Organic Phosphorus.
Sedimentation of orga-
nic phosphorus from the hypolimnion can be described by the following expression
k ,(0.83)?,^
rh
SE
where k ^ i s the recycling c o e f f i c i e n t f o r organic phosphorus within the e p i limnion (day "^), 0.83 i s the proportion of phosphorus sedimenting from the
epilimnion which reaches the hypolimnion, and P
i s the rate of sedimentation
SE
of phosphorus from the epilimnion (kg/day).
It i s assumed that a percentage of the organic phosphorus which
sediments to the hypolimnion from the epilimnion w i l l decompose i n lower waters
70
Figure 6. Adsorption of phosporus on an oxidized calcerous
sediment (Olsen 1958).
71
before reaching the sediment.
The r e c y c l i n g c o e f f i c i e n t , ^ »
r n
r e f l e c t s the
proportion of organic phosphorus which f i n a l l y reaches the bottom of the
lake.
Kajak et al.
(1970) found that of 37 per cent of the organic matter
in the epilimnion which reached the hypolimnion, 19 per cent was decomposed
in hypolimnetic water
and 18 per cent reached the bottom of the lake.
These
r e s u l t s indicate that about half of the organic matter reaching the hypolimnion i s decomposed i n the water before f a l l i n g to the sediment, and thus the
r e c y c l i n g c o e f f i c i e n t f o r the hypolimnion i s approximated
as 0.5/day.
Not a l l of the phosphorus sedimenting from the epilimnion reaches
the hypolimnion.
Assuming horizontal homogeneity of t o t a l phosphorus i n the
water, a percentage equal to the area of the l i t t o r a l zone w i l l sediment i n
the l i t t o r a l .
Since the area of the l i t t o r a l zone i s 17 per cent of the t o t a l
area (Stockner et al. 1972b), 17 per cent of phosphorus sedimenting from the
epilimnion w i l l end up i n the l i t t o r a l and the remainder
reach hypolimnetic waters.
Therefore, 83 per cent of P
(83 per cent) w i l l
w i l l reach the hypo-
SE
limnion.
(3) Resulting Expression f o r Sedimentation From the
Hypolimnion.
The following expression describes sedimentation of inorganic and organic phosphorus from the hypolimnion:
P
SH
= adsorption loss + organic sedimentation
-
where P
(k C
a
V a
-k C
r
V r
)S
d +
k
r h
(0.83)P
S E
i s the sedimentation of phosphorus from the hypolimnion
on
and Sj i s the dry weight of sediment involved i n adsorption (kg).
(kg/day)
72
3.
I n t e r n a l Loading
Submodel
I n t e r n a l l o a d i n g o f phosphorus i n a l a k e i s the amount
from the sediments f o l l o w i n g t h e i n i t i a l
sedimentation
loading
regenerated
gross
sedimentation
process.
c o u l d be c o n c e p t u a l i z e d a s g r o s s
sedimentation
minus i n t e r n a l
(regeneration).
Although
net s e d i m e n t a t i o n
i s t h e amount o f
Net
import-
ance t o " e u t r o p h i c a t i o n l i m n o l o g i s t s " , the mechanisms i n v o l v e d i n g r o s s
sedimentation
and subsequent r e g e n e r a t i o n a r e q u i t e d i f f e r e n t and
m o d e l l e d s e p a r a t e l y i f an a c c u r a t e e s t i m a t e
of n e t s e d i m e n t a t i o n
must be
i s t o be
achieved.
The
importance of i n t e r n a l l o a d i n g t o t h e phosphorus budget o f l a k e s
can be g r e a t , e s p e c i a l l y d u r i n g a n a e r o b i c
generate
c o n d i t i o n s when the sediments may r e -
more phosphorus t o t h e l a k e than incoming streams and groundwater (ex-
ternal loading) contribute.
the e u t r o p h i c B a l d e g g e r s e e
During
two summers of h y p o l i m n e t i c
(Switzerland) gained
f o u r times a s much phosphorus
from sediment r e g e n e r a t i o n than from e x t e r n a l s u r f a c e l o a d i n g
cited
i n Vollenweider
1968).
conditions,
(Bachofen,
The s i t u a t i o n r e v e r s e d d u r i n g a e r o b i c c o n d i t i o n s
when more phosphorus was taken up (on a d a i l y r a t e ) by t h e sediments than had
been r e l e a s e d d u r i n g a n a e r o b i c c o n d i t i o n s .
In t h e c e n t r a l b a s i n o f Lake E r i e i n t e r n a l phosphorus l o a d i n g d u r i n g
anaerobic
c o n d i t i o n s c o n t r i b u t e d 1.1 times
(Burns and Ross 1972).
During
t h e amount from e x t e r n a l l o a d i n g
a e r o b i c c o n d i t i o n s t h e sediments s t i l l
phorus t o t h e o v e r l y i n g water, but the amount was o n l y 25 p e r c e n t
t e r n a l l o a d i n g d u r i n g t h e same p e r i o d .
phosphorus which r e t u r n e d
lost
phos-
of t h e ex-
The p e r c e n t a g e o f sedimented
organic
to t h e water under a e r o b i c c o n d i t i o n s was 25 per cent
(a f i g u r e c o i n c i d e n t a l w i t h t h e p r e c e e d i n g
25 p e r c e n t ) .
During
the two months
73
of anaerobic conditions, 1.7 times the sedimented
organic phosphorus returned
to the water.
Burns and Ross suggest that a p o s s i b l e explanation f o r the low percentage of phosphorus regeneration (25 per cent) during aerobic conditions i s
that most of the orthophosphate
produced
xides.
regenerated from b a c t e r i a l decomposition i s
on the lake bottom i n close proximity to p r e c i p i t a t e d f e r r i c
hydro-
This s i t u a t i o n would lead to the formation of insoluble f e r r i c hydroxy-
phosphate complexes.
While these complexes would l i k e l y dissolve i f conditions
subsequently became anaerobic, they would remain insoluble while the hypolimnion
remained aerobic (Burns and Ross 1972).
(a) Mechanisms Controlling Phosphorus Transport at the SedimentWater Interface.
Five major mechanisms control the transfer of nutrients from
sediments to the hypolimnion:
diffusion;
(1) physical disturbance and mixing;
(3) b i o l o g i c a l uptake;
(2) physical
(4) anaerobic chemical regeneration; and
(5)
decomposition regeneration.
(1) Physical Disturbance and Mixing.
on the exchange of dissolved substances between mud
In h i s c l a s s i c a l papers
and water, Mortimer (1941,
1942) observed that ordinary processes of molecular d i f f u s i o n were extremely
slow i n transmitting material between sediments and water.
Physical processes
that speed up transmission are mixing during overturn periods, horizontal movement of water over the benthos (which increases eddy d i f f u s i o n ) , convection
currents under winter ice cover, and movement of benthic organisms
1941).
(Mortimer
Seiche action would also contribute to eddy d i f f u s i o n at the i n t e r -
face (T.G. Northcote, personal communication).
quantify.
These losses are d i f f i c u l t to
74
Following a period of high winds on Lake E r i e , Kramer et al. (1970)
report increases i n soluble orthophosphate and suspended mineral material in
the
water.
In the l i t t o r a l area of the Bodensee Siessegger (1968) reports
that a g i t a t i o n of the sediment a f t e r storms caused a 100-fold orthophosphate
increase i n the overlying water.
U i t h i n 18 hours of the storm the orthophos-
phate concentration was halved.
Regeneration of phosphorus by t h i s mechanism
i s of more significance f o r l i t t o r a l zones and shallow.lakes than f o r deep lakes
because of greater e f f e c t s on the sediments due to wind, wave and current action.
A c t i v i t y by benthic organisms, such as t u b i f i c i d worms, results
in
phosphorus loss from sediments (Whitten and Goodnight 1967).
feeding
Bottom-
f i s h such as carp and perch species deplete the sediment of organic
forms of phosphorus.
The s i g n i f i c a n c e of these losses from the sediments,
although not q u a n t i f i e d , i s probably not great (Williams and Mayer 1972).
(2) Physical D i f f u s i o n .
Regeneration to the water can occur
as a r e s u l t of d i f f u s i o n of soluble phosphorus out of the sediments due to a
difference i n concentration of soluble phosphorus between the i n t e r s t i t i a l
water
of the sediment and the overlying water (Williams and Mayer 1972).
soluble
phosphorus regenerated may form through diagenesis of sedimented par-
t i c u l a t e phosphorus within the sediments.
the
The
The rate of d i f f u s i o n depends on
concentration difference between the sediment i n t e r s t i t i a l water and the
overlying water, the porosity of the sediment, and the c i r c u l a t i o n of water
over the mud surface (Williams and Mayer 1972).
These variables have not
been determined for Skaha Lake.
According to Williams and Mayer (1972), the role of the oxidized
microzone at the interface i n c o n t r o l l i n g regeneration has not been adequately
75
evaluated. Although i t has been suggested that the microzone acts as a b a r r i e r
to the exchange of phosphorus across the interface because of the presence of
f e r r i c iron, i t i s questionable whether the b a r r i e r i s e f f e c t i v e when the
microzone i s unconsolidated.
Diagenetic formation of hydroxyapatite within sediments (an important
process i n the sediments of Skaha Lake) i s a mechanism which acts i n opposition
to the d i f f u s i o n of soluble phosphate into overlying water (Williams and Mayer
1972).
+2
Ca
For Lake E r i e and Lake Ontario sediments, the concentration of soluble
-3
, PO^ , and OH
ions i n the i n t e r s t i t i a l water of the sediments corresponds
very c l o s e l y to the s o l u b i l i t y product of hydroxyapatite (Sutherland et al. 1966,
Williams and Mayer 1972).
Hydroxyapatite, once formed, i s very u n l i k e l y to
participate in regeneration reactions.
Due to the d i f f i c u l t y
i n modelling the d i f f u s i o n process, the l a c k
of necessary data (especially the phosphorus concentration of i n t e r s t i t i a l s e d i ment water), and the lack of knowledge concerning i t s quantitative r o l e i n the
nutrient budget of lake sediments, modelling t h i s mechanism w i l l not be attempted.
(3)
B i o l o g i c a l Uptake.
Radiophosphorus studies show that l i t t o r a l
vegetation (especially macrophytes) can take up phosphorus from sediments d i r e c t l y , without f i r s t entering the water phase (Pomeroy et al. 1967).
Pomeroy finds
a rapid turnover time of several days between phosphorus i n the s u r f i c i a l
ments of a s a l t water marsh and Spavtina
(marsh grass).
sedi-
Uptake of s o l u b i l i z e d
sediment phosphorus by macrophytes and epiphytic algae probably takes place i n
the
l i t t o r a l zone of Skaha Lake (Stockner et al. 1972a), thereby preventing a
percentage of s o l u b i l i z e d phosphorus from organic decomposition from entering
the
water mass.
However, movement of phosphorus from epiphytic and macrophytic
76
vegetation to the water also occurs, and t h i s process would tend to diminish
the amount of net uptake by the vegetation (Hayes and P h i l l i p s 1958, Confer
1969).
For modelling purposes i t w i l l be considered that net movement of
phosphorus from sediments to water through b i o l o g i c a l uptake i s not s i g n i f i cant i n the o v e r a l l phosphorus budget of the lake.
(4) Anaerobic Chemical Regeneration. Mortimer (1941, 1942) r e ported
that when iron changes
from the f e r r i c form (under aerobic conditions) to
the ferrous form (under anaerobic conditions), i t changes from an insoluble to
a soluble state.
This means that phosphorus previously p r e c i p i t a t e d as i n -
soluble f e r r i c phosphate under aerobic conditions at the sediment-water i n t e r face, becomes soluble when the oxygen i s depleted i n the hypolimnion. The r e sult of the change to anerobic conditions can be a massive increase i n soluble
phosphate i n the hypolimnion of a lake (e.g. Lake E r i e , Burns and Ross 1972).
Although much of this soluble phosphate may r e p r e c i p i t a t e when autumn mixing
reoxygenates the hypolimnion, i t may be only a portion of the phosphorus l o s t
from the sediments during the anaerobic period.
Burns and Ross (1972) report
that the soluble r e a c t i v e phosphorus decreased by approximately 10 per cent
during the overturn, whereas the decrease would have been approximately 53 per
cent i f a l l the anaerobic soluble reactive phosphorus had converted to the
p a r t i c u l a t e form.
These r e s u l t s indicate that a s i g n i f i c a n t part of the s o l -
uble phosphorus (both organic and inorganic) regenerated under anaerobic cond i t i o n s ultimately re-enters the b i o l o g i c a l cycle of Lake E r i e .
Although
anaerobic hypolimnetic conditions have not yet occurred i n Skaha Lake, the
Lake Erie study indicates that a change to anaerobic conditions could result
in a phosphorus release of more than four times the amount released under
aerobic conditions.
77
(5) Decomposition Regeneration.
The
importance of bacteria i n
returning soluble nutrients to the water i n lakes i s stressed by McCoy and
Sarles (1969):
"Bacteria are the prime agents
of the return of dead organic matter (plant
and animal bodies) to the soluble s t a t e . "
This i s accomplished by the mineralization of organic nitrogen as NH*
or
NO^,
-3
and organic phosphorus as PO^
.
McCoy and
balanced mixture of bacteria i s present
Sarles point out that a w e l l -
i n temperate lakes to carry out degra-
dation of c h i t i n , c e l l u l o s e , pectins, proteins and other complex organic compounds.
Measurement of the f l u x between sediment mud
(including bacteria)
and soluble phosphate i s reported by Hayes and P h i l l i p s (1958) to be about
three days i n both d i r e c t i o n s .
sediment and water was
With no bacteria present the exchange between
slowed to 15 days.
Although phosphorus can be regenerated from phytoplankton c e l l s by
a u t o l y s i s i n addition to b a c t e r i a l decomposition, the r e l a t i v e importance of
the processes has not been adequately evaluated
(Hooper 1973).
the assumption i s made that most of the regeneration
Therefore,
occurs through b a c t e r i a l
decomposition.
The assumption i s made that b a c t e r i a l growth i s proportional to
a l g a l growth, and that b a c t e r i a l growth i s l i m i t e d by the same factors of
temperature and nutrients that l i m i t primary production;
assumed that as a l g a l populations
therefore i t w i l l be
increase during the growing season, b a c t e r i a l
populations w i l l increase proportionally and w i l l have the c a p a b i l i t y , under
optimum temperature conditions, of decomposing much of the organic matter produced by primary production.
Evidence for t h i s assumption comes from the work
78
bf Thomas (1969) showing that i n the Swiss Ziirichsee the same growth factors
that stimulate most freshwater algae also stimulate bacteria associated with
them.
Thomas shows that increases i n b a c t e r i a l density are d i r e c t l y propor-
t i o n a l to the phosphate content of the water at 20°C.
As w i l l be shown
i n the submodel on primary production, s i m i l a r r e l a t i o n s h i p s are true f o r
a l g a l production and phosphorus.
On the sediment surface of an aerobic lake with an abundant supply
of dead organic matter
Skaha), temperature
( a reasonable assumption
i n a eutrophic lake such as
w i l l probably be the most important factor c o n t r o l l i n g
the decomposition process.
McCoy and Sarles state that i n a northern temp-
erate climate a low rate of b a c t e r i a l a c t i v i t y i s maintained by r e l a t i v e l y
cold water temperatures
f o r about two-thirds of the year; during the summer
months, however, there i s a " f l u s h " of b a c t e r i a l a c t i v i t y which noticeably
increases the b a c t e r i a l decomposition of o r g a n i c a l l y held phosphorus.
The relationship between temperature
and b a c t e r i a l
decomposition
processes i s reported f o r the b a c t e r i a l community i n the sediments of eutrophic Lake Wingra, Wisconsin (Boylen and Brock 1973).
The r e s u l t s show that the
heterotrophic bacteria i n Lake Wingra sediments do not adapt to the low temperatures (1.0 - 1.5°C) which p r e v a i l i n winter.
Using the rate of glucose
uptake and C O 2 evolution as a measure of the difference i n decomposition
Boylen and Brock (1973) show that at the optimum temperature
rate,
(25° C) under aero-
b i c conditions, decomposition rates were f o u r - f o l d to 14-fold higher than at
the low temperature.
The authors conclude that a consequence of t h i s i s that
b a c t e r i a l decomposition processes should occur at a much slower rate during
winter than during summer (and i n the colder sediments of the hypolimnion),
79
and plant material that had not decomposed before cold weather set i n w i l l
decompose at l e a s t four times more slowly than i n warm sediments.
The r e s u l t s of Boylen and Brock indicate a nearly l i n e a r r e l a t i o n ship between decomposition rates at 5°C and 25°C, and t y p i c a l curves i n d i cate that decomposition occurs approximately four times f a s t e r at the higher
temperature than at the lower.
The l i n e a r i t y of the r e l a t i o n s h i p makes
possible the mathematical formulation of a c o e f f i c i e n t of decomposition, k^.
If we assume that k^ = 1 at 25°C, we can r e l a t e k^ to temperature by:
k, = .04T
d
where T i s sediment temperature
in o
,
C
Now i t i s possible to say that i n the summer when the epilimnion water and
l i t t o r a l sediments have a temperature of 20 - 25°C, organic matter w i l l decompose four times faster than i n the hypolimnetic sediments where the temperature i s 4 - 6°C.
The fact that the average concentration of organic phos-
phorus i n the deep sediments of Skaha Lake i s 3.2 times the average concent r a t i o n i n the l i t t o r a l sediments supports t h i s assumption
(b) Formulation of Internal Loading Submodel.
(Williams 1973).
The assumption i s
made that i n a eutrophic lake such as Skaha Lake, regeneration of phosphorus
from the sediments i s best r e f l e c t e d i n a submodel describing the decomposition
of
organic matter.
Since decomposition i s a function of sediment
temperature,
and since the l i t t o r a l zone i n summer has a much higher temperature than the
deep water sediments, separate submodels are developed for the two zones.
(1) L i t t o r a l Zone Regeneration.
summer temperatures i n the l i t t o r a l
sedimented phosphorus
The assumption i s made that at
(20 - 25°C) b a c t e r i a l decomposition of
i s returned either to l i t t o r a l vegetation or the water
80
mass.
This assumption i s supported by an intensive f i e l d
survey of the
l i t t o r a l sediments which showed the s u r f i c i a l sediments to be v i r t u a l l y devoid of organic matter i n the summer ( J . G. Stockner, personal communication).
The conclusion drawn' from t h i s evidence i s that the organic phos-
phorus which accumulates i n the l i t t o r a l sediments does so during the
winter when decomposition rates are much lower.
With the information that the l i t t o r a l area of Skaha Lake occupies
17 per cent of the t o t a l area of the lake, the following submodel i s proposed:
P
RL
°'
=
1 7 P
SE d
k
where P
i s the regeneration of phosphorus from the l i t t o r a l
RL
D T
(kg/day); P
SE
i s the sedimentation of phosphorus from the epilimnion (kg/day), and k^ i s
the c o e f f i c i e n t of decomposition which i s temperature dependant.
(2) Deep Water Sediment Regeneration.
Regeneration of phos-
phorus from deep water sediments occurs at a slower rate than from the
warmer l i t t o r a l
sediments.
cient of decomposition.
The lower temperature r e s u l t s i n a lower c o e f f i -
The following expression describes regeneration from
deep water sediments:
P
where P
RH
= k P
d SHorg
i s the regeneration of phosphorus from hypolimnetic sediments
k, i s the c o e f f i c i e n t of decomposition, and P„„
d
SHorg
r
i s the amount of organic
phosphorus sedimenting to the bottom of the hypolimnion (kg/day;
the sedimentation submodel, equal to 0.83 P ,k_ ).
OT:
u
(kg/day);
&
according to
81
4.
Primary Production Submodel
The primary production submodel i s formulated f o r the prediction
of the biomass of phytoplankton i n the trophogenic layer, or the upper 8 m
of the lake.
In addition to being of great interest i n the study of the
eutrophication problem, the p r e d i c t i o n of phytoplankton i s a necessary v a r i able i n the sedimentation submodel.
Marked seasonal v a r i a t i o n i n population density i s a characterist i c feature of phytoplankton i n northern temperate
lakes (Odum 1971).
Odum
gives the following d e s c r i p t i o n of a t y p i c a l phytoplankton growth season,
and the r e l a t i o n s h i p with temperature, l i g h t and nutrients:
"Very high densities which appear quickly
and p e r s i s t for a short time are c a l l e d "blooms" or phytoplankton "pulses." In the northern United States ponds
and lakes often exhibit a large early spring bloom and
another, usually smaller, pulse i n the autumn. The spring
pulse, which limnologists sometimes c a l l the "spring flowering", t y p i c a l l y involves the diatoms and i s apparently the
r e s u l t of the following combination of circumstances.
During the winter, low water temperatures and reduced l i g h t
r e s u l t i n a low rate of photosynthesis so that regenerated
nutrients accumulate unused. With the advent of favorable
temperature and l i g h t conditions the phytoplankton organisms, which have a high b i o t i c p o t e n t i a l , increase r a p i d l y
since nutrients are not l i m i t i n g f o r the moment ( i . e . , the
spring bloom). Soon, however, nutrients are exhausted and
the bloom disappears. When nutrients again begin to accumul a t e , n i t r o g e n - f i x i n g blue-green algae, such as Anabaena,
often are responsible for autumn blooms, these organisms
being able to continue to increase r a p i d l y despite a reduct i o n of dissolved nitrogen — that i s , u n t i l phosphorus,
low temperature, or some other factor becomes l i m i t i n g and
halts the population growth."
As the combination of temperature,
l i g h t and nutrient supply changes
seasonally, phytoplankton populations change q u a l i t a t i v e l y as well as quantitatively.
P e a r s a l l (cited i n Hutchinson 1967) a t t r i b u t e s the spring maxima
of diatoms i n English lakes to a temporarily high concentration of S i which
82
comes with the spring freshet.
He concludes that i n d i v i d u a l species have
d i f f e r e n t nutrient requirements, and succeed each other as the waxing popul a t i o n reduces the a v a i l a b l e supply.
The interactions of changing l i g h t
and temperature conditions along with changes i n nutrient supply r e s u l t i n
a very complex s i t u a t i o n .
Dinobryon
divergens
often replaces diatoms at the
end of the spring bloom when Ca and S i l e v e l s drop and the N:P r a t i o r i s e s .
In Douglas Lake, Michigan, A s t e r i o n e l l a bloomed during the autumn overturn
because of phosphorus-rich hypolimnetic waters
(anaerobic i n summer) mixing
with epilimnetic waters (Tucker 1957, c i t e d i n Hutchinson 1967).
(a) Other Phytoplankton Models.
An early model by Fleming, formu-
lated i n 1939, i s described by Patten (1968).
Fleming emphasized grazing
losses i n the following equation to describe the spring diatom bloom i n the
English Channel:
^ | = P [a - (b+ct)]
where P i s phytoplankton concentration; a i s a constant growth rate; and
(b+ct) i s a death rate r e s u l t i n g from zooplankton grazing.
The work of R i l e y and h i s co-workers
(1946, 1949, 1963, 1965) i n
modelling plankton populations i n the ocean represents the f i r s t
attempt to deal q u a n t i t a t i v e l y with the problem.
realistic
According to Patten (1968),
R i l e y , Stommel and Bumpus (1949) produced the f i r s t systems model, a set of
simultaneous d i f f e r e n t i a l equations containing negative feedback loops. In
s i m p l i f i e d form, R i l e y ' s formulation i s :
HP
~ = (PH - R - G - S + T)P
dT
where P i s the rate of change i n phytoplankton density; PH i s the rate of
83
photosynthesis (growth); R i s the rate of r e s p i r a t i o n ; G i s the grazing
rate (loss to zooplankton); S i s the sinking rate of dead c e l l s ; and T i s
the rate of upward movement due to turbulent eddies.
Riley's contribution
i s to r e l a t e the growth rate, r e s p i r a t i o n rate and grazing rate to basic environmental variables —
temperature, r a d i a t i o n , the e x t i n c t i o n c o e f f i c i e n t
of l i g h t i n water, and nutrient concentration. This r e s u l t s i n timev a r i a b l e c o e f f i c i e n t s , as the environmental components change throughout
the year.
Respiration i s determined by temperature, and photosynthesis i s
l i m i t e d by temperature, l i g h t and phosphate concentration. In general, R i l e y
found that observed values f o r phytoplankton density were within 25 per cent
of the calculated values during one annual cycle i n the waters at Georges
Bank o f f the coast of New England.
Steele (1956, 1964) proposed similar models to predict plankton
production i n the Gulf of Mexico and Fladen Ground.
He reports that a steady
state assumption does not e x i s t f o r shallow and deep layers i n the ocean,
and considers each of the two layers to have d i f f e r i n g inputs and outputs.
Steele uses a d i f f e r e n t expression than R i l e y to describe l i g h t penetration
and introduces a v e r t i c a l eddy d i f f u s i o n term, but r e l i e s on the same type
of mass balance formulation.
More recent models consider three major interdependent
systems:
n u t r i e n t s , phytoplankton and zooplankton (Chen 1970, D i Toro et al. 1971).
External environmental parameters
advective flow.
considered are temperature,
radiation and
Parker (1972) adds f i s h as a fourth major component to h i s
model of Kootenay Lake, but uses the same mass balance approach as Chen and
Di Toro.
84
(b) B a s i c P h y t o p l a n k t o n E q u a t i o n .
posed
A d i f f e r e n c e equation i s pro-
to d e s c r i b e p h y t o p l a n k t o n dynamics on a d a i l y b a s i s .
rate coefficients
of a d a i l y
f o r p l a n k t o n growth are d a i l y r a t e s , making the c h o i c e
time s c a l e p a r t i c u l a r l y u s e f u l .
The
p r e s s i o n d e s c r i b e s the biomass o f p h y t o p l a n k t o n
B
vesultinq
biomass
=
=
B
I
initial
biomass
T
+
(G
-
p
a v o w t } l
R
p
f o l l o w i n g g e n e r a l i z e d exi n the t r o p h o g e n i c zone:
—
Z
—
p
( k g ) ; B^
at the b e g i n n i n g o f the time p e r i o d ( k g ) ; G^
(day ^ ) ; R^
(day "*");
out of the t r o p h o g e n i c l a y e r ( d a y ^ ) ; and 0^
radi-
i s the g r a z i n g
as
i s the r a t e o f
Each o f these terms
discussed i n d e t a i l .
(c) P h y t o p l a n k t o n
p l a n k t o n dynamics i s the f a c t
Growth.
A b a s i c problem
As D i Toro et al.
i n m o d e l l i n g phyto-
that d i f f e r e n t s p e c i e s r e a c t d i f f e r e n t l y
the t h r e e most i m p o r t a n t e n v i r o n m e n t a l v a r i a b l e s :
and l i g h t .
temperature,
to
nutrients,
(1971) p o i n t o u t :
"The a v a i l a b l e i n f o r m a t i o n i s not
s u f f i c i e n t l y d e t a i l e d to s p e c i f y the growth
k i n e t i c s f o r i n d i v i d u a l phytoplankton species
i n n a t u r a l environments."
T h e r e f o r e , the pragmatic
approach
I
i n a loss
i s the r a t e of s i n k i n g
a d v e c t i v e l o s s from the o u t l e t o f the l a k e (day ^ ) .
is
p
, ~,
outflow
n u t r i e n t s and
i s endogenous r e s p i r a t i o n r a t e which r e s u l t s
r a t e o f zooplankton
0 )B
i s the d a i l y
o f o r g a n i c c a r b o n i n the p h y t o p l a n k t o n p o p u l a t i o n (day ^ ) ; Z^
c e l l s sediment
—
p
i s the i n i t i a l biomass o f
growth r a t e o f p h y t o p l a n k t o n , dependent on temperature,
ation
S
,,
. , .
.
. ,.
~ r>esp%vat%on - grastng - stnHng
-
where B i s biomass o f p h y t o p l a n k t o n
phytoplankton
Many p u b l i s h e d
o f D i Toro et al.
i s adopted, which i s to
85
ignore the problem of d i f f e r i n g species requirements f o r temperature, nutr i e n t s , and l i g h t .
The basic unit of kg of dry weight of phytoplankton
in the trophogenic zone (computed from concentrations i n mg/1) i s used
for the e n t i r e population, and average c o e f f i c i e n t s for growth and loss
are taken from the l i t e r a t u r e .
(1) Temperature Dependency.
I f nutrients and l i g h t are not
l i m i t i n g , the temperature of the water i s the s i g n i f i c a n t parameter l i m i t i n g
the growth rate of phytoplankton (Di Toro et al. 1971).
D i Toro et al. have
reviewed 22 experiments i n the l i t e r a t u r e which examine maximum growth rates
as a function of temperature, and conclude that a s t r a i g h t - l i n e f i t i s a
reasonable approximation of the data r e l a t i n g the maximum growth rate K^day
to temperature T(°C)(Figure 7):
K
T
=
k l
T
where k^ has values i n the range 0.10±0.025/day
• °C. The c o e f f i c i e n t k^
indicates an approximate doubling of the saturated growth rate for a
temperature change from 10 to 20°C, which i s consistent with the generally
accepted temperature-dependence
1971).
of b i o l o g i c a l growth rates (Di Toro et al.
The upper water temperature range i n Skaha Lake (near freezing to
25°C) f i t s i n t h i s range well enough for modelling purposes.
(2) Light Dependency.
The relationship between l i g h t
and photosynthesis i n water i s w e l l known:
l i g h t at low i n t e n s i t y (e.g.
photosynthesis i s limited by
during the winter), whereas the optimum i n -
tensity photosynthetic production i s limited by other factors (e.g.
ature and nutrients) (Vollenweider 1965).
temper-
Vollenweider (1965) has reviewed
86
o
•o
Temperature
°C
F i g u r e 7. Growth r a t e o f p h y t o p l a n k t o n as a f u n c t i o n o f
temperature ( a f t e r D i Toro e t a l . 1971).
87
s e v e r a l s i m i l a r models f o r c a l c u l a t i n g p h o t o s y n t h e s i s
on
the b a s i s
1952,
of p r i m a r y p r o d u c t i o n
T a i l i n g 1957,
Ryther and
and
light
Y e n t s c h 1957,
measurements
obtained
from
in situ
f l u x i n water
Steele
(Steemann
and
the a t t e n u a t i o n
coefficient
day)
of
(m "*") .
(1964, 1965)
uses a somewhat more e m p i r i c a l
the r e l a t i o n s h i p between l i g h t and
photosynthesis,
appropriate
f o r t h i s model because i t r e q u i r e s
l e s s d a t a and
growth i n h i b i t i o n a t h i g h
K
L
l i g h t i n t e n s i t y (Figure
I
= —
formulation
which seems
accounts f o r
8):
I
exp(l m
ing
•
photosynthetically
to d e s c r i b e
where
These
the
3
r a t e a t l i g h t optimum (g carbon/m
(dimensionless);
layer
Nielson
1960).
2
(g carbon/m ) w i t h
experiments); a f u n c t i o n o f the
active incident l i g h t
light
production
trophogenic
V o l l e n w e i d e r 1958,
models c a l c u l a t e the r a t e o f p r i m a r y p r o d u c t i o n
following information:
i n the
—)
m
i s the r e l a t i v e r a t e o f p h o t o s y n t h e s i s
(a c o e f f i c i e n t between 0 and
1, day
; I
when n u t r i e n t s are not
limit-
i s the average l i g h t i n t e n s i t y
a.
i n the
trophogenic layer(explained
and
i s the l i g h t
I
(langleys/day).
i n the f o l l o w i n g s e c t i o n ,
langleys/day);
i n t e n s i t y a t which p h y t o p l a n k t o n growth i s maximum
Steele
assumes t h a t I
i s a p p r o x i m a t e l y 0.5
I
i n winter
in
a
i n summer, w h i l e R y t h e r (1956) c o n s i d e r s h a l f of t o t a l i n c i d e n t
a.
s o l a r r a d i a t i o n t o be p h o t o s y n t h e t i c a l l y a c t i v e (making I = 0.5 I ) .
Di
m
a
and
0.3
Toro et
I
al.
(1971) use
a f i g u r e of 300
langleys/day
for I .
m
88
tn
in
d>
si
—
100
200
300
Light
400
500
600
700
Intensity ( ly/day)
Figure 8. Relative photosynthesis rate (percent of maximum)
as a function of l i g h t i n t e n s i t y (langleys/day). Theoretical
curve from equation by Steele (1956) and data points from
Manning and Juday (the response of a variety of phytoplankton
populations; c i t e d i n Edmonson 1956).
800
89
The preceding equation includes the symbol I , which represents
the average l i g h t i n t e n s i t y i n the trophogenic layer. The well-known BeerLambert r e l a t i o n describes the decrease of l i g h t i n t e n s i t y with depth i n
water:
1 = 1
z
where I
z
o
exp(-k z)
e
v
i s the l i g h t i n t e n s i t y (langleys/day) at depth z(m); I
cident incoming radiation (langleys/day); k
(m \
&
o
i s the i n -
i s the extinction c o e f f i c i e n t
explained below); and z i s the depth (m).
This r e l a t i o n has been i n -
tegrated for the photosynthetic layerby Riley (1946) to produce an expression
describing the average photosynthetic l i g h t i n t e n s i t y i n the trophogenic
layer:
I
I a =ck z"(l " exp(- ek z))
2
r v
g
where I
i s the average l i g h t i n t e n s i t y i n the trophogenic layer (langleys/
a.
day) and z i s the depth of the trophogenic layer (8 m i n this case). This
expression i s also used by Parsons and Takahashi (1973) i n comparing
growth
rates of two phytoplankton species of d i f f e r i n g c e l l aize.
The extinction c o e f f i c i e n t , k , i s a function of two major facg
tors:
(1) dissolved coloured material and p a r t i c u l a t e inorganic matter, and
(2) phytoplankton c e l l s , both of which reduce l i g h t i n t e n s i t y , thereby i n h i b i t i n g photosynthesis (Chen 1971, Di Toro et al. 1971).
I f the phytoplank-
ton concentration i s large, the e x t i n c t i o n c o e f f i c i e n t i s mainly a function
of this concentration, and the phytoplankton shade themselves from further
growth (Di Toro et al. 1971).
90
The follov;ing expression describes the e x t i n c t i o n c o e f f i c i e n t
as a function of these two causes (Chen 1970, Di Toro et al. 1971):
k
e
= k
+ k
ew
ep
where k
i s the r e s u l t of e x t i n c t i o n from coloured dissolved
ew
l a t e inorganic matter (m "*") and k
(m ^/mg/1 phytoplankton).
and p a r t i c u -
i s a result of phytoplankton
While i t i s d i f f i c u l t to completely
shading
separate
the two f a c t o r s , a measurement of l i g h t absorption during the winter (not
under i c e cover) when production i s minimal i s a good i n d i c a t i o n of k
ew
Edmondson (1956) describes a method for converting Secchi-disk measurements
to e x t i n c t i o n c o e f f i c i e n t s :
ew
D
where C i s an e m p i r i c a l l y determined dimensionless
i s the Secchi-disc transparency
constant of 1.7 and D
(m). The maximum Secchi-disc transparency
i n Skaha Lake i n 1971 was 7 m, which indicates an e x t i n c t i o n c o e f f i c i e n t of
1.7/7 = 0.24/m.
The r e l a t i o n s h i p between a l g a l c e l l density and l i g h t absorption
i s reported by Azad and Borchardt
(1969).
These results are interpreted by
Chen (1970) and D i Toro et al. (1971) i n the following formulation of k
k
ep
= 0.17 B
c
where B^ i s the concentration of phytoplankton
i n mg/1.
The e x t i n c t i o n co-
e f f i c i e n t , k , therefore has been given the following form:
e
k
e
:
= 0.24 + 0.17 B
c
91
The biomass of phytoplankton i n the trophogenic layer(B, kg) i s
3
converted to concentration (B^, kg/km ) through d i v i s i o n by the volume of
3
the trophogenic layer(km ).
*
(Concentration i n kg/km
3
i s converted to con-
,
-6
centration i n mg/1 through m u l t i p l i c a t i o n by the conversion factor 10 ).
The trophogenic layer of Skaha Lake i s calculated to have a depth of 8 m,
2
based on an estimate of the l i t t o r a l area of the north basin of 2.9 km
(Stockner et al. 1972b).
The hypsometric curve of the north basin (Figure
3) indicates that the upper 8 m of water has a volume of approximately
0.124 km .
3
(3) Nutrient Dependency.
The r e l a t i o n s h i p between phyto-
plankton growth and nutrient concentration i s most often expressed by a
Michaelis-Menton
1967,
(or Monod growth k i n e t i c s ) expression (Ketchum 1939, Ketchum
Dugdale 1967, Eppley et al. 1969, Chen 1970, Di Toro et al. 1971, Kramer
et al. 1972, Parsons
and Takahashi 1973).
The Michaelis-Menton
expression
takes the following form:
.
y
-
(
"S\
K
[ N ]
^
+ [N]
)
where y i s the average daily growth r a t e (day ^) ; K^, i s the maximum d a i l y
growth rate (dependent on temperature
and defined i n a previous section, day ^ ) ;
[N] i s the concentration of the l i m i t i n g nutrient i n the trophogenic layer
(mg/1); and K^ i s the Michaelis-Menton, or h a l f - s a t u r a t i o n constant f o r phytoplankton growth with the l i m i t i n g nutrient (Figure 9). The h a l f - s a t u r a t i o n
constant i s defined as the nutrient concentration at which growth i s h a l f of
the maximum growth rate.
92
-2.0
0
1
2
3
4
5
Phosphate concentration,y.q/litre
Figure 9. Growth rate of a phytoplankton population as
a function of phosphorus concentration when phosphorus
is the l i m i t i n g nutrient (Fuhs e_t a l . 1972). Growth rates
are shown at varying p^ values with a h a l f - s a t u r a t i o n constant of approximately 1 ug/1 phosphate.
93
According to Di Toro et al.
(1971),
"There exists an increasing body of experimental evidence to support the use of this funct i o n a l form IMichaelis and Menton]
for the
dependence of the growth rate on the concentration
of e i t h e r phosphate, n i t r a t e , or ammonia i f only
one of these nutrients i s i n short supply."
It w i l l be assumed that phosphorus i s the nutrient i n short supply i n
Skaha Lake, and that approximately h a l f of the supply of t o t a l phosphorus
i n the trophogenic layer i s " b i o l o g i c a l l y a c t i v e , " and therefore p o t e n t i a l l y
available f o r growth (Gachter 1971 makes a s i m i l a r assumption
Swiss lakes).
assumption
According to J . G. Stockner (personal communication),
the
that phosphorus i s the l i m i t i n g nutrient f o r most of the season
i n Skaha Lake i s a reasonable one.
al.
for several
Although bioassay r e s u l t s (Stockner et
1972c) show nitrogen to be more l i m i t i n g than phosphorus during two per-
iods of 1971, phosphorus probably became l i m i t i n g l a t e r i n the summer during
a bloom of blue-green algae {Gleotrichia').
I t i s u n l i k e l y that blue-green
algae, of which many species possess the c a p a b i l i t y to f i x nitrogen d i r e c t l y
from the molecular form i n the trophogenic layer, would be limited by n i t r o gen.
High rates of nitrogen f i x a t i o n have been correlated with high produc-
tion rates of blue-green algae, primarily Anabaena,
menon (Brezonik 1972).
G l e o t r i c h i a , and
Aphanizo-
Phosphorus, there fore, i s generally regarded to be the
most important l i m i t i n g nutrient to the growth of blue-green algae.
gerald (1972) notes that:
". . . i f bioassays are carried out with
mixtures of n i t r o g e n - f i x i n g and nonnitrogen-fixing
phytoplankton, i t might be d i f f i c u l t to interpret
the r e s u l t s , since the n i t r o g e n - f i x i n g species could
be phosphorus limited and the nonfixing algae could
be nitrogen l i m i t e d but have surplus phosphorus. . .
Fitz-
94
tests with in situ algae must be frequent enough so
that trends can be followed and careful scrutiny
given to the species composition of samples tested
at d i f f e r e n t times."
The Michaelis-Menton
c o e f f i c i e n t for phytoplankton
growth with
phosphorus as the l i m i t i n g n u t r i e n t i s known to vary for d i f f e r e n t
a l g a l species.
Di Toro et al. (19 71) have interpreted the r e s u l t s of
s i x i n v e s t i g a t i o n s , and report a v a r i a t i o n between 0.006 and 0.025 mg/1
phosphorus.
Fuhs et al. (1972) report lower values near 0.001 mg/1 f o r
two species of diatoms.
(4) F i n a l Growth Rate Expression.
The growth rate of phyto-
plankton i s assumed to depend on temperature, l i g h t , and n u t r i e n t s , and the
preceeding formulations separately describe the e f f e c t s of these three
limiting factors.
Each of the three formulations can be considered a
"reduction f a c t o r " since each one reduces the t h e o r e t i c a l maximum growth
rate.
Therefore, i t i s r a t i o n a l to multiply the three formulations t o -
gether to arrive at a f i n a l growth rate expression.
The same r a t i o n a l e i s
followed by Ketchum (1939) i n dealing with two n u t r i e n t s , and by Riley (1965),
Chen (1970) and D i Toro et al, (1971) i n dealing with temperature, l i g h t and
nutrients.
Following t h i s procedure,
G
P
the growth rate expression becomes:
x
maximum t h e o r e t i c a l
growth rate dependent on temperature
I
I
j — exp(l - ~ )
m
m
reduction
factor
for
light
x
[P]
reduction
factor
for
phosphorus
95
where [P] i s the concentration of " b i o l o g i c a l l y a c t i v e " phosphorus
(mg/1).
Other terms have been defined previously.
(d) Phytoplankton Losses.
The loss of phytoplankton c e l l s from
the trophogenic layer can be attributed to four major mechanisms:
respira-
tion, grazing by zooplankton, sinking of dead c e l l s , and advection from the
outflow of the lake (Chen 1970, Di Toro et al. 1971).
(1) Respiration Losses.
Endogenous metabolism of algae re-
s u l t s i n degradation of a l g a l protoplasm to supply energy f o r s u r v i v a l
(McKinney 1962).
The chemistry of endogenous metablism i s the same as
the f a m i l i a r one f o r r e s p i r a t i o n :
c
c
7 o
H
<A>
Q
N
+ 6.25 0
5.7 C0 + NH. + 3.4 H„0
o
o
McKinney notes that the demand f o r oxygen i n the absence o f sunlight f o r
photosynthesis can be as great as the photosynthetic production of oxygen.
Using data from Riley et al. (1949), D i Toro et al. (1971) have
established the following r e l a t i o n s h i p f o r a l g a l r e s p i r a t i o n as a function
temperature:
0
5
10
15
20
25
Temperature °C
Figure 10. Algal respiration rate as a function of
temperature (data from Riley, c i t e d i n Di Toro et a l .
1971).
96
Di
Toro et al. conclude that a straight l i n e adequately f i t s these data,
which can be formulated as:
R = K_T
P
2
where R^ i s the endogenous r e s p i r a t i o n rate (day "*"),
i s a constant which
i s approximately 0.005 ± 0.001, and T i s °C.
(2) Grazing by Zooplankton.
ing
in
Loss of phytoplankton by graz-
can be the most s i g n i f i c a n t factor reducing phytoplankton biomass.
s i t u method of measuring
An
the grazing rate of the zooplankton community
(excluding animals less than 70 u) i n a eutrophic lake i s reported by Haney
(1970; c i t e d i n Rigler 1973). Results show that organisms
(.Pseudomonas), yeast (Rhodotorula),
such as bacteria
and small algae (Chlamydomonas)
were
eaten by zooplankton at approximately equal average rates of 0.033/hour i n
the trophogenic layer during summer s t r a t i f i c a t i o n (Rigler 1973).
This
rate corresponds to 0.79/day (the f r a c t i o n o f small algae eaten each day)
i f zooplankton are 100 per cent e f f i c i e n t at a s s i m i l a t i n g t h e i r food.
Based on studies of the a s s i m i l a t i o n e f f i c i e n c y of zooplankton
(Marshall and Orr 1953, Corner et al. 1967, and Conover 1964, 1966; c i t e d
i n Rigler 1973), Rigler (1973) assumes that a reasonable estimate
ciency i s approximately 60 per cent.
of e f f i -
The a s s i m i l a t i o n e f f i c i e n c y i s probably
lower i f blue-green algae make up a s i g n i f i c a n t part of the t o t a l a l g a l population.
The resistance of blue-green algae to grazing i s one reason f o r
large blue-green blooms (Odum 1971).
I t i s suggested that the a s s i m i l a t i o n
e f f i c i e n c y i s h a l f (30 per cent) when blue-green algae dominate the population.
The following expression describes the loss o f algae by grazing:
Z =(K )(K )
p
where Z
p
G
A
i s the rate of grazing loss by zooplankton (day
K
grazing rate with 100 per cent e f f i c i e n c y (0.79 day "*"), and K
i s the
i s the
c o e f f i c i e n t of a s s i m i l a t i o n e f f i c i e n c y (0.3 to 0.6).
(3) Sinking of Phytoplankton C e l l s .
Sinking rates of dead
c e l l s vary according to the s i z e , shape, and chemical
composition
of the
c e l l s , and are therefore a function of the c h a r a c t e r i s t i c s of the algal species.
For example, some species of blue-green algae contain gas vacuoles
which slow their sinking rates (Morris 1967, B e l l a 1970), and some diatom
species sink f a s t e r than others because of a higher proportion of s i l i c a
(Lund 1959).
Estimates
of sinking rates of marine phytoplankton include
3 m/day (Steele 1958), 3 to 6 m/day (Riley 1965),0.5 to 2.0 m/day (Smayda
1970), and 0.29 to 0.73 m/day (Walsh and Dugdale 1971).
B e l l a (1970) r e -
ports an average sinking rate of 0.75 to 1.0 m/day for a l l freshwater a l gae excpet blue-greens, which he assumes sink very slowly.
reports the sinking rates of freshwater
diatoms to vary between 0.19 m/day
for A s t e r i o n e l l a species to 0.91 m/day for Melosira
data i t appears that a reasonable
Lund (1959)
species.
From these
estimate of the sinking rate i s between
0.5 and 1.0 m/day.
Using t h i s estimate, the d a i l y loss of algae from the trophogenic layerby sinking would be s i x to 12 per cent (e.g.
0.06/day).
0.5 m/day * 8 m =
An expression describing the rate of sinking losses i s :
S = V IT
p
s' t
98
where S i s the rate of sinking losses (day
p
toplankton sinking (m/day), and T
), V
s
i s the v e l o c i t y of phy-
i s the thickness of the trophogenic
layer(m) .
(4) Advection Losses.
Because of the r e l a t i v e non-motility
of phytoplankton, some loss w i l l occur through hydrologic flow at the outl e t of the lake (Uhlmann 1972).
The following expression describes this
rate of l o s s :
Where Op i s the rate of outflow loss of phytoplankton
(day
), Q i s the
3
d a i l y discharge from the outlet of the lake (m /day), and V
i s the volume
3
of the Crophogenic layer(m ).
5.
Hypolimnetic Dissolved Oxygen Submodel
Although i t i s not necessary to predict dissolved oxygen i n
the hypolimnion i n order to model phosphorus and phytoplankton, this i n f o r mation serves as a useful check on other parts of the model.
status of hypolimnetic water has great importance
The oxygen
i n regulating the phosphorus
retention capacity of the sediments (see regeneration submodel).
Therefore,
i t i s of value to be able to predict the approximate number of years before
the hypolimnion becomes anaerobic ( i f present phosphorus loading rates conr
tinue).
Through other submodels, enough information i s a v a i l a b l e to formu-
l a t e a s i m p l i f i e d oxygen depletion model for the hypolimnion.
This submodel describes oxygen conditions during the s t r a t i f i e d
period of the year, and the assumption
i s made that the entire lake i s
saturated with dissolved oxygen during mixing periods.
Since the "modelling
99
year" begins at spring mixing, the hypolimnion w i l l be saturated with
dissolved oxygen f o r the i n i t i a l conditions.
Except for a minor amount
of eddy d i f f u s i o n of oxygen from the epilimnion (ignored i n this
submodel),
the beginning of s t r a t i f i c a t i o n i s o l a t e s the hypolimnion from receiving
additional dissolved oxygen u n t i l the autumn mixing period.
The hypolim-
nion w i l l gradually undergo oxygen depletion during summer s t r a t i f i c a t i o n ,
and the assumption i s made that the rate of depletion i s a d i r e c t function
of the amount of organic matter sedimenting i n t o the region below the thermocline.
The conclusion of Burns and Ross (1972) that approximately 88 per
cent of the hypolimnetic oxygen of Lake E r i e was consumed i n the decay of
organic matter supports t h i s assumption.
Decomposition of organic matter
i s assumed to proceed according to the following r e a c t i o n (Fogg 1953):
C
5
?
H
Q
g
0
2 3
N + 6.25 0
2
-> 5.7 C0 + NK^ + 3.4 H 0
2
2
Therefore, f o r each 5.7 moles of C decomposed (equivalent to 68.5 g-atoms
C), 6.25 moles of 0
2
are used (200 g-atoms).
With the information that
phytoplankton are 53 per cent by dry weight carbon (on the average, Fogg
1953), i t i s concluded that f o r each 129 g-atoms of phytoplankton decomposed, 200 g-atoms o f oxygen are used.
Converting to a simpler r a t i o ,
for each gram of phytoplankton decomposed, 1.55 g of oxygen i s used.
The following formulation describes the use of oxygen through
decomposition i n the hypolimnion:
100
DO
(.4 B S
dc
C F
phytoplankton
sinking
from
epilimnion
where D0^
c
.83)
(1.55)
coefficient
of
oxygen
use
coefficient
of
decomposition
i s the dissolved oxygen used i n decomposition (mg/1 • day); .4
i s the proportion of phytoplankton not recycled within the epilimnion, and
therefore reaching the hypolimnion and l i t t o r a l sediments; B^ i s the concentration of phytoplankton biomass i n the epilimnion (mg/1); S
p
i s the
rate of sinking of phytoplankton c e l l s (day * ) ; .83 i s the proportion of
lake area involved i n hypolimnetic sedimentation; 1.55
i s the stoichiometric
c o e f f i c i e n t of oxygen use per mg of phytoplankton decomposed; k^ i s the
temperature-dependent c o e f f i c i e n t of decomposition (defined i n the regeneration submodel); and
i s the temperature of the hypolimnion (°C).
CHAPTER V
RESULTS
A.
VERIFICATION OF THE MODEL FOR SKAHA LAKE*
Three trophic indicators are considered the most important
for v e r i f i c a t i o n of the model:
(1) the t o t a l phosphorus concentration
i n the upper mixed layer of the lake (the whole lake during mixing);
(2) the phytoplankton concentration i n the trophogenic layer; and
the minimum dissolved oxygen concentration i n the hypolimnion.
(3)
Collec-
tion and analysis of these limnological data are discussed i n Appendix
B.
During the year of simulation (March 1969 to March 1970), the
t o t a l input phosphorus from a l l known sources was
24,500 kg (see Table
A-3) of Appendix A f o r percentages of d i f f e r e n t sources).
Variations
of input and output of phosphorus to and from Skaha Lake during the
simulation year are shown i n Figure 11.
t r a t i o n i n March 1969 was 27 yg/1
The i n i t i a l phosphorus
concen-
(conditions of complete mixing; Stein
and Coulthard 1971).
1.
Total Phosphorus Concentration
(a) Upper Mixed Layer.
In the process of mathematically simulating
a n a t u r a l system, the modeller generally learns something
of h i s basic assumptions.
about the v a l i d i t y
While the i n i t i a l simulation of the phosphorus
concentration i n the upper mixed layer (Figure 12) indicates a reasonable
The following r e s u l t s pertain to the north basin, except where the
south basin i s s p e c i f i c a l l y discussed.
101
102
500
120
180
240
TIME(DAYS)
300
Figure 11. Loading rate of phosphorus to Skaha Lake, 1969-70
(upper curve) and phosphorus outflow rate (lower curve).
360
103
0
60
120
180
240
TIME(DAYS)
300
F i g u r e 12.
Phosporus c o n c e n t r a t i o n i n s u r f a c e water o f Skaha
Lake, 1969-70, w i t h no m o d i f i c a t i o n o f o r i g i n a l assumptions
( c i r c l e s i n d i c a t e o b s e r v e d v a l u e s and s o l i d l i n e s i m u l a t e d
values).
360
104
fit
to the shape of the r e a l data, there are two s i g n i f i c a n t discrepancies.
The f i r s t i s that minimum simulated concentrations i n midsummer are consistently too high, and the second i s that the f i n a l simulated concentration
is too low.
The f i r s t discrepancy could be caused by:
(1) the sedimenta-
tion rate of phosphorus loss from the epilimnion i s underestimated; or (2)
the rate of eddy d i f f u s i o n of phosphorus from the hypolimnion to the
epilimnion i s overestimated.
To evaluate the f i r s t , the c o e f f i c i e n t of eddy d i f f u s i o n was
reduced by 20 per cent (a maximum reasonable margin of e r r o r ) , but no
appreciable difference was observed i n the simulated phosphorus concentration.
However, when the sedimentation of phosphorus from the e p i l i m -
nion was doubled
(Figure 13), the f i t was considerably improved
midsummer minimum values.
f o r the
Doubling the phosphorus sedimentation i s a
reasonable change i n the o r i g i n a l assumption
f o r the following reasons.
The sedimentation submodel i s d i r e c t l y dependent on the biomass of phytoplankton i n the trophogenic layer (Chapter IV).
As stated i n Chapter IV,
this i s a conservative estimate of sedimentation loss because other organisms (bacteria, zooplankton, fish) also sediment
the amount of phosphorus i n the upper layer.
to the bottom and decrease
Therefore, losses occurring
from the sedimentation of other organisms would tend to increase losses from
the epilimnion. In addition, losses may occur by mechanisms not modelled,
such as the chemical p r e c i p i t a t i o n of inorganic phosphorus minerals l i k e
apatite (Golterman 1973).
(Rates of phosphorus loss by sedimentation from
the epilimnion are shown i n Figure 14. The lower curve represents regeneration from l i t t o r a l sediments by b a c t e r i a l decomposition).
105
100
Q_
CO
o
zn
CL.
0
60
120
180
240
TIME(DAYS]
300
Figure 13. Phosphorus concentration i n surface water of
Skaha Lake, 1969-70, with the sedimentation rate from the
epilimnion doubled ( c i r c l e s indicate observed values and
s o l i d l i n e simulated values).
360
106
500
o 200
|
150 1
P
100 t
Q_
120
180
240
TIME(DRYS)
Figure 14. Simulated sedimentation rate of phosphorus
from the epilimnion of Skaha Lake, 1969-70 (upper curve)
and regeneration rate from l i t t o r a l sediments (lower
curve).
360
107
The second discrepancy apparent i n the simulated r e s u l t s of
Figure 13 shows the lake l o s i n g phosphorus between the mixing period
of March 1969 (day 1) and the same period i n March o f 1970 (day 360).
The simulated curve shows the lake with a f i n a l concentration of 26 yg/1,
whereas a n a l y t i c a l data showed that the lake a c t u a l l y increased i n concentration to 33 yg/1.
A p l a u s i b l e explanation for this discrepancy i s
that the estimated regeneration rate of sedimented phosphorus from the
sediments to the hypolimnion
i s too low.
By increasing the regeneration
rate three times, a f i n a l concentration of 31 yg/1 was simulated, while
an increase of four times resulted i n a f i n a l concentration o f 35 yg/1.
A correct simulated concentration of 33 yg/1 was achieved by increasing
the regeneration rate 3.5 times
(Figure 15).
Apparently, b a c t e r i a l decom-
p o s i t i o n rates are greater than expected, or there are other factors acting
to increase the rate of phosphorus regeneration from the sediments.
Several
possible mechanisms, such as d i f f u s i o n , turbulent mixing, and chemical r e generation are discussed i n Chapter IV.
Estimated sedimentation
losses from the hypolimnion
ation are shown i n Figure 16 (estimates according to revised
and regenerassumptions).
The sedimentation losses are divided i n t o organic and inorganic components
i n Figure 17. Organic sedimentation
i s a dynamic function o f phytoplank-
ton production, while inorganic sedimentation by adsorption i s shown as a
r e l a t i v e l y constant process.
(b) Hypolimnion Phosphorus.
During 1969-70 phosphorus determinations
were made to a depth of only 20 m i n Skaha Lake, which has a maximum depth
of 57 m.
As phosphorus concentrations often tend to increase i n the hypo-
108
100
120
180
240
TIME(DRYS)
300
Figure 15. Phosphorus concentration i n surface water of
Skaha Lake, 1969-70, with the sedimentation rate from the
epilimnion doubled and the regeneration rate from deepwater sediments X 3.5 ( c i r c l e s indicate observed values
and s o l i d l i n e simulated values).
360
109
Figure 16. Simulated sedimentation rate of phosphorus
from the hypolimnion of Skaha Lake, 1969-70 (upper curve)
and the regeneration rate from deep-water sediments
(lower curve).
110
F i g u r e 17.
S i m u l a t e d s e d i m e n t a t i o n r a t e s o f o r g a n i c phosphorus (upper curve) and i n o r g a n i c phosphorus (lower curve)
from the h y p o l i m n i o n o f Skaha Lake, 1969,-70.
Ill
limnion of deep lakes during summer s t r a t i f i c a t i o n
(Golterman 1973), the
measurements from Skaha are not considered s u f f i c i e n t for v a l i d a t i o n purposes.
Simulated averages for the entire hypolimnion
(Figure 18) i n d i -
cate a maximum concentration of over 50 pg/1.
2.
Phytoplankton
Production
Simulation of phytoplankton
biomass' (Figure 19) indicates that
the timing o f peaks could not be p r e c i s e l y predicted.
The simulated peak
of the f i r s t bloom lagged 20 to 30 days behind the r e a l peak, and could
not be modified by manipulation of growth c o e f f i c i e n t s (within l i m i t s
reported i n the l i t e r a t u r e ) .
The low growth period around day 90 after
the f i r s t bloom was not simulated accurately, and was probably due to
the omission of a dynamic zooplankton
grazing model.
With the assumption
of a constant grazing r a t e , losses from grazing are underestimated
phytoplankton
3.
a t high
production.
Dissolved Oxygen i n the Hypolimnion
According to the submodel i n Chapter IV, dissolved oxygen i n the
hypolimnion
i s d i r e c t l y dependent on phytoplankton
of 20 to 30 days between
production, and the l a g
real and simulated values (Figure 20) i s a r e f l e c -
tion of the lag i n the phytoplankton
simulation.
Agreement between real
and simulated values at the end of summer stagnation (about 6 mg/1) i s r e l a t i v e l y close.
Because oxygen use i n the hypolimnion
i s an i n d i r e c t mea-
sure of the amount of organic matter produced i n the lake and sedimented
to
the hypolimnion,
the values a t the end of summer stagnation are an
approximate i n d i c a t i o n of the sum of organic productivity during the growing
season.
112
CD
o
cx
100
90 I
80
70 •
60 ••
y
501
o
40 -
CO
30 ••
g 20}
m
o_ 10
co
o
0
IE
CL
0
——I
60
1
1
1
1
1
h—i
1
1
1
1—
H
120
180 240
TIME(DAYS)
1
1
1
(-
300
Figure 18. Simulated phosphorus concentration i n the
hypolimnion of Skaha Lake, 1969-70.
360
113
Figure 19. Phytoplankton biomass i n the trophogenic
layer of Skaha Lake, 1969-70 (dashed l i n e indicates
observed values and s o l i d l i n e simulated values).
114
F i g u r e 20.
D i s s o l v e d oxygen c o n c e n t r a t i o n i n the hypol i m n i o n o f Skaha Lake, 1969-70 ( c i r c l e s i n d i c a t e o b s e r v e d
v a l u e s and s o l i d l i n e s i m u l a t e d v a l u e s ) .
115
4.
Simulation of the South Basin of Skaha Lake
The model i s programmed so that the outflow of phosph6rus from
the north basin i s equal to the inflow to the south basin.
The smaller
3
south basin with a volume of 0.041
km
and a mean depth of 15 m (the same
3
figures f o r the north basin are 0.517
p o t e n t i a l than the north basin.
km
and 28 m), has greater eutrophic
In addition, p r e v a i l i n g north winds i n
summer b r i n g f l o a t i n g a l g a l matter from the north basin to the south.
V e r i f i c a t i o n of simulated values f o r the south basin was
simi-
l a r to v e r i f i c a t i o n f o r the north basin (no figures are presented).
More
eutrophic conditions i n the south basin are evidenced by more measured
phosphorus at the end of the year (37 yg/1 compared to 33 yg/1 f o r the
north basin), a higher phytoplankton
peak (5.5 mg/1
compared to 4.6
mg/1
for the north basin), and less hypolimnetic dissolved oxygen at the end
of stagnation (5.4 mg/1
5.
compared to 6.6 mg/1
f o r the north basin).
V e r i f i c a t i o n for 1970-71 and 1972-73
During the next year (March 1970
hydrologic conditions occurred.
to March 1971),
quite d i f f e r e n t
While 1969-70 was nearly an average hydro-
l o g i c year (11 per cent higher than the average discharge from Skaha Lake;
Table A-4 i n Appendix A), 1970-71 was
an exceptionally dry year, with only
47 per cent of the average discharge (48 years of record).
With this hydro-
l o g i c flow and a phosphorus loading of 25,000 kg (a two per cent increase
over the previous year), the model predicts a substantial phosphorus i n crease:
from 33 yg/1 i n March 1970
to 53 yg/1 i n March 1971.
This predic-
tion i s within 12 per cent of the measured concentration of 60 yg/1 for
A p r i l 1971
(Williams 1972).
No phytoplankton or dissolved oxygen data are
116
available f o r the summer of 1970.
No data i s a v a i l a b l e f o r the spring and summer of 1972, making
i t impossible to v e r i f y the model f o r 1971-72.
During this period hydro-
l o g i c conditions were average (14 per cent higher than 1969-70), and phosphorus loading was approximately the same as i n the previous
two years.
During the period March 1972 to March 1973 s i g n i f i c a n t changes
occurred i n both phosphorus loading and hydrologic flow.
This was the
f i r s t year the phosphorus removal system i n the Penticton sewage treatment
plant was operating e f f e c t i v e l y , r e s u l t i n g i n 50 to 60 per cent removal o f
phosphorus from municipal sources (Haughton et al. 1974).
This resulted i n
an o v e r a l l loading decrease of approximately 33 per cent from the previous
year.
An unusually heavy snowpack resulted i n the highest yearly flow on
8
record through Skaha Lake:
10.4 X 10
3
m
(884,000 a c r e - f t ) , o r approxi-
mately twice the flow of 1969-70 (an average year).
With these new loading and hydrologic conditions, the model predicts
a t o t a l phosphorus concentration of 16 yg/1 for the spring of 1973 i n the
north basin, a large decrease from 42 yg/1 the previous spring.
Lake data
for the spring of 1973 indicates a concentration o f 13 yg/1 i n the north
basin (B.C. P o l l u t i o n Control Branch, courtesy of E. R. Haughton).
The
modelled value i s therefore within 23 per cent of the a n a l y t i c a l value.
Based on this low spring phosphorus concentration, the model predicts s i g n i f i c a n t l y lower phytoplankton growth during the summer of 1973 (peak of
2.9 mg/1), probably not i n the bloom category.
munication) confirms
during 1973.
A. M. Thomson (personal com-
that there were no serious a l g a l problems i n Skaha Lake
117
B.
SENSITIVITY ANALYSES
Two
types of s e n s i t i v i t y are important
i n this simulation.
The
f i r s t i s the s e n s i t i v i t y of the model to the major " f o r c i n g functions":
phosphorus loading and hydrologic discharge.
The second i s the s e n s i t i v i t y
of the model to changes i n the 15 p h y s i c a l and b i o l o g i c a l c o e f f i c i e n t s
(con-
stants) used i n the submodels.
1.
S e n s i t i v i t y of Phosphorus Loading and Hydrology
Simulation results of the three trophic i n d i c a t o r s (phosphorus,
phytoplankton,
and hypolimnetic dissolved oxygen) are shown i n Figure
21a.
For comparison with subsequent simulations, a key value of each i n d i c a t o r
i s chosen:
(1) the concentration of t o t a l phosphorus at the end of the
year; (2) the peak value of phytoplankton
biomass; and
concentration of dissolved oxygen i n the hypolimnion.
21a) these values are:
dissolved oxygen 6.6
(3) the minimum
For 1969-70 (Figure
phosphorus 33 yg/1, phytoplankton
4.6 mg/1,
and
mg/1.
Simulations at varying loading and hydrologic discharge are presented i n Figures 21b - 21f.
Figure 21b shows the indicators with the phos-
phorus loading doubled (49,000 kg/year).
The e f f e c t of this hypothetical
loading i s to increase the phosphorus concentration to 64 yg/1
to increase the phytoplankton
peak to 6.3 mg/1
the hypolimnetic dissolved oxygen to 1.9 mg/1
(from 33),
(from 4.6), and to decrease
(from
6.6).
Simulation at h a l f of the o r i g i n a l loading (12,250 kg/yr) (Figure
21c) indicates quite d i f f e r e n t trophic conditions.
Phosphorus concentration
decreases to 19 yg/1 by the end of the year, the phytoplankton
peak i s 3.2
118
(b) Loading doubled
(a) Loading and discharge
for 1969-70
Q_
tn
o
X
Q.
60
120 180 240
TIME(DflYS)
60
300
120 180 240
TIME(DAYS)
300
360
(d) Discharge doubled
(c) Loading halved
60
120 180 240
TIME(DAYS)
300
360
(e) Discharge halved
-I 15
60
120 180 240
TIME(DAYS)
300
(f) Loading halved and
discharge doubled
360
15
o
u
cn
ZD
ce
o
X
Qin
o
X
0-
60
120 180 240
TIME(DAYS)
300
360
60
120 180 240
TIME(DAYS)
300
Figure 21. Simulated phosphorus ( s o l i d l i n e ) , phytoplankton
(short dashes) and hypolimnetic dissolved oxygen (long dashes)
with varying phosphorus loading and hydrologic discharge,
Skaha Lake, 1969-70.
360
119
mg/1, and hypolimnetic dissolved oxygen decreases only to 9.4 mg/1.
Trophic conditions s i m i l a r to effects of halving the loading are
simulated by doubling the hydrologic discharge (Figure 21d; the o r i g i n a l
loading of 24,500 kg i s maintained).
22 yg/1, the phytoplankton
oxygen
Phosphorus concentration decreases to
peak i s 3.5 mg/1, and the hypolimnetic dissolved
minimum i s 9.0 mg/1.
Halving the discharge
(while maintaining
origi-
n a l loading) produces simulated conditions s i m i l a r to the e f f e c t s of doubling
the loading (Figure 21e):
phosphorus increases to 47 yg/1,
phytoplankton
concentration peaks a t 5.3 mg/1, and hypolimnetic dissolved oxygen reaches
a minimum of 4.6 mg/1.
Doubling the discharge and halving the loading simultaneously
produce s i g n i f i c a n t l y lower trophic conditions (Figure 21f): phosphorus
decreases to 12 yg/1, phytoplankton
peaks at 3.0 mg/1, and dissolved oxygen
reaches a minimum of 11.6 mg/1.
I t i s s i g n i f i c a n t that large changes i n trophic status may theoret i c a l l y occur i n only one year as a r e s u l t o f variations i n hydrology and
phosphorus loading.
This theory was tested during 1972-73 (as described i n
the previous s e c t i o n ) , and the r e s u l t s show that although s i g n i f i c a n t changes
did occur during the year of high runoff and decreased
impact was evident during the following year.
loading, an even larger
Hence, the hydrologic and
loading condit ions occurring from March 1972 to March 1973 resulted In a
decrease i n spring phosphorus concentration of 26 yg/1 (from 42 to 16). The
lower phosphorus concentration resulted i n
s i g n i f i c a n t l y lower phytoplank-
ton production during the summer of 1973, and no serious a l g a l blooms.
120
2. S e n s i t i v i t y of P h y s i c a l and B i o l o g i c a l
Coefficients
The s e n s i t i v i t y of 15 physical and b i o l o g i c a l c o e f f i c i e n t s on
the simulation of phosphorus concentration at the end of the year (March
1970)
i s shown i n Table VII.
The range of each c o e f f i c i e n t as reported
in the l i t e r a t u r e (Chapter IV) i s shown i n column 2, and the value used i n
the simulation i s shown i n column 3.
The simulated
phosphorus concentra-
tion (using the c o e f f i c i e n t values i n column 3) i s shown i n column 4.
The
r e s u l t i n g phosphorus concentration when the c o e f f i c i e n t i s set at i t s minimum value (with a l l other c o e f f i c i e n t s remaining the same) i s shown i n column
5, and the concentration with the c o e f f i c i e n t at i t s maximum value i s shown
i n column 6.
The maximum per cent deviation from the simulated concentration
(33 yg/1) i s shown i n column 7.
position
The analysis shows the c o e f f i c i e n t o f decom-
(k^) to be the most s e n s i t i v e , with a maximum p o s i t i v e deviation of
15 per cent.
This s i m p l i f i e d s e n s i t i v i t y analysis does not explore the
i n t e r a c t i v e s e n s i t i v i t y o f the 15 c o e f f i c i e n t s as they vary with respect
to each other, but i t does give an approximate index of r e l a t i v e s e n s i t i v i ties .
Table VIII explores the s e n s i t i v i t i e s of the same c o e f f i c i e n t s
with respect to the phytoplankton peak, and indicates much greater deviations
than with respect to phosphorus concentration.
cient appears to be the Michaelis-Menton
The most sensitive
half-saturation
constant
coeffi(K^), which
can cause an increase of 56 per cent i n simulated phytoplankton biomass when
the minimum value reported i n the l i t e r a t u r e i s used i n the model.
ing v e l o c i t y
The sink-
(Vg) i s apparently the second most sensitive c o e f f i c i e n t , caus-
ing a maximum positive deviation of 39 per cent i n phytoplankton biomass.
TABLE V I I
SENSITIVITY OF COEFFICIENTS ON PHOSPHORUS CONCENTRATION
COEFFICIENT
RANGE REPORTED
IN LITERATURE
VALUE
USED
SIMULATED
CONCENTRATION
FOR VALUES
IN COLUMN 3
CONCENTRATION
USING MINIMUM
VALUE
CONCENTRATION
USING MAXIMUM
VALUE
MAXIMUM
PECENTAGE
DEVIATION
FROM COLUMN 4
I
d
k
k
d
k
rh
V
T
K
v
pb
G
s
2
k
k
Z
«H
kl
re
k
1
.03 - .05
80 - 120
.4 - .6 •
±20%
.15 - .19
.007-.015
150-300
.4 - .7
.6 - .9
.5 - 1.5
.004- .006
.15 - .25
.001 -.03
.075 -.125
.3 - .5
.04
100
.5
.17
.009
200
.6
.79
1.0
.005
.20
.01
.10
.4
33
33
33
33
33
33
33
33
33
33
33
33
33
33
33
29
36
34
34
32
33
32
32
33
33
33
33
33
33
33
38
30
32
33
34
32
33
33
33
33
33
33
33
33
33
+15
+ 9
+ 3
+ 3
± 3
- 3
- 3
- 3
0
0
0
0
0
0
0
DEFINITION OF COEFFICIENTS
k^ = c o e f f i c i e n t of decomposition
k = c o e f f i c i e n t of a d s o r p t i o n
cl
k
= c o e f f i c i e n t of r e c y c l i n g i n hypolimnion
k
= c o e f f i c i e n t of eddy d i f f u s i o n
v
= c o e f f i c i e n t of a d s o r p t i v e r e l e a s e
k , = c o e f f i c i e n t o f phosphorus i n biomass
1^ = l i g h t i n t e n s i t y o f maximum growth
K
= c o e f f i c i e n t o f zooplankton a s s i m i l a t i o n
A
K
G
re
coefficient of grazing
v e l o c i t y of s i n k i n g of phytoplankton c e l l s
c o e f f i c i e n t of r e s p i r a t i o n
c o e f f i c i e n t o f l i g h t e x t i n c t i o n f o r p l a n k t o n biomass
Michaelis-Menton h a l f - s a t u r a t i o n
coefficient
c o e f f i c i e n t o f maximum growth
c o e f f i c i e n t of r e c y c l i n g i n e p i l i m n i o n
TABLE VIII
SENSITIVITY OF COEFFICIENTS ON PHYTOPLANKTON PRODUCTION
COEFFICIENT
1
A
hi
l
pb
G
k
k
. re
k
k
k
K
e p
d
2
k
a
vr h
a
k
k
k
n
RANGE REPORTED
IN LITERATURE
?
.001
.5
.4
150
.075
.007
.6
.15
.3
- .03
- 1.5
- .7
- 300
- .125
- .015
- .9
- .25
- .5
±20%
.03 - .05
.004 - .006
80 - 120
.4
- .6
.15 - .19
VALUE
USED
3
.01
1.0
.6
200
.10
.009
.79
.20
.4
.04
.005
100
.5
.17
SIMULATED
CONCENTRATION
FOR VALUES
IN COLUMN 3
4
4.56
4.56
4.56
4.56
4.56
4.56
4.56
4.56
4.56
4.56
4.56
4.56
4.56
4.56
4.56
CONCENTRATION
USING MINIMUM
VALUE
CONCENTRATION
USING MAXIMUM
VALUE
' MAXIMUM
PERCENTAGE
DEVIATION
FROM COLUMN 4
5
6
7
7.13
6.35
5.99
5.24
3.62
5.04
5.56
5.26
5.11
4.09
4.34
4.69
4.65
4.60
4.52
2.51
3.39
4.12
3.29
5.69
3.55
4.18
4.01
4.11
4.13
4.78
4.43
4.47
4.52
4.60
+56
+39
+31
-28
+25
-22
+22
+15
+12
-10
±5
±3
±2
±1
±1
123
C.
EDDY DIFFUSION
Eddy d i f f u s i o n of phosphorus from the hypolimnion to the e p i -
limnion cannot be v e r i f i e d , as t h i s movement cannot be d i r e c t l y measured.
According to the eddy d i f f u s i o n submodel (Chapter IV), "loading" of phosphorus to the epilimnion by eddy d i f f u s i o n from the hypolimnion can, during
a short part of the summer s t r a t i f i c a t i o n period, contribute nearly as much
phosphorus as external loading (Figure 22).
The figure shows that for a
few days of the summer, the model simulates
a supply of 250 kg/day to the
epilimnion by eddy d i f f u s i o n .
During t h i s time the predicted
concentration
difference between the epilimnion and hypolimnion reached a maximum of
AO yg/1.
124
500
450
I
H
1
1
120
180
240
TIME(DAYS)
1
1
1
1
300
1
1
H
360
Figure 22. Loading rate of phosphorus from external sources
to Skaha Lake, 1969-70 (upper curve) and simulated " i n t e r n a l
loading" to the epilimnion by eddy d i f f u s i o n (lower curve).
CHAPTER VI
DISCUSSION
A.
INTERPRETATIONS AND
LIMITATIONS
The s e d i m e n t a t i o n submodel assumes a d i r e c t
tween p h y t o p l a n k t o n p r o d u c t i o n and phosphorus
IV).
This
relationship
s e d i m e n t a t i o n (Chapter
r e l a t i o n s h i p i s e v i d e n t i n midsummer when the s e d i m e n t a t i o n
of dead o r g a n i c m a t t e r r e s u l t s
i n low v a l u e s of t o t a l phosphorus
c e n t r a t i o n i n the e p i l i m n i o n d u r i n g the peak o f the growing
( F i g u r e 13).
Because t o t a l phosphorus
phate i s m o d e l l e d ,
r a t h e r than d i s s o l v e d
and not s i m p l y l o s s e s
by organisms.
d e s c r i b e a l a k e which
The
uses the phosphorus
orthophos-
through uptake o f s o l u b l e
r e c e i v e s phosphorus
to
i n a form a v a i l a b l e f o r growth
a v a i l a b l e through d e c o m p o s i t i o n ) ,
i n the p r o d u c t i o n o f o r g a n i c matter, and then s e d i -
ments a p o r t i o n of the dead p a r t i c u l a t e o r g a n i c phosphorus.
sense, the t o t a l phosphorus
curve ( F i g u r e 13)
f o r s o l u b l e o r t h o p h o s p h a t e , which
1973);
season
low v a l u e s d u r i n g the summer appear
(or makes incoming p a r t i c u l a t e phosphorus
d u r i n g the growing
con-
these low v a l u e s must r e f l e c t s e d i m e n t a t i o n o f p a r -
t i c u l a t e phosphorus,
phosphate
be-
that t o t a l phosphorus
d u r i n g the h e i g h t of the growing
this
i s s i m i l a r to the curve
u s u a l l y reaches n o n - d e t e c t a b l e l e v e l s
season i n a p r o d u c t i v e l a k e
But the f a c t
In
season may
(Hutchinson 1957,
remains a t d e t e c t a b l e l e v e l s
make i t a more u s e f u l
c a t o r than orthophosphate of p o t e n t i a l primary p r o d u c t i o n .
125
Rigler
indi-
126
1.
Sedimentation From the Epilimnion
Simulated phosphorus sedimentation from the epilimnion appears
to have been i n i t i a l l y underestimated by a factor of approximately two
(Chapter V). This discrepancy can be interpreted i n several possible
ways.
F i r s t , i t could be assumed that sedimentation of phosphorus by
a l g a l organisms accounts for only half of the actual amount, and that
sedimentation by other organisms (bacteria, zooplankton, f i s h ) must at
least double the amount.
This assumption
was made i n f i t t i n g the simulated
curve to the r e a l data (Chapter V).
Secondly, i t i s possible that other mechanisms are responsible
for sedimentation of p a r t i c u l a t e phosphorus from the epilimnion. One
p o s s i b i l i t y i s that p r e c i p i t a t i o n of phosphorus minerals such as apatite
takes place.
Because no chemical p r e c i p i t a t i o n submodel was formulated
(for the reasons discussed i n Chapter IV), this p o s s i b i l i t y cannot be
quantitatively explored.
Adsorption losses from the epilimnion to s e d i -
ment muds are probably not great, as only 17 per cent of the area of the
epilimnion (the l i t t o r a l ) i s i n contact with
2.
sediments.
Regeneration of Phosphorus from Deep-water Sediments
A s u r p r i s i n g finding of the simulation analysis was that three
to four times the amount of phosphorus was apparently released from the
sediments than could be explained by processes of b a c t e r i a l
decomposition.
Several explanations are possible, the most obvious one being that much
of the phosphorus sedimenting through the hypolimnion did not reach the
sediments i n the f i r s t place, and was decomposed en route
or chemical mechanisms.
by b i o l o g i c a l
This explanation would mean that the c o e f f i c i e n t
127
of recycling f o r the hypolimnion
(k j )
1 S
considerably higher than the
0.5/day value (±0.1) reported i n the l i t e r a t u r e (Chapter IV).
A second explanation i s that sedimented phosphorus i s regenerated three to four times faster to the water than can be explained by
processes of b a c t e r i a l decomposition.
Other mechanisms, such as d i f f u -
sion, p h y s i c a l disturbance by benthic organisms, turbulence during
mixing periods, and chemical s o l u b i l i z a t i o n are p o s s i b i l i t i e s (discussed
i n d e t a i l i n Chapter IV).
Regeneration
through turbulence during mixing
periods does not appear l i k e l y , however, as r e a l data does not show a
marked concentration increase at the beginning of these periods (Figure
12).
3.
Phytoplankton
Production
Simulated phytoplankton
growth (Figure 19) does not begin u n t i l
about day 70 when the growth rate (a function of temperature, l i g h t and
nutrient conditions) exceeds the loss rate (a function of grazing, r e s p i r ation, sinking, and advection losses from the south end of the lake).
i n i t i a l exponential growth phase i s temporarily reversed
The
around day 90 by
phosphorus deficiency caused by sedimentation of phosphorus-bearing a l g a l
c e l l s , and by self-shading e f f e c t s .
The major probable reason that the
simulated r e v e r s a l i s not as great as the r e a l data indicates i s the omission of a dynamic zooplankton
during high a l g a l growth.
submodel which would increase grazing losses
The lack of adequate zooplankton
data f o r Skaha
Lake precludes the v a l i d a t i o n of such a submodel.
The second simulated growth phase (peak at day 100) i s terminated
again by^phosphorus sedimentation
and self-shading, but at this higher
128
growth l e v e l the effects are more severe.
A t h i r d peak occurs around
day 150 because of continuing favorable conditions of temperature,
and nutrients.
light
Losses by sinking and advection exceed growth after this
peak, and no net growth occurs a f t e r day 210 when temperature and l i g h t
conditions become unfavorable.
The e f f e c t s of phosphorus on the growth rate are separated
from those of temperature and l i g h t i n Figure 23.
This analysis excludes
the e f f e c t s of losses (grazing, r e s p i r a t i o n , sinking and advection) on
the net growth rate, and focuses on only the growth factors.
The upper
curve represents the simulated daily growth rate as a function of only
temperature and l i g h t , while assuming that there i s an abundance of a v a i l able phosphorus.
The lower curve represents the growth rate with a l l
three l i m i t i n g factors included.
I f the assumption
i s accepted that
phosphorus i s the l i m i t i n g nutrient f o r most of the growing season, the
difference between the two curves indicates the s p e c i f i c e f f e c t of phosphorus l i m i t a t i o n on phytoplankton growth.
Several simplifying assumptions
have been made i n the formula-
t i o n of the primary production submodel which l i m i t
diction.
i t s accuracy of pre-
D i f f e r e n t rates of phosphorus uptake, sinking, and grazing pre-
ference by zooplankton f o r d i f f e r e n t phytoplankton species have not been
modelled.
Data from Skaha Lake (Stein and Coulthard 1971) show that the
f i r s t phytoplankton peak was dominated by diatoms and p h y t o f l a g e l l a t e s ,
while the second was dominated by blue-green species.
Differences i n
the Michaelis-Menton h a l f - s a t u r a t i o n constant f o r phosphorus uptake,
sinking rate, and grazing rate can be s i g n i f i c a n t between diatoms and
129
Figure 23. Simulated phytoplankton growth rates showing
the l i m i t i n g effects of temperature and l i g h t (upper curve)
and the l i m i t i n g effects of temperature, l i g h t and phosphorus (lower curve), Skaha Lake, 1969-70.
130
blue-green algae (Chapter IV), and these differences have been averaged i n
the model.
A better f i t between r e a l and simulated values could probably
be achieved by modelling the two a l g a l groups separately.
Given these l i m i t a t i o n s and s i m p l i f y i n g assumptions,
the results
indicate that t o t a l phosphorus can be used as a measure of the most l i m i t ing nutrient i n the simulation of phytoplankton production i n Skaha Lake.
The assumption
that approximately h a l f of the t o t a l phosphorus i s a v a i l a b l e
for growth (Gachter 1971)
appears to be reasonable.
In order to investigate
the e f f e c t s of other possible l i m i t i n g nutrients on phytoplankton production
(e.g.
B.
nitrogen, carbon), a d d i t i o n a l models would have to be formulated.
APPLICATION TO MANAGEMENT OF THE EUTROPHICATION PROBLEMS OF SKAHA LAKE
In this section an assessment i s made of the hypothetical long-
range (20-year) e f f e c t s of four d i f f e r e n t phosphorus management p o l i c i e s on
the eutrophication of Skaha Lake.
I.
The four management p o l i c i e s are:
No phosphorus removal and no growth i n the Penticton region
II.
60 per cent phosphorus removal (approximately the removal with
chemical p r e c i p i t a t i o n at the Penticton sewage treatment plant
i n 1972-73; Haughton et al. 1974) and a "high" population
growth projection of three per cent per year (Okanagan Basin
Agreement F i n a l Report 1974)
III.
60 per cent phosphorus removal and "low" growth (approximately
1.5 per cent per year)
IV.
Complete removal of a l l phosphorus from municipal waste
(equivalent to a spray i r r i g a t i o n system of municipal waste
disposal)
Policy IV assumes that 60 per cent of the phosphorus loading to
Skaha Lake i s from Penticton municipal wastes (Haughton et a l . 1974), and
131
that the remaining
40 per cent from a g r i c u l t u r a l and n a t u r a l sources r e -
mains at a constant l e v e l .
The annual population growth estimates of
three per cent and 1.5 per cent r e s u l t i n a yearly increase i n phosphorus
input of approximately
two per cent and one per cent, as only 60 per cent
of the annual input comes from municipal sources.
Canada-British Columbia Okanagan
As reported i n the
Basin Agreement F i n a l Report (1974), the
growth estimates are considered linear rather than exponential for the
20-year period.
In order to approximate the type of hydrologic v a r i a b i l i t y
typi-
c a l of the Okanagan Basin, outflow discharges from Skaha Lake for the 20-year
period preceeding the year of simulation (1949-1969) are used.
O
period yearly flows varied from 2.29 X 10 m
During t h i s
O
Q
(187,000 acre-ft) to 7.95
X 10 m
(646,000 a c r e - f t ) (see Table A-5 of Appendix A).
The 20-year simulations of the four management p o l i c i e s are not i n tended to be predictions of the trophic state of Skaha Lake 20 years from
now.
F i r s t , the hydrologic v a r i a t i o n s of the next 20 years are impossible to
predict.
Secondly,
the s i m p l i f y i n g assumptions and l i m i t a t i o n s inherent i n
the submodels make future predictions a risky exercise.
These simulations
are, therefore, only an attempt to show general trends that might be
ex-
pected i n the trophic indicators with the hydrologic v a r i a t i o n that occurred
from 1949
to 1969.
The i n i t i a l conditions chosen for each of the four sim-
ulations are the trophic conditions for the modelling year 1969-70:
phosphorus concentration of 33 yg/1, a phytoplankton
hypolimnetic dissolved oxygen minimum of 6.6 mg/1.
peak of 4.6 mg/1,
a final
and a
These same trophic i n d i -
cators are then modelled for a 20-year period with each of the four management p o l i c i e s .
132
The results of p o l i c y I (no treatment
and no growth) appear to
keep the lake i n as high or higher trophic state than i t was i n 1970
(Figure 24).
Except during r e l a t i v e l y wet years
(e.g. years 3 and 11),
the phosphorus concentration fluctuates around the i n i t i a l value of 33 yg/1
u n t i l the occurrence
of four r e l a t i v e l y dry years (years 12 - 15).
The
low flow causes the modelled concentration to exceed 60 yg/1, with associated high phytoplankton
biomass (over 6 mg/1) and low hypolimnetic dissolved
oxygen (nearly 1 mg/1, dangerously
close to anaerobic conditions).
Using
the serious bloom conditions of 1969 as a reference point (Stein and Coulthard 1971), phytoplankton
peaks appear to i n d i c a t e bloom conditions during
each of the 20 years.
The r e s u l t s of p o l i c y II (high growth and 60 per cent removal;
Figure 24) show at f i r s t an
improvement i n trophic conditions, but
by year 12 the s i t u a t i o n returns to the i n i t i a l eutrophic s t a t e .
By year
20 conditions have become nearly the same as the trophic state i n year 20
for p o l i c y I.
Under p o l i c y I I I (low growth and 60 per cent removal; Figure 24),
there i s again improvement at f i r s t , but by year 14 the s i t u a t i o n i s back
to
the i n i t i a l trophic s t a t e .
The dry period does not appear to a f f e c t
the lake as s e r i o u s l y as with the higher loading rates of p o l i c y I I , but
a l g a l growth appears to remain i n the bloom category.
To investigate the e f f e c t s of removing a l l of the phosphorus
from municipal sources (e.g. spray i r r i g a t i o n ) , a 20-year period with a
60 per cent reduction (no growth) was simulated (Figure 24).
Trophic con-
133
NO PHOSPHORUS REMOVAL AND NO
GROWTH
I
e
^
o
E
14
A
A-
Phosphorus
Phvtoolanhton
Di s o l v e d o x y g e n
12 g
Iroli
I
\
/\
V'/
— V *
—
i
S
60
— •
|
,'\
1/
o
40
i
i
PhosphofuS
O
8
60% PHOSPHORUS REMOVAL AND HIGH GROWTH
70
Phytoplankton
Dissolved
A
/
y
x>
> —
6
|
8
3
0
•6
4
v
\
V
/
/
8
10
tn
12
y . a r i
14
—
°"
\ ,'
—
n6
IB
a
A
\
V
10
o
>•
o
Tim*
I
K
v
^
2
A
oxygen
s
0
10
20
in
12
14
yt a r t
Figure 24. Hypothetical effects of four different phosphorus management p o l i c i e s on the long-range eutrophication
of Skaha Lake.
IS
18
\
134
d i t i o n s show s i g n i f i c a n t improvement:
occur and phytoplankton
growth appears to remain at a tolerable l e v e l
during most of the period.
when the phytoplankton
no low dissolved oxygen conditions
Even during an exceptionally dry year
(15)
peak reaches a l e v e l that could be considered a
minor bloom, the peak i s only h a l f of the i n i t i a l value.
These simulations support the predictions of Stockner
and
Pinsent (1974) concerning the r e l a t i o n s h i p between future phosphorus
loading and the trophic state of Skaha Lake (Figure 25).
Stockner
and
Pinsent have established trophic c r i t e r i a on the basis of hydrologic
retention time, mean depth, phytoplankton
and periphyton production, d i s -
solved oxygen depletion, and other limnological data.
above the " c r i t e r i a " area i n d i c a t e a moderate
Values within and
to high trophic s t a t e , and
the p r o b a b i l i t y of moderate to serious a l g a l blooms during most years.
With phosphorus removal by advanced ("tertiary") treatment,
Stockner
and
Pinsent predict the p r o b a b i l i t y of frequent a l g a l blooms f o r moderate, high,
and low population growth rates (I, I I , and III) after 1980.
With complete
removal of municipal phosphorus ("land treatment"), an acceptable trophic
state with infrequent a l g a l blooms i s predicted.
This "steady s t a t e " s i t u a -
tion could, however, be upset i f phosphorus loading from Okanagan Lake i n creased s i g n i f i c a n t l y .
C.
SUITABILITY OF THE MODEL FOR OTHER LAKES
The model has been formulated
for a lake with r e l a t i v e l y high
primary production, making i t more s u i t a b l e for eutrophic than o l i g o t r o p h i c
lakes.
The key assumption of the sedimentation
submodel i s that sedimenta-
135
O
I
I
1970
I
1980
1 :
1990
I
2000
I
2010
I
2020
YEAR
Figure 25. Predictions of the trophic status of Skaha
Lake with present phosphorus loading p o l i c i e s , t e r t i a r y
treatment f o r phosphorus removal, and land disposal of
sewage. Each policy i s considered f o r three projected
growth scenarios. The area within and above the " c r i t e r i a "
zone i s considered moderately to highly eutrophic (from
Stockner and Pinsent 1974).
136
tion of phosphorus
i s a d i r e c t function of primary production i n the tropho-
genic layer, thus ignoring possible sedimentation by chemical p r e c i p i t a t i o n .
While i t seems reasonable to assume that much of the soluble phosphorus
i n a eutrophic lake such as Skaha i s u t i l i z e d i n . the production of organic
matter, this may not be the case i n oligotrophic lakes such as Okanagan or
Kalamalka.
Chemical p r e c i p i t a t i o n of phosphorus minerals such as apatite
probably plays a greater r o l e i n the phosphorus
c e l l a et al. 1972, Lee 1970).
cycle of such lakes (Por-
Therefore, this model appears to be more
suited to eutrophic lakes such as Osoyoos.
A chemical p r e c i p i t a t i o n sub-
model would probably be a necessary addition f o r application of the model
to an oligotrophic lake such as Kalamalka.
CHAPTER VII
SUMMARY AND
CONCLUSIONS
A simulation model of the phosphorus cycle i n eutrophic
Skaha
Lake shows t o t a l phosphorus to be a u s e f u l indicator for the p r e d i c t i o n
of trophic states.
Difference equations and
a d a i l y time scale are used
i n a mass balance model which accounts for the dynamic s t r a t i f i c a t i o n regime
of the lake. T o t a l phosphorus movement between epilimnion, hypolimnion,
and sediments i s detailed i n a series of submodels.
submodel predicts loading
An eddy d i f f u s i o n
from the hypolimnion to the epilimnion which can
equal external loading for short periods of the summer.
A phosphorus s e d i -
mentation submodel predicts organic sedimentation on the basis of primary
production and inorganic sedimentation from adsorption
regeneration submodel considers
considerations.
A
the temperature-dependent decomposition
rates of sedimented phosphorus. A primary production submodel accounts
for temperature, l i g h t and phosphorus dependency, as w e l l as r e s p i r a t i o n ,
grazing, sinking and
advection losses.
tions were necessary i n the formulation
succeeded i n simulating
of detailed submodels, the model
three key trophic indicators reasonably w e l l .
on known phosphorus loading and
agreement was
Although many s i m p l i f y i n g assump-
Based
three years of limnological data, reasonable
found between r e a l and simulated t o t a l phosphorus concentra-
t i o n , phytoplankton biomass, and hypolimnetic dissolved oxygen.
137
136
The model i s considered applicable to other eutrophic lakes,
but not to o l i g o t r o p h i c lakes without
ing sedimentation losses from
the i n c l u s i o n of a submodel d e s c r i b -
phosphorus mineral p r e c i p i t a t i o n .
The i n -
clusion of a submodel describing regeneration of phosphorus by d i f f u s i o n
from sediments could improve p r e d i c t a b i l i t y , as r e s u l t s show that three
to four times more phosphorus apparently returns to the lake from deepwater sediments than possible by b a c t e r i a l decomposition
alone.
This f i n d -
ing shows the model to be a u s e f u l research tool f o r i n d i c a t i n g areas needing further research.
Improved simulation of phytoplankton
production
could probably be achieved with the i n c l u s i o n of a zooplankton
submodel
and extension to include the s p e c i f i c growth dynamics of more than one
a l g a l group.
The Michaelis-Menton
h a l f - s a t u r a t i o n constant appears to be
the most s e n s i t i v e c o e f f i c i e n t i n the primary production submodel.
The probable e f f e c t s of four phosphorus management p o l i c i e s
are assessed using 20 years of hydrologic data (1949-69) and the eutrophic
conditions of 1970 as a s t a r t i n g point.
While no attempt i s made to pre-
d i c t the trophic status of the lake for the next 20 years, d e f i n i t e trends
are apparent.
With no phosphorus removal and no increase i n loading over
the hypothetical 20-year period, phytoplankton
blooms increase i n i n t e n s i t y
and hypolimnetic dissolved oxygen approaches zero, while phosphorus concentrations are greater than 60 yg/1.
With 60 per cent removal of municipal
phosphorus and conditions of either low or high economic growth i n the Pent i c t o n region, the eutrophic conditions of 1970 are again reached within 12
to 14 years.
Algal blooms and hypolimnetic dissolved oxygen d e f i c i t s are
p a r t i c u l a r l y serious during dry years.
With 100 per cent municipal phospho
139
removal, trophic conditions appear to improve s i g n i f i c a n t l y , with the p o s s i b i l i t y of minor a l g a l blooms during only dry years.
These results indicate
that complete removal of the phosphorus from municipal sources appears to
be the most r a t i o n a l long-range management p o l i c y .
Percentage removals
associated with advanced waste treatment appear to be only a temporary
solution.
These conclusions demonstrate that a t h e o r e t i c a l model to pred i c t trophic indicators i n a lake can be useful as both a research tool
and a p r a c t i c a l planning aid f o r decision-making.
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APPENDIX A
INPUT DATA FOR SKAHA LAKE
TABLE A - l
MIXING AND EDDY DIFFUSION DATA (North Basin)
D
A
T
E
EPILIMNION
VOLUME
(km )
3
15 March 1969
1 A p r i l 1969
15 A p r i l 1969
1 May . 1969
15 May
1969
1 June 1969
15 June 1969
1 July 1969
15 July 1969
1 August 1969
15 August 1969
1 September 1969
15 September 1969
1 October 1969
15 October 1969
1 November 1969
15 November 1969
.1 December 1969
15 December 1969
1
15
1
15
1
January 1970
January 1970
February 1970
February 1970
March 1970
HYPOLIMNION
VOLUME
(km )
3
THERMOCLINE
VOLUME
(kin )
THERMOCLINE
THICKNESS
(m)
COEFFICIENT OF
EDDY DIFFUSION
(cm /sec)
2
0
0
.024
.048
.070
.080
.090
.106
.114
.120
.125
.144
.160
.184
.210
.280
.517
0
0
.517
.517
.459
.415
.377
.35 7
.337
.315
.307
.303
.302
.285
.273
.253
.233
.187
0
.517
. .517
0
0
.034
.054
.070
.080
.090
.096
.096
.094
.090
.088
.084
.080
.074
.050
0
0
0
0
0
2.0
3.0
5.0
5.0
6.0
5.0
5.0
5.0
5.0
7.0
7.0
7.0
6.0
2.0
0
0
0
0
0
.077
.077
.051
.077
.020
.077
.077
.077
.077
.154
.077
.077
.077
.077
0
0
0
0
0
0
0
0
.517
.517
.517
.517
.517
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
\
TABLE A - l (Continued)
MIXING;DATA (South Basin)
DATE
15
1
15
1
15
1
15
1
15
1
15
1
15
1
15
1
15
1
15
March 1969
A p r i l 1969
A p r i l 1969
May 1969
May 1969
June 1969
June 1969
July 1969
July 1969
August 1969
August 1969
September 1969
September 1969
October 1969
October 1969
November 1969
November 1969
December 1969
December 1969
1
15
1
15
1
January 1970
January 1970
February 1970
February 1970
March 1970
EPILIMNION
VOLUME
(km )
0
0
.002
.014
.014
.014
.014
.014
.014
.014
.014
.014
.018
.024
.030
.036
.041
0
0
0
0
0
0
0
HYPOLIMNION
VOLUME
(km )
3
.041
.041
.036
.022
.016
.016
.016
.016
.016
.016
.016
.016
.012
.008
.006
.003
0
.041
.041
.041
.041
.041
.041
.041
THERMOCLINE
VOLUME
(km )
3
0
0
.003
.013
.011
.011
.011
.011
.011
.011
.011
.011
.011
.009
.005
.002
0
0
0
0
0
0
0
0
THERMOCLINE
THICKNESS
(m)
0
0
1.0
2.0
4.0
6.0
6.0
6.0
6.0
6.0
6.0
6.0
6.0
6.0
3.0
2.0
0
0
0
0
0
0
0
0
155
TABLE A-2
RADIATION AND EPILIMNION TEMPERATURE
NET RADIATION*
(langleys/day;
average f o r month)
DATE
15
1
15
1
15
1
15
1
15
1
15
1
15
1
15
1
15
1
15
March 1969
A p r i l 1969
A p r i l 1969
May 1969
May 1969
June 1969
June 1969
July 1969
July 1969
August 1969
August 1969
September 1969
September 1969
October 1969
October 1969
November 1969
November 1969
December 1969
December 1969
1
15
1
15
1
January 1970
January 1970
February 1970
February 1970
March 1970
315
361
553
569
579
500
312
203
89
47
82
163
EPILIMNION
TEMPERATURE
(°C)
1.8
3.0
5.8
8.4
11.3
14.8
18.6
20.2
20.4
20.6
20.6
18.4
15.2
13.0
11.2
9.6
7.8
5.8
4.0
3.0
2.4
1.8
1.2
1.4
1 langley = 1 g calorie/cm^; measured,with Eppley 180
Pyranometer at Summerland, B.C.; reported i n Monthly
Radiation
Summary, Dept. Transport, Meteorol. Branch,
Gov. of Canada, 1969-1970.
Stein and Coulthard 1971.
156
TABLE A-3
ESTIMATED PERCENTAGES OF TOTAL PHOSPHORUS ENTERING SKAHA LAKE
FROM KNOWN SOURCES, 1969-71*
S O U R C E
Municipal sewage (Penticton)
Okanagan Lake (via Okanagan River)
Tributary streams (natural sources)
Septic tanks ( v i a ground water)
D u s t f a l l and p r e c i p i t a t i o n
Agriculture ( v i a streams)
Septic tanks (via streams)
Ground water (natural sources)
Industry
Storm sewers
Ground water (other sources)
TOTAL
PERCENTAGE
59.7
21.9
7.6
5.3
3.5
0.7
0.4
0.3
0.3
0.2
0.1
100.0%
(24,500 kg from
March 1969 to March 1970)
Haughton et al. 1974 (includes estimates of storm sewer
loading from Hendren and Oldham 1972 and ground water loading
from Kennedy et al. 1972)
TABLE A-4
MONTHLY OUTFLOW HYDROLOGY FROM SKAHA LAKE,
March 1969 to March 1970*
MONTH
15 March - 31 March
April
May
June
July
August
September
October
November
December
January
February
1 March - 15 March
TOTAL
DISCHARGE (Acre-ft)
32,800
51,300
85,000
40,600
37,200
34,800
34,100
31,700
22,900
19,800
15,100
14,300
4,800
426,000
Although monthly values are shown here, d a i l y values were
used i n computing inflow and outflow of phosphorus (from Surface Water
Summary f o r B r i t i s h Columbia, Gov. of Canada, Dept. Transport).
The average discharge for 48 years of record i s
386,000 a c r e - f t / y r .
158
TABLE A-5
YEARLY OUTFLOW HYDROLOGY FROM SKAHA LAKE, 1949 to 1973
(15 March to 15 March of the following year)
YEAR
1949
1950
1951
1952
1953
1954
1955
1956
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
DISCHARGE (acre-ft/yr)
450.2
524.0
635.6
417.3
416.8
530.9
456.2
436.6
408.4
646.0
337.1
341.6
286.8
187.2
446.2
432.2
243.6
313.0
418.2
426.0
182.9
486.1
844.0
*
From Surface Water Summary f o r B r i t i s h Columbia, Gov. of
Canada, Dept. Transport
APPENDIX B
COLLECTION AND ANALYSES OF LIMNOLOGICAL DATA
During 1969-70 sampling of phosphorus, phytoplankton
oxygen i n Skaha Lake was bimonthly
and dissolved
from 1 May to 15 September and monthly
the remainder of the year (Stein and Coulthard 1971).
Water samples f o r
chemical and b i o l o g i c a l analyses were taken i n two transects:
the north basin and one across the south basin.
data from each transect was averaged
one across
For use i n the model,
to give one value f o r each basin.
At each point on the transects water samples and measurements were taken
at 0, 3, 6, 12, and 18 m (Stein and Coulthard 1971).
Depending on the
thickness of the epilimnion, values from the surface, 3 m and 6 m were
averaged
1.
f o r an epilimnion concentration.
Total Phosphorus
T o t a l phosphorus i n the lake was determined
method described by Gales et al. (1966).
according to the
This method involves a c o l o u r i -
metric determination a f t e r treatment with s u l f u r i c acid and p e r s u l f a t e .
A s i m i l a r method was used to determine t o t a l phosphorus i n the
Okanagan River inflow to Skaha Lake.
This method i s described by Fee (1971):
. . .a colourimetric determination on an auto-analyser
with ammonium molybdate and stannous chloride a f t e r 30 minutes
i n an autoclave with s u l f u r i c acid and potassium p e r s u l f a t e ;
determination done on shaken sample."
11
159
160
2.
Phytoplankton
Water samples for a l g a l analyses were counted with a Sedgwick-
Rafter counting chamber and 100X magnification with a compound
(Coulthard and Stein 1969).
A l g a l biomass was
microscope
reported i n units of c e l l s / m l .
For c o l o n i a l or filamentous algae i t was not f e a s i b l e to count i n d i v i d u a l
cells,
and the following scale was used
(Coulthard and Stein 1969):
Bacillariophyceae (diatoms)
A s t e r i o n e l l a formosa Hass
C y o l o t e l l a glomevata Bachm.
Cymbella sp.
Melosira
spp.
Naviaula
sp.
Pinnularia
sp.
Stephanodisous
sp.
T a b e l l a r i a sp.
8
1
1
1
1
1
1
1
Chlorophyceae (green algae)
Mougeotia
sp.
12-15
Chrysophyceae (chrysophtes)
Dinobryon
sp.
1 cell
= 1 unit
Cryptophyceae (cryptomonads)
Cryptomonas ovata Ehrbg.
1 cell
= 1 unit
Cyanophyceae (blue-green algae)
Anabaena
flos-aquae
(lyngb.) Breb.
Bos toe sp.
Oscillatoria
acutissima
Kuff
Dinophyceae ( d i n o f l a g e l l a t e s )
Certa-ium k i v u n d i n e l l a
(O.F. Mull.) Duj.
cells
cell
cell
cell
cell
cell
cell
cell
=
=
=
=
=
=
=
=
1
1
1
1
1
1
1
1
unit
unit
unit
unit
unit
unit
unit
unit
c e l l s = 1 unit
12-15
12-15
cells
cells
12-15
c e l l s = 1 unit
1 cell
1 unit
1 unit
= 1 unit
Phytoplankton biomass was converted from c e l l s / m l to dry weight
concentration i n mg/1.
This conversion can be v a r i a b l e depending on the
species of phytoplankton, and an
average value of 100 c e l l s / m l =0.3
mg/1
161
dry weight was used (Chen 1970, Di Toro et al. 1971).
3.
Dissolved Oxygen
Dissolved oxygen values were obtained with a membrane electrode
oxygen/temperature probe (YSI-54) (Stein and Coulthard 1971).
For compara-
tive purposes, at l e a s t one set of determinations i n each transect was
made using the modified Winkler method.