From the numerical model to the educational software: Lake Life

Annls
Limnol.
28 (2) 1992 : 175-189
From the numerical model to the educational software : Lake Life
J . M . Thébaulti
M.J. Salençon
2
Keywords : Ecosystem model, educational software, hydroelectric reservoir.
« Lake Life » is a software program designed to introduce the lay person to lacustrian ecology and to the basic concepts of hydraulic management. Having become familiar with the dynamics of the trophic system as well as the mechanisms leading to eutrophication, the user may experiment with managing the reservoir of his choice. Change over time
in the principal elements in the ecosystem is calculated by a mathematical model. This paper first presents the successive
steps in development of the model :
— choice of variables : three plankton groups, fish, nutrients, oxygen ;
— representation of complex mechanisms : for example, the vertical structure simulated in two layers ;
— transcription into equations.
This recapitulation will initiate the reader into the problems of modeling an ecosystem.
We shall then analyse a few simulated situations : variations in plankton groups in three situations with increasing
trophism, and one example of the impact of turbining on the fish and planktonic populations and on oxygenation of
the hypolimnion. The quite realistic behavior of the simulations makes this software an excellent teaching tool.
Du
m o d è l e numérique au logiciel
didactique : la vie d u
lac
Mots clés : Modèle d'écosystème, logiciel didactique, retenue hydroélectrique.
« La Vie du lac » est un logiciel destiné à initier un public non averti à l'écologie lacustre et aux notions fondamentales
de la gestion hydraulique. Après avoir pris connaissance du fonctionnement de la chaîne trophique ainsi que des mécanismes conduisant à l'eutrophisation, l'utilisateur a la possibilité de gérer une retenue de son choix. L'évolution dans
le temps des principales composantes de l'écosystème est calculée par un modèle mathématique. Nous présentons ici
les étapes successives qui ont permis l'élaboration du modèle :
— le choix des variables : trois groupes planctoniques, poissons, nutriments, oxygène ;
— la schématisation de mécanismes complexes : par exemple la structure verticale simulée en deux couches ;
— la mise en équations.
Cette démarche constitue une bonne initiation à la modélisation d'un écosystème.
Nous analysons ensuite quelques simulations : l'évolution des communautés planctoniques dans trois situations de
trophie croissante, puis un exemple de l'impact du turbînage sur les populations et sur l'oxygénation de l'hypolimnion.
Le comportement suffisamment réaliste des simulations permet d'utiliser ce logiciel comme support de cours pour
l'enseignement.
1. Introduction
« L a k e Life » is a s o f t w a r e p r o g r a m designed to
describe for a lay public the m a n n e r in which a lacustrian ecosystem reacts t o disturbances, whether natural or related to h u m a n activities. M a k i n g use of
1. L a b o r a t o i r e d ' H y d r o b i o l o g i e , U R A 6 9 5 d u C N R S , U n i v e r sité P a u l S a b a t i e r , 118, R o u t e d e N a r b o n n e , 31062 T o u l o u s e
Cedex, France.
2 . E l e c t r i c i t é d e F r a n c e , D i r e c t i o n d e s E t u d e s et R e c h e r c h e s ,
D é p a r t e m e n t E n v i r o n n e m e n t , 6, Q u a i Watier, 78401 C h a t o u
Cedex, France.
a n i m a t e d images, a choice of information level, a n d
a user-friendly m o u s e , it gives a n attractive present a t i o n of the v a r i o u s c o m p o n e n t s in a lacustrian
ecosystem : nutrients, phyto- and zooplankton, fish,
etc. It also describes the principal mechanisms at
work : t h e r m a l stratification, interaction of v a r i o u s
kinds a m o n g t h e links in t h e trophic chain a n d t h e
d y n a m i c s of e u t r o p h i c a t i o n .
Once these fundamental concepts have been review e d , the user is a s k e d to choose a lake type c h a r a c terized b y t h e period required for renewal of w a t e r ,
Article available at http://www.limnology-journal.org or http://dx.doi.org/10.1051/limn/1992015
176
J.M. THEBAULT, M.J.
a n d t o assume c o n t r o l over its future by m a n a g i n g
n u t r i e n t c o n c e n t r a t i o n s , p a r a m e t e r s of hydraulic
m a n a g e m e n t ( w i t h d r a w a l levels a n d p e r i o d ) as well
as a n y s t o c k i n g with y o u n g fish. Critical p e r i o d s
( d u r i n g which water is unfit for s w i m m i n g , fish sur­
vival, etc.) a r e indicated by a l a r m s . T h e u s e r ' s g o a l
is, of c o u r s e , t o fight e u t r o p h i c a t i o n while integra­
t i n g t h o s e m e c h a n i s m s which c o n t r i b u t e t o m a i n t a i ­
ning water quality.
In o r d e r for a simulation closely to a p p r o a c h rea­
lity, it is necessary t o use a numerical m o d e l which
s i m u l a t e s the ecosystem d y n a m i c s . T h e great n u m ­
ber of possible responses the model may give, depen­
ding o n the user's choice and the history of the reser­
v o i r , precludes use of pre-established scenarii. T h e
m o d e l performs « on-line » calculation of variations
in the m a i n ecosystem c o m p o n e n t s , before the user's
eyes, enabling h i m to visualize continually the reper­
cussions of his system m a n a g e m e n t . This a p p r o a c h
closely parallels t h a t m a d e of decision-support
m o d e l s , a n d is, for t h a t r e a s o n , a g o o d i n t r o d u c ­
t i o n t o o n e of t h e key functions of m o d e l i n g .
T h e « L a k e Life » model is a simplified version
o f t h e c o m p u t e r c o d e perfected for study of P a r e l o u p L a k e ( T h é b a u l t & Salençon 1992).
T h i s p a p e r presents the c o n c e p t s b e h i n d the
m o d e l , t h e choice of t r o p h i c n e t w o r k a n d variables,
as well as t h e simplifying h y p o t h e s e s it was neces­
s a r y t o m a k e . O n e of the m a j o r p r o b l e m s c o n f r o n ­
t i n g us w a s t o find a c o m p r o m i s e b e t w e e n the
m o d e l ' s complex form of representation, integrating
t o a high degree present hydrobiologjcal k n o w - h o w
in t h e field of reservoir ecology, a n d a calculating
t i m e which seemed reasonable for a m i c r o c o m p u t e r .
T h e p u r p o s e of t h e model is a b o v e all p e d a g o g i ­
cal ; for this r e a s o n , it is essential t h a t t h e simula­
tions be characteristic — even caricatures, in a sense
— so as t o c o n s t i t u t e « teaching cases » w h i c h can
easily b e assimilated b y t h e user. O n l y t h e p r e d o ­
m i n a n t system m e c h a n i s m s have t h e r e f o r e been
selected. W i t h apologies t o the specialists, we have
simplified t o t h e extreme the m o r e complex
mechanisms.
F o r all these r e a s o n s , this m o d e l can absolutely
n o t b e used as a m a n a g e m e n t t o o l , a n d even less as
a research t o o l .
T h e s o f t w a r e r u n s on A t a r i or P C - c o m p a t i b l e
c o m p u t e r s ; simulation of o n e year requires approxi­
m a t e l y t w o m i n u t e s ' calculating t i m e . T h i s is
SALENÇON
(2)
between 1000 a n d 5000 times faster than the time
it would take similar c o m p u t e r s t o run an actual
m a n a g e m e n t m o d e l of the P a r e l o u p type.
2. Description of the model
2.1. Physical structure
T h e physical structure of the system is o n e of the
elements in the p r o g r a m which required the grea­
test simplification, essentially for reasons of com­
puter memory. T h e water mass is divided vertically
into two h o m o g e n e o u s layers which represent sea­
sonal thermal stratification. T h e surface layer, the
epilimnion, is separated from the b o t t o m layer, the
hypolimnion, by a t h e r m o c l i n e . T h e b o t t o m layer
is in contact with sediment.
Each layer is characterized by its t e m p e r a t u r e ,
volume, depth and m e a n illumination. The dyna­
mics of the two water masses are simulated in two
phases : o n e phase of homogeneity in winter, when
only the epilimnion exists, a n d o n e phase of strati­
fication in s u m m e r , when the thermocline level is
constant. It was impossible t o introduce the tran­
sient spring thermoclines, variations in depth of the
thermocline or the g r a d u a l deepening of the ther­
mocline in a u t u m n . T h u s , the onset of stratification
and the a u t u m n mixing are instantaneous !
Inflow and outflow of water are represented very
schematically : inflow is always localized in the sur­
face layer ; outflow due to turbining may be at the
surface or on the b o t t o m , with the user free to deter­
mine the outlet level for each season.
The program proposes a choice among three types
of reservoir, characterized by the period required for
water renewal : a short.residence time of from two
weeks to a m o n t h ( G r a n g e n t , for example), from
o n e to three m o n t h s (as for C h a m b o n , for exam­
ple), a n d on the order of one year for reservoirs with
a p r o t r a c t e d residence t i m e (such as P a r e l o u p and
Sainte-Croix). T h e length of the period of stratifi­
cation a n d exchange between the two layers differ
according to the type of reservoir : in the first case,
no stratification is introduced ; in the second, there
is stratification, but t h e r e is nonetheless a low but
constant a m o u n t of exchange between the two
layers ; in the third case, stratification lasts from late
spring t o m i d - a u t u m n , and there is no exchange
except in the event of t u r b i n i n g . F o r the last two
(3)
FROM THE
NUMERICAL
MODEL TO THE EDUCATIONAL
SOFTWARE
: LAKE
LIFE
177
reservoir types, t u r b i n i n g t h r o u g h the lower outlet
triggers m o v e m e n t from t h e epilimnion t o w a r d the
hypolimnion.
T h e fish prey o n z o o p l a n k t o n . We a s s u m e here
that the population is homogeneous over time,
which permits introduction of a single v a r i a b l e .
There are two possible sources of phosphorus and
nitrogen : c o n c e n t r a t i o n s from upstream and any
discharge of water containing some concentrations
of these same elements. T h e residence time deter­
mines the annual inflow-outflow rate. All variables,
with the exception of fish, are withdrawn by
turbining.
Detritus is composed of algae a n d dead a n i m a l s ,
p h y t o p l a n k t o n which has settled, and m a t t e r n o t
assimilated by animals. Bacteria a r e not simulated
in this m o d e l . We assume that they are c o n s t a n t l y
effective in mineralizing organic matter.
2.2. The variables
Oxygen is a n i m p o r t a n t indicator of w a t e r q u a ­
lity, a n d determines the possibility for survival of
m o s t fish species. This variable is therefore inclu­
ded in the model.
Forcing variables :
These variables are directly entered into the model
a n d are therefore not calculated :
— respective volumes of the two layers a n d of
the sediment,
— inflow a n d outflow rates,
— c o n c e n t r a t i o n of N a n d P in inflow,
— m e a n light energy in the epilimnion, represen­
ted schematically by a sine curve with a period of
365 days. It is supposed that light energy in the hypo­
limnion is t o o low t o permit algal growth ;
— the t e m p e r a t u r e of each layer, also represen­
ted by a sine curve. D u r i n g stratification, the h y p o ­
limnion t e m p e r a t u r e remains low and stable.
State variables in t h e m o d e l :
T h e model is based o n a p h o s p h o r u s budget,
which is to say t h a t all variables, with the exception
of nitrogen a n d dissolved oxygen, are expressed in
p h o s p h o r u s units.
Phytoplankton are divided into two groups : algae
which may be c o n s u m e d by the z o o p l a n k t o n , and
Cyanobacteria, capable of fixing atmospheric nitro­
gen a n d not c o n s u m e d by t h e z o o p l a n k t o n .
In order t o limit the n u m b e r of variables, we do
not simulate silica a n d therefore d o not distinguish
a diatom group.
Nutrients : b o t h g r o u p s of algae need p h o s p h o ­
rus. We have introduced nitrogen as it may be a limi­
ting factor. It is c o n s u m e d by both groups of algae,
but is n o t indispensable to Cyanobacteria.
Z o o p l a n k t o n : o u r experience at P a r e l o u p led us
t o distinguish a single g r o u p of herbivorous zoo­
p l a n k t o n , as the i m p a c t of c a r n i v o r o u s z o o p l a n k ­
ton is limited in c o m p a r i s o n with prédation by
plankton-grazing fish.
2.3. Modeled processes
T h e d i a g r a m of the model dynamics is s u m m a r i ­
zed in Figure 1 ; all equations and variables in Tables
1, 2, 3, 4 and 5.
Phytoplankton
T h e factors for phytoplankton production include
light, t e m p e r a t u r e and nutrient concentration : all
factors which can curb the p h y t o p l a n k t o n g r o w t h
rate, especially in ranges of values far off o p t i m u m
values.
We have used M o n o d ' s equation (1942), a hyper­
bolic function which is well suited t o description of
the relationship between phytoplankton growth a n d
nutrient concentration. We have chosen a similar
e q u a t i o n to represent the effect of light and t e m p e ­
r a t u r e , introducing a threshold value below which
t h e r e is n o g r o w t h . These functions are less sophis­
ticated t h a n those used in m o r e complete m o d e l s
(Steele 1962, Parker 1974, Eilers & Peters 1988, Tal­
bot et al. 1991) : in particular, they d o not simulate
t h e d r o p in growth rate at high t e m p e r a t u r e s or
u n d e r conditions of photo-inhibition, which is less
i m p o r t a n t in this model. They are, on t h e other
h a n d , far simpler t o calculate.
Real g r o w t h is defined as the product of a maxi­
m u m g r o w t h rate and the three limiting factors.
T h e t w o groups of algae need p h o s p h o r u s a n d
nitrogen for development. T h e first group is limi­
ted b y the least a b u n d a n t element (Leibig law :
D r o o p 1974, 1975, Rhee 1978).
C y a n o b a c t e r i a are limited only by a p h o s p h o r u s
deficit ; they are capable of fixing atmospheric nitro­
gen w h e n mineral nitrogen is lacking.
178
(4)
J.M. THEBAULT, M.J. SALENÇON
Factors in disappearance : prédation by zooplankt o n a n d sinking a r e the factors for d i s a p p e a r a n c e
o f t h e first g r o u p of algae. A t least two causes m a y
b e f o u n d for m a j o r variations in sinking speed. O n e
is physical, related to turbulence in the m e d i u m , and
c a n n o t b e simulated here ; t h e other d e p e n d s on
n u m e r o u s factors such as cell size, t e m p e r a t u r e , age
o f the p o p u l a t i o n or lack of n u t r i m e n t . W e chose
this latter factor for o u r model, linking sinking speed
t o g r o w t h limitation d u e t o n u t r i e n t s .
N a t u r a l m o r t a l i t y is considered to be a negligible
f a c t o r in c o m p a r i s o n to p r é d a t i o n a n d sinking.
C y a n o b a c t e r i a c a n generally not develop in a turb u l e n t m e d i u m a n d at low t e m p e r a t u r e s (Steinberg
& H a r t m a n 1988, Z o h a r y & Breen 1989). A s we d o
n o t s i m u l a t e t u r b u l e n c e , we have linked m o r t a l i t y
in this g r o u p of algae to t e m p e r a t u r e ; field
o b s e r v a t i o n s at P a r e l o u p indicate t h a t , generally
speaking, agitation in the w a t e r mass is at its maxim u m level in winter a n d spring, when the temperature is the lowest.
Zooplankton
T h e rate of ingestion depends primarily in the
short term on t e m p e r a t u r e a n d nutrient concentration. W e have simplified the model p r o p o s e d by
Thébault (1985) which permits simulation of their
c o m p o u n d e d effect. T h e function linking ingestion
to the quantity of available prey has been replaced
by a hyperbolic function (Mullin et al. 1975). T o
this, we have added a threshold below which feeding is nil. Only the « m a x i m u m feeding » coefficient is a function of the t e m p e r a t u r e . This simplification permits a considerable reduction in the number of coefficients needed.
Rates of assimilation a n d n a t u r a l mortality are
constant. P r é d a t i o n by fish, the principal cause of
Phytoplankton growth
Grazing
F i g . 1. D i a g r a m o f t h e d y n a m i c s o f t h e b i o l o g i c a l m o d e l .
F i g . 1. D i a g r a m m e d e f o n c t i o n n e m e n t d u m o d è l e b i o l o g i q u e .
(5)
FROM THE NUMERICAL MODEL TO THE EDUCATIONAL SOFTWARE : LAKE
z o o p l a n k t o n disappearance, is directly proportional
t o the fish p o p u l a t i o n .
179
LIFE
T a b l e 1. S e d i m e n t a t i o n p r o c e s s .
T a b l e a u 1. L a s é d i m e n t a t i o n .
Fish
W e assume that the population is stable over time,
neither increasing n o r decreasing under n o r m a l
c o n d i t i o n s of o x y g e n a t i o n . Below a first threshold
for concentration of dissolved oxygen, the most fra­
gile fish (the S a l m o n i d a e ) die. If concentrations
of dissolved oxygen c o n t i n u e to d r o p , no fish
survive.
Detritus a n d n u t r i e n t s
Detritus settles at a constant rate. P h o s p h o r u s and
nitrogen are mineralized from detritus, in w h a t is
n o m o r e t h a n t r a n s f o r m a t i o n from an o r g a n i c t o a
mineral f o r m , the speed of which is t e m p e r a t u r e d e p e n d e n t . W e do n o t distinguish t h e different
forms of nitrogen o r p h o s p h o r u s . A fraction of these
elements is stored in sediment a n d later released into
t h e h y p o l i m n i o n w h e n it is anoxic (insufficient
oxygen).
3aX
3Xi
x
3t
Sedimentation
;
' 3z
in top layer
V i ^ At
= -S
aXi
X l
to bottom layer
Sedimentation
in bottom
layer
Dissolved oxygen
Dissolved oxygen is p r o d u c e d as a result of p h o ­
tosynthesis a t t r i b u t a b l e t o p h y t o p l a n k t o n a n d
gaseous exchange at t h e air-water interface, o r rea e r a t i o n . Such e x c h a n g e is faster from a u t u m n to
spring, the p e r i o d d u r i n g which wind speed is gene­
rally h i g h e r .
V
2
^ 2 At
=
S
X l
aXi-S
from top
layer
Sedimentation
X 2
aX
2
to sediment
into sediment
layer
2.4. Numerical considerations
As certain g r o w t h rates are extremely high (a high
value for the derivative), o n e needs to have a small
integration time s t e p . W e usually use the Runge a n d
K u t t a f o u r t h - o r d e r m e t h o d for numerical integra­
tion (Legras 1971) in solving differential e q u a t i o n s
in biological m o d e l s . While this m e t h o d is highly
simple, it calculates the totality of the equations a n d
related s u b r o u t i n e s four times per time s t e p . T h e
finite difference m e t h o d is quicker (as c a l c u l a t i o n
is performed once only), b u t less precise for an iden­
tical t i m e step. E r r o r d u e t o numerical i n t e g r a t i o n
(and to a lesser degree t o c o m p u t e r error) can be esti­
m a t e d by calculating a m a s s budget. A c o m p r o m i s e
between acceptable e r r o r for this type of software
a n d speed in calculation led us to solve e q u a t i o n s
b y m e a n s of finite differences with a t i m e step of
1/10 of a d a y .
V ^S-=S
At
s
X l
aX
2
for X = A , C, D
a = mean area of the lake.
In order to simplify expressions, sedimentation
c o r r e s p o n d i n g to each layer i and variable X
has been written in table 2 :
O
3Xi
180
J.M. THEBAULT, M.J.
(6)
SALENÇON
T a b l e 2. S y s t e m of d i f f e r e n t i a l
equations.
T a b l e a u 2. L e s y s t è m e d e s é q u a t i o n s
différentielles.
In water layers
3Ai
-G
R
.
=
S I , .
T
dAi
(GA-VJ-)A,-^Z-. - A
S
=(a rz-Hz-|4Z - P F
z
F
= (ccfpf - N ) F
F
SÇl.
3t
3D
„ , ,„
. „,
,
,„ . S „
„_3D:
m C , + « l - a ) r + | i ) Z + « l - a ) p + Hf)F - (m, + ^ - ) D , - V - g p
c
c
2
-gp =
^ .
z
3Ai
S A
+
V
z
z
3Di
d
F
F
^
I
A
I
1
=
r
m,D np
- (VN + - ^ ) N
2
a l
2
+ <p N
N
p
A
c
^
S
m
In sediment
^
s
1
A
= max ( 0 , . X + 0 ( g + g ) - i ^ m D
dD
F
X ^ - + m D , n p - g A ] n p - gcCinp - ^JN
3D
= \|/pP
+ m D
2
^jp = ¥NN
_
2
r
2
- cppP.s
s
+ ni D np - cp N
r
s
3D;
2
a
= Xpi nwD -g A -gcC -ii-P
dNi
dt
D
.
.„
...
.
.r, ,
S ^
« ! - z ) r z + Uz)Z + ( ( L - a ) P + J1 )F - (m, + ^ ) D - V
+
+
U
F
N
s
I
l
- ^ - O,
F
2
D
(7)
FROM THE NUMERICAL MODEL TO THE
EDUCATIONAL SOFTWARE : LAKE
181
LIFE
T a b l e 4 . P r o c e s s e s r e p r e s e n t e d in t h e m o d e l .
T a b l e a u 4 . L e s p r o c e s s u s r e p r é s e n t é s d a n s le m o d è l e .
Phytoplankton
growth
Effect of light
if
1
1|(D =
I X D ,
CT|
"
K] + I - 2GJT
if I <
Table 3. Model variables.
Effect of
1,(1) = 0
13,
température
Tableau 3. Les variables du modèle.
ifT>r&R
RRFT) = — - ~ ^ —
k + T - 2t5r
ifT£ti3
1 (T)= 0
t
Forcing
variables
I
M e a n solar i r r a d i a n c e in the u p p e r layer
T] (Tj)
T e m p e r a t u r e of t h e u p p e r (lower) layer
Effect of
T
T
nutrients
V[ (V2)
V o l u m e of the u p p e r (lower) layer
1
M
= l for C y a n o b a c t e r i a
Vg
V o l u m e of the s e d i m e n t layer
1
M
= M i n ( l p . \ ) f o r o t h e r algae
X^,
X
p
C o n c e n t r a t i o n o f v a r i a b l e s N and P i n the i n f l o w
E
Inflow in t o p layer
Sj
O u t f l o w from l a y e r i, i - 1 , 2
Growth
p
N
rate : g = g 1 , 1 1
T
Cyanobacteria
M
mortality
if T < D3
1
m
m (T)=Mmaxfl-- c
\
State
0m
variables
Aj
P h y t o p l a n k t o n g r a z e d by h e r b i v o r o u s z o o p l a n k t o n , i = l
Cj
Cyanobacteria, i = l
Z
H e r b i v o r o u s z o o p l a n k ton
ifT>ro
m (T)=0
ifl <ras
s (l ) = v
c
M
F
Fish
Dj
Detritus. i=1.2,S
Pj
Dissolved inorganic phosphorus. i=l,2,S
Nj
D i s s o l v e d i n o r g a n i c n i t r o g e n . i = l ,2.S
Oj
Dissolved oxygen, i=l,2
A
M
m i
,
1 - M
Zooplankton
Effect of temperature
ingestion
on
r,n.,(T) = t z
Ingestion
K-rz + f
rate
i = 1 : t o p layer
i = 2 : b o t t o m layer
i = S : sediment layer
IF A > GJA.
RZ(A)=R,
ifA<0J
r (A)=0
A
2
Pish
Ingestion
rate
ifZ>0Jz
pKZ) =
ifZ£GJ
p (Z)=0
z
Xf-
F
Nutrient regeneration from
m,(T) = a , e&
T
detritus
rate
182
J.M. THEBAULT, M.J.
SALENÇON
(8)
3. Simulation results
Table 5. Model parameters.
T a b l e a u 5. Les paramètres d u m o d è l e .
Phytoplankton
k , Kp k . k
l
p
parameters
Half-sa lu radon coefficient for limitation by respectively
light, temperature, phosphorus and nitrogen
n
OBj, Uij
Light and tempera cure threshold for growth
y
Maximum growth rate for algae
0„
Temperature threshold for Cyanobacteria mortality
jl .„
maximum mortality rate for Cyanobacteria
np
N : P ratio for all variables
w
Sedimentation
V
parameters
Maximum sedimentation rale
M
ffl
Nutrient threshold below which set! i men talion begins
s
V
Constant sedimentation rate for detritus
D
yf
V
N
Uptake of P and N by sediment
<Pp, t p
N
Release of P and N from sediment
r
Animal
tp
parameters
Maximum ingestion rale at optimal temperature for
respectively zooplankton and fish
Half-saturation coefficient for r ^ f T )
tD
Threshold concentration of algae for zooplanlnon feeding
A
(Bg
Threshold concentration of zooplankton for fish feeding
* .
Half-saturation coefficient for r ( A ) and p (Z)
O j , Op
Assimilation rate
U^ U
Mortab'ty rate
A
z
F
Nutrient regeneration and oxygen parameters
p.
1
Coefficients for
«1,07)
Diffusion of oxygen at the lake surface
•p
Oxygen produced by photosynthesis
•„
Oxygen used in organic decay of detritus
0
Saturated oxygen concentration
—
F
T h e most interesting simulations from an educational point of view are those related to reservoirs
where the residence time is seasonal o r a n n u a l . T h e
management scenarii the user adopts here can significantly modify the future of the reservoir, unlike
the case of the reservoir with a low residence time
where it is impossible to exercise any influence o n
eutrophy in t h e river.
In o u r model, when there is no hydroelectric
power generation, the flow left above the d a m is
equal t o inflow from the watershed. W e can suppose t h a t , in this case, the lake behaves like a natural lake.
W h e n the nutrient concentrations are low (Simulation 1, Fig. 2), we note a springtime increase in
phytoplankton, followed by an increase in herbivorous zooplankton. In the summer, when the lake is
stratified, nutrients become a growth-limiting factor in the surface layer for the phytoplankton, which
decline rapidly d u e to active consumption by the
z o o p l a n k t o n . In a u t u m n , cooling in the surface
layers triggers mixing of the nutrient-deficient epilimnion with the nutrient-rich hypolimnion, leading
to a new development of plankton communities.
In the hypolimnion, dissolved oxygen is consumed in decay of settled detritus. The autumn mixing
p r o m p t s the d r o p in mean oxygen values for the
entire water mass. As the d e m a n d for oxygen in the
hypolimnion is not very high in this simulation, we
note n o significant hypoxia following the mixing.
If we increase the phosphorus concentrations upstream (Simulation 2, Fig. 3), the behavior of the
springtime plankton is identical to that in the previous simulation but the biomass is greater. As phosp h o r u s is highly concentrated in inflow, nitrogen
becomes a limiting factor in the epilimnion before
phosphorus. This situation, linked to the rise in temperature and the decreased turbulence, fosters the
development of Cyanobacteria, which assimilate
excess phosphorus and fix dissolved atmospheric
nitrogen. During the a u t u m n mixing, the impact of
Cyanobacteria is so great that other algae can n o
longer develop. T h e Cyanobacteria decline when the
medium is more turbulent a n d the temperatures
lower. In this case, as the Cyanobacteria are not consumed, there is only one period of zooplankton
development, in the spring.
(9)
FROM THE NUMERICAL MODEL TO THE EDUCATIONAL
SOFTWARE : LAKE
LIFE
183
At the end of summer, the hypolimnion is anoxic,
a n d the a u t u m n mixing triggers a serious d r o p in
oxygen concentrations t h r o u g h o u t the water mass,
which may be fata! to certain fish species.
the first and second simulations, depending o n the
year (Salençon & C a p b l a n c q 1987, Salençon et al.
1988, 1989, 1990a, 1990b). The third s i m u l a t i o n
could apply to a highly eutrophicated reservoir.
If high p h o s p h o r u s concentrations are maintained over several years (Simulation 3, Fig. 4), o n e
reaches a m o r e p r o n o u n c e d situation of e u t r o p h y ,
with m a j o r declines in oxygen level, even in the
epilimnion.
Figure 5 shows the effect of two other possible
types of hydraulic management : the initial conditions and inflow concentrations are identical to those
in Simulation 2 ; summer turbining is through either
the u p p e r or lower outlets. Here we note a m a j o r
decrease in Cyanobacteria a n d a marked a u t u m n
peak for consumable algae and z o o p l a n k t o n .
T h e model results correspond closely t o observations o n a n u m b e r of sites. For example, the first
simulation could well apply to Sainte-Croix, an oligotrophic lake ( P o u r c h e r & Salençon 1990). Variations in the p l a n k t o n communities at P a r e l o u p
situate this particular reservoir somewhere between
T h e level of the turbining outlet has n o m a j o r
effect o n variations in the epilimnic p o p u l a t i o n s .
Turbining t h r o u g h t h e lower outlet, on t h e o t h e r
h a n d , does permit better reoxygenation of t h e
F i g . 2 . S i m u l a t i o n 1. A n o l i g o t r o p h y l a k e w i t h n o h y d r o e l e c t r i c p o w e r g e n e r a t i o n . A n n u a l v a r i a t i o n i n p l a n k t o n c o m m u n i t i e s ( c o n s u m a b l e a l g a e , C y a n o b a c t e r i a a n d z o o p l a n k t o n ) [a] a n d i n d i s s o l v e d o x y g e n in t h e e p i l i m n i o n a n d h y p o l i m n i o n [ b ] . D i s s o l v e d o x y g e n
is e x p r e s s e d a s a p e r c e n t a g e o f t h e c o n c e n t r a t i o n u n d e r c o n d i t i o n s o f
Fig. 2. Simulation
saturation.
1. C a s d ' u n l a c o l i g o t r o p h e s a n s p r o d u c t i o n h y d r o é l e c t r i q u e . E v o l u t i o n a n n u e l l e d e s c o m m u n a u t é s
planctoniques
( a l g u e s c o n s o m m a b l e s , c y a n o p h y c é e s e t ^ o p l a n c t o n ) ( a ) e t d e l ' o x y g è n e d i s s o u s d a n s l ' é p i l i m n i o n et l ' h y p o l i m n i o n ( b ) . L ' o x y g è n e
dissous est e x p r i m é en p o u r c e n t a g e de la c o n c e n t r a t i o n à
saturation.
184
J.M. T H E B A U L T , M.J.
(10)
SALENÇON
—PHYTO
—CYANO
— ZOO
/'A
J
F
M
A
M
J
J
A
S
O
N
D
N
D
100
80
60
40
20
J
J
F
F
M
M
A
A
M
M
J
J
J
J
A
S
A
S
O
O
N
D
Fig. 3 . S i m u l a t i o n 2. A n n u a l variation in p l a n k t o n communities ( c o n s u m a b l e algae, Cyanobacteria a n d z o o p l a n k t o n ) [a], in dissolved
o x y g e n i n t h e e p i l i m n i o n a n d h y p o l i m n i o n [ b ] , a n d i n n u t r i e n t s ( P a n d N ) i n t h e e p i l i m n i o n [ c ] . D i s s o l v e d o x y g e n is e x p r e s s e d a s
a percentage of the concentration under conditions of saturation. T h e high nutrient concentrations a n d the absence of
m a n a g e m e n t foster t h e d e v e l o p m e n t of
hydraulic
Cyanobacteria.
F i g . 3 . S i m u l a t i o n 2. E v o l u t i o n a n n u e l l e d e s c o m m u n a u t é s p l a n c t o n j q u e s ( a l g u e s c o n s o m m a b l e s , c y a n o p h y c é e s e t z o o p l a n c t o n ) ( a ) ,
d e l ' o x y g è n e d i s s o u s d a n s l ' é p i l i m n i o n et l ' h y p o l i m n i o n (b) e t d e s n u t r i m e n t s ( P e t N ) d a n s l ' é p i l i m n i o n ( c ) . L ' o x y g è n e
dissous
e s t e x p r i m é e n p o u r c e n t a g e d e la c o n c e n t r a t i o n à s a t u r a t i o n . L e s a p p o r t s i m p o r t a n t s d e n u t r i m e n t s et l ' a b s e n c e d e g e s t i o n h y d r a u l i q u e f a v o r i s e n t le d é v e l o p p e m e n t d e s c y a n o p h y c é e s .
(11)
FROM THE
NUMERICAL MODEL TO THE EDUCATIONAL SOFTWARE
: LAKE
J
F
M
A
M
J
J
A
S
O
N
D
J
F
M
A
M
J
J
A
S
O
N
D
LIFE
F i g . 4 . S i m u l a t i o n 3 . A n e u t r o p h i c l a k e . A n n u a l v a r i a t i o n in p l a n k t o n c o m m u n i t i e s ( c o n s u m a b l e a l g a e , C y a n o b a c t e r i a a n d
185
zooplank-
t o n ) [a] a n d in d i s s o l v e d o x y g e n i n t h e e p i l i m n i o n a n d h y p o l i m n i o n [ b ] . D i s s o l v e d o x y g e n is e x p r e s s e d a s a p e r c e n t a g e o f t h e c o n c e n tration under conditions of
saturation.
Fig. 4. Simulation 3. C a s d ' u n lac e u t r o p h e . E v o l u t i o n annuelle des c o m m u n a u t é s planctoniques {algues c o n s o m m a b l e s , c y a n o p h y c é e s
et z o o p l a n c t o n ) ( a ) e t d e l ' o x y g è n e d i s s o u s d a n s r e p i l i m n i o n e t P h y p o l i m m o n ( b ) . L ' o x y g è n e d i s s o u s e s t e x p r i m é e n p o u r c e n t a g e
d e la c o n c e n t r a t i o n à
saturation.
hypolimnion than does turbining t h r o u g h the upper
outlet, by fostering exchange between epilimnion
and hypolimnion.
It would b e unwise t o turbine t h r o u g h the lower
outlet at the end of s u m m e r , when the hypolimnion
is anoxic ; oxidation a n d precipitation of iron a n d
m a n g a n e s e , together with the potential effects on
d o w n s t r e a m river quality, are clearly pointed out to
the novice hydraulic m a n a g e r .
We must r e m e m b e r t h a t the model takes into
account the a c c u m u l a t i o n of nutrients in the sedim e n t , where concentrations may become very high.
W h e n the h y p o l i m n i o n is anoxic, p h o s p h o r u s (and
t o a lesser degree, nitrogen, through de-nitrification)
is released into t h e water m a s s , proportionally
increasing the a m o u n t available t o algae at t h e t i m e
of deepening of the thermocline. Therefore, when
the lake is highly e u t r o p h i c a t e d , it would be a mistake to imagine t h a t the situation will rapidly
improve if concentrations are reduced. T h e m o d e l
represents well the inertia attribuable to t h e q u a n tity of nutriment stored in the sediment. T h e m o s t
effective a n n u a l hydraulic management a p p r o a c h is
to turbine at the surface in spring, to eliminate a
m a x i m u m of algae a n d z o o p l a n k t o n so as t o
decrease the fraction in the sediment, and at the b o t t o m in s u m m e r , to eliminate detritus which m a y
have settled and oxygenate the hypolimnion as m u c h
as possible. It m a y take several years to r e t u r n to
acceptable conditions.
186
J . M . T H E B A U L T , M.J.
J
F
M
A
M
J
J
F
M
A
M
J
A
J
(12)
SALENÇON
S
O
N
D
N
D
N
D
100
80
60
40
20
0
J
A
S
O
100
80
60
40
20
J
F
M
A
M
J
J
A
S
O
F i g . 5 V a r i a t i o n i n p l a n k t o n c o m m u n i t i e s in t h e c a s e o f t u r b i n i n g d u r i n g t h e s u m m e r [ a ] . I m p a c t o f t h e c h o i c e o f o u t l e t l e v e l o n o x y g e ­
n a t i o n in t h e w a t e r m a s s : t u r b i n i n g t h r o u g h t h e l o w e r [b] or u p p e r o u t l e t [c].
F i g . 5 . E v o l u t i o n d e s c o m m u n a u t é s p l a n c t o n i q u e s d a n s l e c a s d ' u n t u r b i n a g e p e n d a n t l ' é t é ( a ) . E f f e t d u c h o i x d e la p r i s e d ' e a u
sur
l ' o x y g é n a t i o n d e la m a s s e d ' e a u : t u r b i n a g e p a r la p r i s e de f o n d (b) o u d e s u r f a c e (c).
4. Conclusion
While « Lake Life » is a n educational software
p r o g r a m permitting the user to e m b a r k , mouse in
h a n d , on a discovery of lake ecosystems, it is at the
s a m e t i m e a simplified version of an actual compu­
ter code developed in the course of scientific
research.
T h e a p p r o a c h followed in developing this pro­
gram is identical t o that followed in development
of ecosystem models used in lacustrian ecology
studies.
T h e modeled processes are relatively simplified,
though the m o d e l ' s response is on the whole most
satisfying.
(13)
FROM THE NUMERICAL
MODEL
TO
THE EDUCATIONAL SOFTWARE : LAKE
187
LIFE
T h e r e are m a n y potential uses for this software :
as a teaching a i d , in sensitizing hydraulic m a n a g e ment specialists, in informing the general public, etc.
Gentil S. 1982. — A n a l y s e de s y s t è m e e n écologie. U n e
A s the user retains control over pollutants discharged, hydraulic management and stocking with young
fish, he can visualize the repercussions of his decisions o n the ecosystem as a w h o l e . In this way, he
discovers the m e c h a n i s m s which lead t o e u t r o p h i cation as well as t h e difficulties o n e encounters in
trying t o find remedies.
J a r g e n s e n S . E . 1976. — A n e u t r o p h i c a t i o n model f o r a l a k e .
d e c a s ( L a c d ' A i g u e b e l e t t e ) . I n Modélisation
et simulation
eau
des systèmes
et végétation.
Modelling,
Ecol.
2 : 147-165.
J e r g e n s e n S.E., M e j e r H . & Friis M . 1978. — E x a m i n a t i o n
a l a k e m o d e l . Ecol.
Modelling.
Kremer J.N. & Nixon S.W.
tem.
Simulation
1 9 7 8 . — A coastal
and analysis.
of
4 : 253-278.
marine
ecosys-
E c o l o g i c a l Studies 2 4 , S p r i n g e r -
Verlag, Heidelberg : 217 p .
L e g r a s J . 1 9 7 1 . — M é t h o d e s et techniques
que.
de t'analyse
numéri-
D u n o d , Paris : 323 p.
tériennes.
In addition t o t h e authors mentioned in this text,
a n u m b e r of w o r k s dealing with modeling aquatic
ecosystems might be consulted : Bierman 1976,
C a n a l e et al. 1976, Jorgensen 1976, Jorgensen et al.
1978, Kremer & Nixon 1978, G a r ç o n 1981, Spain
1982, Salençon et al. 1984, Thébault 1984, Riley &
Stefan 1988, A n d e r s e n & Nival 1989.
Dominante
E d i t i o n s d u C N R S , Paris : 17-62.
M o n o d J . 1 9 4 2 . — Recherches
To find out more
étude
mathématique
de l'environnement.
sur la croissance
des cultures
bac-
Hermann, Paris : 210 p.
M u l l i n M . M . , S t e w a r t E . F . & F u g l i s t e r F . J . 1975. —
Ingestion
by p l a n k t o n i c g r a z e r s as a f u n c t i o n of c o n c e n t r a t i o n o f f o o d .
Limnol.
Oceanogr.,
20 : 259-262.
P a r k e r A . 1974. — E m p i r i c a l functions relating m e t a b o l i c
pro-
c e s s e s in a q u a t i c s y s t e m s t o e n v i r o n m e n t a l v a r i a b l e s . J.
Res.
Board
Can.,
31 : 1 5 5 0 - 1 5 5 2 .
P o u r c h e r A . M . & Salencon M . J . 1990. — Modélisation d u p l a n c t o n d a n s u n e r e t e n u e o l i g o t r o p h e : S a i n t e - C r o i x s u r le V e r d o n . Hydroécol.
Appt.,
1 : 91-134.
R h e e G - Y u l l 1978. — Effects of N : P . a t o m i c ratios a n d nitrate
limitation
Ack nowledgements
o n algal g r o w t h , cell c o m p o s i t i o n ,
u p t a k e . Limnol.
« L a k e Life » was developed for the E D F « Mission Environm e n t » , in c o l l a b o r a t i o n w i t h t h e M y r i a d
firm,
which contribu-
t e d t h e g r a p h i c s a n d t h e u s e r i n t e r f a c e . It exists n o w in t h e F r e n c h
v e r s i o n , a n d will s o o n b e a v a i l a b l e in E n g l i s h , f o r u s e o n
PC-
Oceanogr.,
and
nitrate
23 : 10-25.
Riley M . J . & S t e f a n H . G . 1988. — M 1 N L A K E : a d y n a m i c l a k e
water
quality
simulation
model.
Ecol.
Modelling,
43 :
155-182.
Salençon M . J . , Merle G. & S a b a t o n C. 1984. — L e réseau
de
c o m p a t i b l e c o m p u t e r s (3 1 / 2 " a n d 5 1 / 4 " d i s k e t t e s ) a n d o n A t a r i
m e s u r e s h y d r o b i o l o g i q u e s d e la r e t e n u e d e G r a n g e n t ( L o i r e ) ;
S T . It m a y b e o r d e r e d f r o m t h e M i s s i o n E n v i r o n m e n t f o r F F 9 5 .
a n a l y s e p a r t i e l l e d e s r é s u l t a t s . Cahiers
E L E C T R I C I T E D E F R A N C E , Mission Environnement,
r u e d e Ea B a u m e , 7 5 0 0 8
26,
tereau,
du laboratoire
de
Mon-
15 : 7 - 1 2 .
S a l e n ç o n M . J. & C a p b l a n c q J. 1987. — E t u d e de la r e t e n u e d e
Paris.
M Y R I A D S.A.R.L., 4 rue de Bordeaux, 31200 Toulouse.
P a r e l o u p . Bilan des t r a v a u x réalisés en
1986 d a n s l e c a d r e
de la c o n v e n t i o n E D F - M i n i s t è r e d e l ' E n v i r o n n e m e n t .
Rap-
p o r t H E - 3 1 / 8 7 . 5 , Electricité d e F r a n c e , Paris : 26 p .
References
S a l e n ç o n M . J . , T h é b a u l t J . M . & C a p b l a n c q J. 1 9 8 8 . —
A n d e r s e n V. & Nival P . 1989. — Modelling of
phytoplankton
p o p u l a t i o n d y n a m i c s i n a n e n c l o s e d w a t e r c o l u m n . J.
biol.
Ass.
U.K.,
mar.
B i e r m a n V . J . Jr. 1976. — M a t h e m a t i c a l m o d e l of t h e selective
e n h a n c e m e n t of blue green algae by nutrient enrichment. In :
tic ecosystems,
biochemical
processes
in
aqua-
A n n A r b o r S c i e n c e s , M i c h i g a n : 1-31.
C a n a l e R . P . , D e P a l m a L . M . & Vogel A . H . 1976. — A p l a n k t o n b a s e d food w e b m o d e l for L a k e Michigan. In : C a n a l e R . P .
( E d . ) : Modelling
tems,
biochemical
processes
in aquatic
ecosys-
D r o o p M . R . 1974. — T h e n u t r i e n t status o f algal cells in contibiol.
Ass.
U.K.,
54 : 825-855.
D r o o p M . R . 1975. — T h e n u t r i e n t s t a t u s o f algal cells in b a t c h
c u l t u r e . J. mar.
biol.
Ass.
Eilers P . H . C . & Peeters J . C . H .
d a n s le c a d r e de l a C o n v e n t i o n E D F - M i n i s t è r e d e l ' E n v i r o n -
U.K.,
43 p .
S a l e n ç o n M . J . , T h é b a u l t J . M . & C a p b l a n c q J. 1989. —
Etude
d e la r e t e n u e d e P a r e l o u p . Bilan d e s t r a v a u x réalisés e n 1 9 8 8
d a n s le c a d r e d e l a C o n v e n t i o n E D F - M i n i s t è r e d e l ' E n v i r o n n e m e n t . R a p p o r t H E - 3 1 / 8 9 . 1 3 , E l e c t r i c i t é de F r a n c e , P a r i s :
77 p .
S a l e n ç o n M . J . , T h é b a u l t J . M . & C a p b l a n c q J . 1990a. —
Etude
d e la r e t e n u e d e P a r e l o u p . Bilan d e s t r a v a u x réalisés e n 1 9 8 9
A n n A r b o r Sciences, Michigan : 33-74.
n u o u s c u l t u r e . J. mar.
de la r e t e n u e d e P a r e l o u p . B i l a n d e s t r a v a u x réalisés e n 1 9 8 7
n e m e n t . R a p p o r t H E - 3 1 / 8 8 . 2 3 , Electricité de F r a n c e , P a r i s :
69 : 6 2 5 - 6 4 6 .
C a n a l e R . P . ( E d . ) : Modelling
Etude
d a n s le c a d r e d e la C o n v e n t i o n E D F - M i n i s t è r e d e l ' E n v i r o n n e m e n t . Rapport H E - 3 1 / 9 0 . 1 7 , Electricité de France, Paris :
67 p .
S a l e n ç o n M . J., T h é b a u l t J . M . & C a p b l a n c q J . 1990b. —
55 : 5 4 1 - 5 5 5 .
1988. — A m o d e l for t h e rela-
Etude
d e la r e t e n u e d e P a r e l o u p . S y n t h è s e d e s t r a v a u x r é a l i s é s d a n s
tionship between light intensity a n d the rate of p h o t o s y n t h e -
le c a d r e d e l a C o n v e n t i o n E D F - M i n i s t è r e d e l ' E n v i r o n n e m e n t
s i s i n p h y t o p l a n k t o n . Ecol.
(mars 1 9 8 6 - mars 1990). R a p p o r t H E - 3 1 / 9 0 . 2 3 , Electricité
Modelling,
42 : 199-215.
G a r ç o n V. 1981. — M o d é l i s a t i o n n u m é r i q u e d ' u n
écosystème
a q u a t i q u e . A p p l i c a t i o n a u réservoir d e G r a n g e n t sur la Loire.
T h è s e d e 3* cycle. U n i v e r s i t é P a r i s 7, P a r i s : 2 3 0 p .
de France, Paris : 40 p.
Spain J . D .
1 9 8 2 . — Basis
microcomputer
models
in
A d d i s o n - W e s l e y , R e a d i n g , M a s s a c h u s e t t s : 354 p .
biology.
188
Steele J . H .
J . M . T H E B A U L T , M.J.
1962. — E n v i r o n m e n t a l control of
i n t h e s e a . Limnol.
Oceanagr.,
photosynthesis
forming Cyanobacteria and the eutrophication of lakes and
Biol.,
A comparative study a n d mathematical modeling of temper a t u r e a n d light o n g r o w t h of three microalgae
useful for wastewater treatment.
Water
Res.,
potentially
25 : 465-472.
1984. — Modélisation des premiers niveaux
réseau trophique pélagique marin. Mise au point de
les et s i m u l a t i o n d e séries e x p é r i m e n t a l e s . T h è s e d e 3
Université Paris 7, Paris : 94 p.
stylifera
D a n a ) . Effets de la t e m -
p é r a t u r e e t d e l a c o n c e n t r a t i o n d e n o u r r i t u r e . J. Exp.
Biol.
EcoL,
Mar.
93 : 223-234.
Thébault J.M. & Salençon M.J. — Simulation mode! of a meso-
20 : 279-287.
T a l b o t P . , T h é b a u l t J . M . , D a u t a A. & D e la N o u e J., 1991. —
Thébault J.M.
T h é b a u l t J . M . 1 9 8 5 . — E t u d e e x p é r i m e n t a l e d e la n u t r i t i o n d ' u n
c o p é p o d e c o m m u n (Temora
7 : 137-150.
Steinberg C E . W . & H a r t m a n n H . M . 1988. — Planktonic bloomr i v e r s . Fresh.
(14)
SALENÇON
du
modue
cycle,
trophic
reservoir
m o d e l . Ecol.
(Lac
Modelling
de
Pareloup,
France) :
Biological
(in p r e s s ) .
Z o h a r y T . & Breen C h . 1989. — Environmental factors
r i n g t h e f o r m a t i o n o f Microcystis
a h y p e r t r o p h i c l a k e . Hydrobiologia,
aeruginosa
favou-
hyperscums in
178 : 1 7 9 - 1 9 2 .
(15)
FROM THE NUMERICAL MODEL
LA VIE DU
LAKE
LAC
Electricité d e France
Mode
TO THE EDUCATIONAL SOFTWARE : LAKE
Myriad
d'emploi
LIFE
Electricité de F r a n c e
Myriad
Instructions for use
Allumez votre ordinateur avec une disquette système M S - D O S
( v e r s i o n 3 o u 5) d a n s l e l e c t e u r A . L e l o g i c i e l n e p e u t
n e r a v e c la v e r s i o n 4 d e
189
LIFE
fonction-
MS-DOS.
Start u p y o u r c o m p u t e r w i t h M S - D O S system disk in disk drive
A . O n c e t h e s y s t e m is l o a d e d , eject t h e s y s t e m d i s k a n d
it w i t h t h e Lake
Life
replace
disk. T y p e L A K E , followed by « return » :
U n e fois le s y s t è m e c h a r g é , e n l e v e z la d i s q u e t t e s y s t è m e et
r e m p l a c e z - l a p a r l a d i s q u e t t e La vie du lac. T a p e z L A C s u i v i d e
r e t o u r - c h a r i o t . U n e f o i s l a v e r s i o n d u j e u c h o i s i e et le l o g i c i e l
c h a r g é , l a d i s q u e t t e p e u t ê t r e r e t i r é e d u l e c t e u r . La vie du lac p e u t
également être copiée dans un répertoire du disque dur.
t h e p r o g r a m w i l l l o a d a n d s t a r t u p . A s s o o n as y o u c h o o s e t h e
Si v o u s p o s s é d e z u n e s o u r i s , celle-ci d o i t ê t r e i n s t a l l é e a v a n t
d e l a n c e r La vie du lac ( s e r e p o r t e r a u m a n u e l d ' i n s t a l l a t i o n d e
votre souris).
r u n n i n g Lake
L e logiciel n é c e s s i t e u n e m é m o i r e d ' a u m o i n s 512 K o p o u r f o n c tionner. Les cartes g r a p h i q u e s Hercules, C G A et E G A sont a u t o matiquement reconnues.
g a m e level y o u w a n t a n d t h e disk d r i v e l i g h t goes o f f , e j e c t t h e
d i s k a n d p u t it a w a y
carefully.
I f y o u h a v e a m o u s e a n d w o u l d l i k e t o u s e it, y o u m u s t
i n s t a l l it ( f o l l o w t h e i n s t r u c t i o n s i n y o u r u s e r ' s m a n u a l )
Lake
Life
first
before
Life.
calls for at least 512 K o of m e m o r y . Y o u r g r a p h i c s
c a r d i s a u t o m a t i c a l l y d e t e c t e d i f it i s a H e r c u l e s , C G A o r E G A . .