This model of the D. Forrester type, constructed in differential equations, predicts the food and mineral supply for the factors biosphere population, depending on two socio-economic factors, until about the year 2500. If contemporary rates of natural resources utilization are maintained and there is no management of the environment, food resources will begin to limit human population growth after 2200, and mineral resources will after 2300. A decrease in the biosphere pollution, increase in effective agricultural production, and discovery of new energy sources may forestall or completely avert the onset of a crisis situation. Conservation measures, according to the model, are to a considerable extent realizable only if carried out simultaneously in both areas

Moiseyev, N. N.

English

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( P A S A - T H - 7 6 0 4 2 )  A GLOBAL B I O G E O C E N O T I C A L  1380-20920 
B I O S P H E R E  S I H U L A T I O N  (National A e r o n a u t i c s  
land Space A d m i n i s t r a t i o n )  12 p 
CSCL 138 Unclas 
-76042 
HC AO2/LIP A 0 1  G3/45 46768 
A GLOBAL BIOGEOCKNOTICAL BIOSPHERE SIMULATION 
N. N. Moiseyev, Yu. M. Svirezhev, 
V. F. Krapivin, and A. M. Tarko 
Translation of "Globaltnaya imitatsionnaya blogeotsenoticheskaya modelt 
biosfery," in: Biogeofizicheskiye i matematicheskiye metody issledovaniye 
geosistem [3iogeophysical and Mathematical Methods in Geosystem Research], 
Moscow, 1978, p g .  37-49. 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
WASHINGTON, D.C. 20546 MARCH 1980 
_ ___--- - - r- -'- ' . -- -.---7---  --,--r--=r--- -- 
.7- -&=- ~ - 
- 
--- I-'- 
A GLOBAL BIOGEOCENOTICAL BIOSPHERE SIMULATION 
N. N. Moiseyev, Yu. M. Svlrezhev, 
V. F. Krapivin, and A .  M. Tarko 
USSR Academy of Sciences Computation Center, 
Institute of Electronics and Radiotechnology 
Recently-performed research on developing simulation methods has /37* 
made it possible to construct a general model of the biosphere involving 
socio-economic, physico-chemical, and ecological processes. In following 
the basic concepts in models of the D. Forrester [1971] type, we shall 
consider the cause-and-effect links existing in the biosphere between 
such elements as the energy of solar radiation (El, the concentration 
of C 0 2  (C) and O2 (01, atmospheric turbidity (B), temperature (T), 
population (g, G), humus (S SG), and the nekson (r) and phytoplankton g ' ($1 in the world's oceans (fig, 1). We shall divide dry-land vegetation 
into three types, differing in productivity and participating with 
varying degrees of intensity In other ecological processes: forests 
(PL, QL), agricultural vegetation (PX, Q X ) ,  and other vegetation (PE, QL). 
In order to calculate socio-economic heterogeneities existing in 
8 the biosphere, dry-land area (S = 0.73805 X 10 h2) is divided into 
two regions, in each of which the processes under study may proceed 
at differing rates. 
2 It is given that a solar radiation energy of Eo = 1.94 cal/cm min. 
enters the biosphere and is used by biospheric photosynthetic elements. 
Here the value of E (t) reaching the Earth's surface is determined by /39 
-
the atmosphere's turbidity and may be calculated using the formula 
E (t) = Eo(t) *exp (-aB - $1, where the coefficient of atmospheric 
4 
absorption of solar energy due to dust and clouds a = 11.643 X 10- , 
and the transparency index of the pure atmosphere 6 = 6.487. The 
dustiness of the atmosphere is determined by the number of atmospherkc 
7 dust particles resulting from dust storms (5.4 X 10 tons/year), volcanic 
9 eruptions, solid and liquid fuel combustion (4.3 X 10 tons/year), and 
expulsion from various kinds of metallurgical and chemical works, cement 
9 plants, and other sources (3.5 X 10 tons/year). 
"umbers in the margin indicate pagination in the foreign text. 1 
Fig. 1. Diagram of the cause- /38 
-
and-effect ties in the global 
biogeocenotlc biosphere simula- 
tion. Designations are explained 
In the text. 
It is considered that in /39 
- 
ocean and dry-land areas the 
coefficients of solar energy 
use are K = 0.07, Kp = KQ = 0.5. 4J 
The productivity of the ocean 
and land ecosystems is determined 
by the intensity of photosyn- 
thesis, which depends upon the 
discrepancy between optimal and 
actual illumination, the amount 
of fertilizers applied, and 
pollution in the corresponding 
environments. The quantity of 
applicable fertilizers is deter- 
ri~ined by the proportion of expend- 
able mineral resources (U g, U G )  Phytomass production increases in propor- 
tion to the increase in atmosp5 .eric C02 concentration until C *  = 0.2% and 
decreases in proportion to the increase in O2 content to hpproximately 
0* = 21%, so that 
As in the work of M. E. Vinogradov et al. (1973), we shall write 
2 differential equations describing the change in phytomass (in tons/km ): 
where R R,,  and R are the rates of increase in $, R, and Q, subject /40 O Y  A Q - 
to illumination, the concentrations of C 0 2  and 02, and environmental 
pollution. R p  and R also depend upon the distrtbutioc of sub-forest Q 
i areas (SL) and agricultural vegetation (SX). The formula for R p ,  for I example, is: 
t 
t 
gp = np ~ ~ ~ ~ ~ ; ' e x p [ m ,  ( 1 -  EE;')][~ -erp(-r2 P)]. 
where 
2 Here Eb is the optimal illumination for phot~synthesis P (rcal/m /day); 
(1 BL , B:~), and B L ~ )  are P/B coefficients for L, X, and c, respectively; 
A! is the coefficient of proportionality; M4, Mp, and M are the rates Q 
of I$, P, and Q desiccation; t tp, and tp are values for energy exchange 
I$' 
expenditure; K is the coefficient reflecting the value for the quota 13 
and proportion of the producer "j' in the nutritional allowance Ri of 
consumer "i" (i,j = g, $, P, Q, f, G, F). 
We shall assume that nekton is harvested by the regions at intensities 
of A (t) and AG(t), maximum P/B is the coefficient r equal to Kr, and the 
g 
limitation in growth of r because of pollutions 5 and Z in regions 1 an9 
! I 
i 
I1 are described by the function $I = exp[-dr(py+eZ)], where p and 9 are 
proportions of all pollutions falling from rcgions 1 and I1 into the 
2 
ocean. Thus the change in biomass r (tons/km ) may, as ic the work of 
M. E. Vinogradov et al. (1973), be described by the equation: 
where 
R -  = K,.P[~ -exp @)]w, 
" r is the instantaneous mortality rate, and tr i o  the value for energy 
exchange expenditure. 
We shall describe the population growth in both regions by calcu- 
lating the relationship of btrth and mortality rates to the mltrition 
equation FRa = Va/a, the material standard if living 
-- /41
! a  7 : -  . \ r' 
c i  - L  !tL[i \ , ! - S ~ , , ) E \ ~ ~  
environmental pollution, ntmospheric C 0 2  and O2 content, and population 
density. Here Vi is the principal (basic resources) of the i region; 
si, uRi9 and UZi are the proportions of principal investments for the 
i region in the development of agriculture, renewal of mineral resources, 
and environmental conservation, respectively. 
The equation for g is: 
E L ~ = ~ - & ~ P ~ - K ~ M ~  ( t ~ / ~ g  (to)], V t t g Z ' / q  9 
i vg - ~ ~ @ r n + ~ ~ ,  ! kgrI ( { -U-V)+C(~( ;~  s!)+ 
* r n  s;))s;'+ ( 4 -  st'' + s q ]  p.  
9; S 4 
The equation for G is similar in form. 
I Change in animal food in both regions is determlned by the rate of animal growth, which depends upon the gaseous makeup of the atmosphere, 
the  availability of a vegetable diet for animals, mortality rate, rate 
of energy exchange with the environment, and consumption by the populace. 
The equaticn for f, for example, has the following form: 
where 
Vf = KfpP + KfrIV, and V is the amount of harvestable nekton needed by 
the animals. 
i In order to calculate the physioiogical effect of 02and C02 concen- 
I trations in living organisms, we shall cite the following relationship 
of the expenditure and energy exchange of element "aw: ta = t: . t:, and 
I 
I 
P I I  t b r c t t h o ,  C B C ~ ;  t uo. O>On ; 
t h =  
tho, c c  io,c,l; tz0 -$t(t:,-t:;), o f  D,:; 
These relationships reflect the increased respiratory expenditure of 
animals and humans, with a C02 concentration elevated beyond the 
threshhold of Ca and an O2 concentration below Oa. 
We shall descibe the effect of human agricultural activity on 
the environment by calculating the amount of energy required for popu- 
lation respiration, mineral resource utilization, and the generatiom 
of pollution. We shall calculate possible ways to manage these elements 
which will make it possible to prevent environmental degradation by 
organizing the intelligent use and conservation of resources, and by 
imposing closed production cycles which fully utilize wastes and pollu- 
tion. Without detailing methods for achieving control, we shall propose 
that the following time functions are characteristic for the scientific 
and technological progress of both regions: K (KZ) is the pollution t 
generation per individual person (a characteristic of the standard of 
living and the technology of production in a society); T* (Tk) is the t 
pollution resorption rate index; M (MG) is the inter~sity of non-renewable 
(i g resource expenditure; THT is the time interval necessary for transfer 
(i) to new resources in the i region; tX and tAi) are the times needed by 
the i region for maximum incorporation of all lands suitable for culti- 
vation and achievement of the maximum possible productivity for 
agricultural cultivation. /43 
- 
We may write the following equation to describe the process of 
pollution generation and utilization (1st region): 
B= * , j t ) g z v ~ - ~ , - u ~ 9 v 4 c ; ~  1 d t - - 
where Z V , = Z ~ ~ [ ~ - ~ ~ D ( - ? ~ V ~ ~ ) J ,  C,,= ",,+~;,ezp[-n~~(t-t~)1, 
T~ ( t ) = ~ ;  (t)[abs+a\g2::g~ 
We shall describe the change in biospheric gaseous makeup by calcu- 
lating the following natural and anthropogenic processes. Assme that 
O2 and C02 exchange between the atmosphere and ocean is described by 
L. Makhtts (1971) model, the source of O2 output on dry land is the 
phytomass, O2 consumption occurs during respiration of element "av at 
a rate of ya = vataaWa and takes place in the resource combustion 
process at rates of b and bGO per person in regions 1 and 11, respec- go 
tlvely. Carbon is assimilated by the plants -.f region 1 (111, in the 
form of C02 from the atmosphere, at rates of OhCRp (OiCRQ) by forests, 
OipRp (OigRQ) by agricultural vegetation, and BFCRp (OiCRQ) by other 
types of plants; it is liberated in the process of element "av respiretion 
,- -. -.-7 - -.17 - - X -7-v -w -- r_E- ---7 - -- . , 
--- .r- -^ -- -------- ___q.Rn-=---- 
v-" 
k 
! at a rate of 8, - $,taaoa, given off during resource combustion at a 
1 rate of b (bOC), and by the decomposition of dead vegetation at a rate gc i Of )IS* 
7 
We shall describe atmospheric turbiditv with the following equation: 
dB 
d t 
dT 
--= N , % + N , Z * N , ~ ~ C ~ + N I ~ ~ C G - $  +YB dt I i 
where N1 and Ng (N2 and N4) are the amounts of pollution and smoke 1 t 
generated by region 1 (11) into the atmosphere, pg i 8  the rate of.cboud 1 
cover alteration due to temperature fluctuations, TG is the rate of 
natural clarification of the atmosphere due to dust settling. We shall /44 
-
present the following relationship between temperature, illumination, and 
alterations in biosphere gaseous makeup through the use of models such 
as that described by M. I. Budyko (1971). 
The remaining model equations, reflecting the dynamics of mineral 
resource alteration M (MG), the principal i'., (Val ind capital investment g -. 
S1 (S2) in agriculture investment for region 1, have the following 
forn (Gelovani et al., 1976): 
i S L  t (u s F9 So,- 5,)r;d , 
-ucg(t -t.) 
where ~ ~ ~ ' a ~ ~ h ( ~ + ~ ~ )  3 C q '  c‘&+c&e I 
The model described above has been expressed in FORTRAN in the form 
of a program for the UVK M-4030. Calculation of all its components for 
100 years requires 1 hour of machine time, which makes it possible to 
carry out assorted experiments on the model. 
The prognosis for biosphere condition without any management and 
maintenance of rates of natural resource utilization, pollutioll generation, 
forest reduction, etc., is shown in fig. 2. Here, beginning in the year 
2050, population density w i l . 1  fluctuate while maintaining a general 
Fig. 2. Prognosis for biospheric component 
dynamics if contemporary rates of natural 
resource utilization are maintained. Explan- 
ation of the desigcations may be found In 
the text. Values for variables are in rel- 
etive units. Their values in 1970 are shown. 
Fig. 3. Prognosis for biospheric component 
dynamics if rates of influence on the bio- 
sphere and distribution of capital investment 
are decreased. Explanation in the text. 
Designations are the same as in fig. 2. 
2 tendency t o  i n c r e a s e .  By 22b3 it w i l l  r e a c h  185 persona/km . The tem- 
p e r a t u r e  of t h e  lower atmosphere w i l l  i n c r e a s e  0.8 '~,  and t h i s  w i l l  l e a d  i 
2 t o  a r a p i d  growth of  v e g e t a t i o n  (217 tons/km i n  2200). When t > 2200, 
e x i s t i n g  food p r o d ~ c t i o n  r a t e s  w i l l  s ta r t  t o  l i m i t  human p o p u l a t i o n  
growth. Mineral  energy s o u r c e s  w i l l  become t h e  l i m i t i n g  f a c t o r  a f t e r  
2300. Consequently,  even i f  e x i s t i n g  development rates f o r  contemporary /46 
, 
human s o c i e t y  a r e  main ta ined  i n  t h e  b iosphere ,  a c c e p t a b l e  conditions f o r  
human e x i s t e n c e  w i l l  con t inue  f o r  a t  least  t h e  nex t  250 y e a r s .  During 
t h i s  p e r i o d ,  mankind must f i r s t  s o l v e  t h e  problem o f  e s t a b l i s h i n g  an  
e q u i l i b r i u m  u i t h  t h e  environment and d i s c o v e r  new energy s o u r c e s ,  
Now l e t ' s  have a look a t  some h y p o t h e t i c a l  s i t u a t i o n s  which might 
a r i s e  i n  t h e  f u t u r e .  F igure  3 shows t h e  r e s u l t s  of  a s i m u l a t i o n  which 
presupposed t h a t  by t h e  y e a r  2000 bo th  r e g i o n s  w i l l  h a l v e  p o l l u t i o n  
g e n e r a t i o n  r a t e s ,  non-renewable r e s o u r c e  expend i tu re  w i l l  be reduced 5O%, 
riekton h a r v e s t i n g  w i l l  d rop  1 b % ,  a g r i c u l t u r a l  c a p i t a l  w i l l  i n c r e a s e  up 
t o  45%, and c a p i t a l  investment  U = URG = 10% and Ucg = UZG = 5%. By Rg 
2000, 80% o f  t h e  l and  a r e a  s u i t a b l e  f o r  farming w i l l  be u t i l i z e d ,  animal  
husbandry p r o d u c t i v i t y  and P/R -- t h e  c o e f f i c i e n t  o f  a g r i c u l t u r a l  vege- 
t a t i o n  -- i n c r e a s e  1 . 5  aqd 4 t imes ,  r e s p e c t i v e l y ,  r e l a t i v e  t o  1970 l e v e l s ,  
l and v a l u e s  f o r  T*, Tz, and TG d e c r e a s e  30%. c 
i In  t h i s  c a s e ,  a p p a r e n t l y ,  t h e  system e n t e r s  a  q u a s i - s t a t i o n a r y  mode 
2 
, where popu la t ion  d e n s i t y  f l u c t u a t e s  from 50-200 persons/krn . E i t h e r  C 0 2  
o r  food become t h e  l i m i t i n g  f a c t o r  a t  v a r i o u s  s t a g e s .  Non-renelTable 
1 r e s o u r c e s  become l i m i t e d  a f t e r  t h e  yea r  2300. I f  mankind succeeds  i n  
swi t ch ing  t o  a new l e v e l  of  r e s o u r c e  utilization by t h e n ,  t h e  "ca ta s t rophef '  
w i l l  be a v e r t e d .  
Model c a l c u l a t i o n s  i n d i c a t e  t h a t  t h e  worst gaseous c o n d i t i o n s  i n  
t h e  atmosphere may s e t  i n  b y  2070,  i f  coord ina ted  i n t e r - r e g l o n  management 
i s  no t  achieved .  C02 c o n c e n t r a t i o n  would exceed 0.0748%. 
The model we examined h e r e ,  I 
as p r e l i m i n a r y  c a l c u l a t i o n s  have 
./ , demons t r a t ed ,  i s  f l e x i b l e  enough 
/ 
/ 
/ /  
t o  r e f l e c t  t h e  n a t u r a l  and a n t h r o -  
emf>, / 
/ 
pcgenic  p r o c e s s e s  i n  t h e  b i o s p h e r e .  
/ m-2%---d 
+= =-+/ It may, t h e r e f o r e ,  be used t o  s t u d y  
a05 - A%--- b 50, --,---- 
& /  
a s s o r t e d  h y p o t h e t i c a l  s i t u a t i o n s  
I i n  o r d e r  t o  f i n d  a d o p t a b l e  a c t i o n s  
I 
t 
f o r  c o n t r o l l i n g  t h e s e  p r o c e s s e s .  /48 
1970 2070 2f?O Allowance f o r  r e g i o n s l i t y  i n  t h e  - i 
Fig .  4 .  Changes i n  a tmospher ic  CO, model may make i t  p o s s i b l e  t o  ! 
L c o n c e n t r a t i o n  when t h e r e  i s  a d l s -  e v a l u a t e  t h e  r o l e  o f  t h e  r e g i o n s  
c reyancy  i n  n a t u r a l  r e s o u r c e  u t i l i -  
z t i o n  r a t e s  f o r  two b i o s ~ h e r i c  i n  t h e  fa te  o f  t h e  b i o s p h e r e .  
r e g i o n s ,  E x p l ~ n a t i o n  i n -  t h e  t e x t .  S p e c i f i c a l l y ,  flg, 4 shows t h e  
Atmospheric CO concen:rations a r e  
exp res sed  i n  p a r c e n t s  . dependence o f  a tmosphe r i c  C 0 2  
c o n c e n t r a t i o n  on t h e  r e l a t i o n s h i p  
between i n i t i a l  r e g i o n a l  component c o n d i t i o n s ,  w i t h  t h e  assumpt ion  t h a t  
r e g i o n  1 implements measures  t o  conserve  t h e  environment and r e g i o n  I1 
r e t a i n s  t h e  same r a t e  o f  a f f e c t i n g  i t .  Only i f  0 2 50 can  r e g i o n  I1 
i ndependen t ly  adopt  measures  t o  m a i n t a i n  a  C02 c o n c e n t r a t i o n  w i t h i n  
0.04%. 
REFERENCES 
1. B a t c h e r ,  S . ,  a n d  E. C : ~ a r l s o n ,  a t m c s f 9  
[ I n t r o d u c t i o n  t o  ~ t m o s p h e r i c  P u b l i s h i n g  House, 
2. G e l o v a n i ,  V.  A . ,  V. A .  Yegorov, V. B. M i t r o f a n o v ,  A .  A .  F i o n t k o v s k i y ,  
"The Role  of Management I n  t h e  F o r r e s t e r  G l o b a l  Mcdel", I n :  
[Froblems i n  C y b e r n e t i c s ] ,  "&auka" P u b l i s h i n g  
3. ' ~ I n o ~ r a d o v ,  M . E . ,  V. F. K r a p l v l n ,  V .  V. Menshu tk in ,  P .  S. Fleysh t ran ,  
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A global biogeocenotical biosphere simulation

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