SYSTEM DYNAMICS SIMULATION MODELLING OF “KASTELA
BAY” REGIONAL SYSTEM
Ante Munitié, Marko Tomasevié, Panéo Ristov Frane, Mitrovié
University of Split
Marittime Faculty
CROATIA
ante.munitic@ pfst.hr, marko.tomasevi¢@ pfst.hr, panco.ristov@ pfst.hr,
frane.mitrovic@ pfst.hr
Abstract
Although large developed System
dynamics model can be applied on
different ecological system in this paper it
is applied on Kastela region in Croatia.
The Computer Simulation Sub model of
The Ecological Regional Subsystem of the
"KASTELA BAY" is an extra relevant
submodel of The System Dynamics
Computer Simulation Model of the
“KASTELA BAY” which has been
developed with the help of System
Dynamics. It is, in its essence, a
continuous model because it is presented
as a system of non-linear differential
equations. At the same time, it is a discrete
model, because it is presented as a system
of linear differential equations (System
Dynamics DY NAMO - software package).
Its DT (length of intervening time =
computation interval) is chopped in full
accordance with the Sampling Theorem
(Shannon and Koteljnikov). The System
Dynamics Computer Simulation Model of
the "Kastela Bay" also employs certain
experience gathered by experts who had
worked on the preparation of projects:
"Blue Plan" and "The Methodological
Basis for the Scenario of the Management
of Natural Resources of the "Kastela Bay""
(1991).
Keywords: System Dynamics Modelling;
Ecological model; sub model RSKB
1. Characteristics of the Regional
System of the “Kastela Bay”
RSKB - The Regional System of the
“Kastela Bay” (Figure 1.) is presented as
an entity consisting of six relevant
subsystems: 1. Population, 2. Economic
activities, 3. Social activities (social and
national income), 4. space and the
environment, 5. economic output (social
and welfare activities) and 6. socio-
economic development policy. The RSKB
is analysed as a “whole” consisting of the
four subregional communes: KASTELA,
SPLIT, SOLIN and TROGIR (Figure 1.).
ee rept wns
-
es a Sa A iibh a
Figure1. The Regional System of the
“Kastela Bay” - RSKB
These communities communicate with the
following entities/environments: 1. The
Republic of Croatia (without RSKB), 2.
Independent recognised countries of the
former Yugoslavia (without current
Yugoslavia), 3. The Mediterranean
countries (without Yugoslavia) and 4. the
rest of the world (the remaining developed
countries, except those of the
Mediterranean). The RSKB could be
presented as a tudimentary
communicational model which fully
corresponds to the relevant environment: 1.
CROATIA, 2. FORMER YUGOSLAVIA,
3. MEDITERRANEAN and THE REST
OF THE WORLD (Figure 2.).
“' ST
RSKB
REGIONAL SYSEM OF
a THE «KASTELA BAY» \
THE REST OF we, \ FORMER
WORED, 'UGOSLAVIA
Figure2. Rudimentary Structural Inter-
Communicational Model of RSKB
The Regional System of the “KASTELA
BAY”- RSKB in a local social and
“whole” context, is the territory defined by
the acquatorium and the area around the
Kastela Bay, the mountain ranges and the
Adriatic sea. It is situated in the middle of
the Eastern Adriatic Coast. The national
context is defined as the area of the
Republic of Croatia. At the same time,
RSKB is part of the Mediterranean
Regional Socio-Ecological System and the
Rest of the World-Socio-Ecological
System too, and the corresponding
territory, ie. the “continental, maritime
and aerial space” which communicate with
the environment. System Dynamics
Highly-aggregated Structural Model of
RSKB could be represented as “a whole”.
2. System dynamics simulation sub
model of the ecological subsystem of the
“Kastela Bay”
This sub model consists of the: 1.
qualitative (mental, verbal and structural)
and 2. quantitative (mathematical and
computer) System Dynamics Simulation
Models. The Ecological Subsystem of the
“Kastela Bay” has six subsections: 1.- air
pollution; 2.- land pollution; 3.- sea
pollution; 4.- pollution of the seabed with
radioactive particles, other organic and
inorganic matter; 5.- external pollutants
(RSKB environment) & 6.-_ intemal
pollutants (The RSKB environment has
five parts: 6.1. urban areas (settlements,
tourist accommodation, industry and
services, transport and residential areas),
6.2. agriculture, 6.3. archaeological sites,
6.4. exploitation, and 6.5. forests and other
areas).
The system dynamics model of the
ecological subsystem of the RSKB has
four pollution sectors: 1. Air, 2. Land, 3.
Sea, and 4. The seabed. Each of these has
three pollution subsections: 1. radioactive
particles, 2. other particles (heavy metals)
and 3. biological cells.
Using the “analogy” principle between the
“a continuous dynamic cycle of water
particles interacting with the
environment”, and the “a continuous
dynamic cycle of radioactive particles
pollution and other particles pollution
interacting with Air, Land, Sea and the
Seabed, makes it possible to present the
continuous Ecological Subsystem of
RSKB with the following simplifications
of the natural cycle of pollution between
AIR, LAND, SEA and the SEABED with
the RSKB and its environment, or in short:
the structural model (Figure 3.).
g {=
J —
Figure3. Highly-aggregated Structural
Ecological Sub model of the RSKB
feel
7
i
\
GG
This ecological highly-aggregated
structural sub model, in reality, has many
more material and information flows or
negative and positive feedback loops, then
presented here, and some of them cause
consequence variables, mixed between
themselves and their environment.
Endogenous material and information
flows are: material and social standard of
living of the RSKB, internal pollutant,
urbanisation, land use, natural resources,
population, economy, — socio-cultural
framework, development policy, etc., and
the exogenous flows are: pollutants in
Croatia, former Y ugoslavia, Mediterranean
and Rest of the World social systems.
But we must bear in mind that RSKB and
its environment exist in total harmony with
natural laws, and we have to take into
consideration the influence of: 1.- wind, 2.-
precipitation and 3.- sea-currents. All of
these causes or/and consequence variables
built into our ecological model represent
these variables through "multiplex inter
communication channels":1.“A”, 2. “B” ,
3.“C”and 4. “D”. In a global structural
sense, the sublimated model - the
Ecological Subsystem of the RSKB, made
in accordance with System Dynamics,
could be presented as shown in Figure 4.
2.1, System dynamics qualitative model
of the ecological regional
subsystem of the "Kastela Bay"
In accordance with all these
methodological cognitions and other
natural and social laws, it is possible to
work out this elementary qualitative model
of the pollution subsection of the AIR,
LAND, SEA and SEABED of the RSKB
in structural-mental-verbal forms in a
system dynamics way. Each of the
pollution material flows and levels (in this
case: 1.-radioactive particles, 2.-other
particles and biological cells) could be
presented with the analogous structural
model in a System Dynamics
POWERSIM-symbolic way (Figure 5.).
The global input rate of the radioactive
pollution at the AIR-RSKB depends on the
three variables:
Figure4. Rudimentary System Dynamics
Structural Model of the Ecological
Subsystem of the RSKB
1, IRPRA - input radioactive pollution rate
of AIR as the sum of the two components
1.1.IPFERPA -input pollution flow of the
exterior pollutants. The IPFERPA depends
on the three variables:
1.1.1.NPREPA - normal pollution rate of
the exterior pollutants in AIR-RSKB,
1.1.2.CEECA - catastrophic radioactive
pollution events in the environment with
consequences to AIR-RSKB (Chemobyl),
and
1.1.3.WCQFA - wind consequence factor.
The WCQFAA-wind consequence factor
depends of the:
1.1.3.1.SWG - simulated wind - generator,
respectively as an empirical-statistic
software model.
1.2.IRPIA - internal radioactive pollution
input flow of AIR. The IRPIA depends of
the three variables:
1.2.1.INRRAP - intemal normal rate of
radioactive AIR pollution. The INRRAP
depends of the:
1.2.1.1.RIKB - regional income of the
RSKB.
1.2.2. CIERPAA-catastrophic internal
events of radioactive pollution of AIR-
RSKB.
1.2.3.WCQFA-wind consequence factor.
The WCQFA-wind consequence factor
depends of the:
1.2.3.1.SWG - simulated wind-generator,
respectively as an empirical-statistic
software model.
2.VRRPS - vaporising rate of radioactive
pollution from the SEA into the AIR. The
VRRPS depends of the three variables:
2.1.RPLS - radioactive pollution level of
the SEA -RSKB,
2.2.AVTRPSA - average vaporising time
of radioactive pollution from the SEA into
AIR-RSKB,
2.3.WCQFA-wind consequence factor.
3.VRRPLA - _ vaporising rate of
radioactive from the LAND to the AIR-
RSKB. The VRRPLA depends of the
three variables:
3.1.RPLL-radioactive pollution level of
the LAND-RSKB,
3.2.ATRVPLA - average time of
radioactive pollution vaporising from
LAND into AIR,
3.3.WCQFA-wind consequence factor.
Seven rate variables make an impact on the
RPLA-radioactive pollution level of AIR.
Three of them are input material flows:
IRPRA; VRRPS; VRPRLA; and four of
them are output material flows: NRARA-
natural radioactive assimilation (decay)
rate of AIR; ORPRAE-outflow of
radioactive pollution rate from AIR into
the environment; RPSRAL-radioactive
pollution sedimentation rate from AIR to
the LAND; RPSRAS-radioactive pollution
sedimentation rate from AIR to the SEA.
In general, this qualitative radioactive
pollution model of the ecological sub
sector of AIR-RSKB is very suitable for
the presentation of other radioactive
particles, other material particles and
biological cells ecological RSKB-AREA
sub sectors such as: LAND, SEA and
SEABED, because all the material flows
(radioactive particles, other material
particles and biological cells) in AIR,
LAND, SEA and SEABED of the RSKB
have a high degree of the natural system
dynamics analogy. This means that this
model is going to be a _ general
representative (modular) for the dynamics
behaviour of the 1. Radioactive particles,
2. Other material particles and 3.
Biological cells in AIR, LAND, SEA and
SEABED of the RSKB and every other
pollutant material, which makes it possible
to treat it as an analogous global structural
model.
System Dynamics Structural Simulation
Model of the Ecological Radioactive
Pollution Sub sector of the RSKB, in the
DYNAMO (or POWERSIM)-graphic
symbol icons, could be presented as shown
in Figure 4.
The level of the “global radioactive
pollution” of the RSKB is presented here
in two ways: 1.SSRPKB-simple sum of
the AIR, LAND, SEA and SEABED
radioactive pollution levels of RSKB, and
2.VSRPKB- vector sum of the AIR,
LAND, SEA and SEABED radioactive
pollution of RSKB. It is essential to show
that this model must have three exogenous
simulated generators:
1.-“SWG”-simulated wind generator,
which has indirect consequential influence
on the following variables: IPFERPA-
input pollution flow of the exterior
radioactive pollutant in the RSKB-AIR,
ORPRAE- outflow of radioactive
pollution rate from AIR to the
environment, IRPIA-intemal radioactive
pollution input flow of AIR;
2.“SPG”-simulated precipitation
generator-which has indirect consequential
influence on the following three variables:
RPSRAL-radioactive pollution
sedimentation from AIR to the LAND,
ERPL-external radioactive pollution rate
of LAND, IRPL-intemal radioactive input
flow rate of the LAND;
2.2, System Dynamics quantitative
model of the ecological regional
subsystem of the “Kastela Bay”
This System Dynamics Quantitative Model
has been made in full accordance with the
System Dynamics Methodology and
DYNAMO PROFESSIONAL PLUS and
POWERSIM software package. The
authors of this model have used a practical
“software modular principle’ and have
constructed several models of the different
media (RSKB’s AIR, LAND, SEA, and
SEABED) and different pollution
(radioactive particles, other material
particles and biological cells). Due to
limited space in this paper, the authors are
going to show only one computer
simulation sub model: the radioactive
pollution in the AIR, LAND, SEA and
SEABED of the RSKB. As the foundation
for determining this quantitative model, the
presented qualitative (mental, verbal and
structural) system dynamics universal
model (Figures 1.,2.,3.,4., and 5.) and other
heuristic knowledge about radioactivity
natural laws can be used.
2.2.1, Behavioural dynamics of
radioactive pollution of the RSKB
Behavioural dynamics of this “System
Dynamics Computer Simulation Model of
the Radioactive Pollution Subsystem of
RSKB” is presented in the following
figures, where those variables have the
following meaning: SPG-Simulated
Precipitation Generator, SWG-Simulated
Wind Generator; SSCE-Simulated Sea-
current Generator, RPLA-Radioactive
Pollution Level of AIR; RPLL-Radioactive
Pollution Level of LAND; RPLS-
Radioactive Pollution Level of the SEA;
RPLSB-Radioactive Pollution Level of the
SEABED; and RIKB-Regional Income of
the “Kastela Bay”.
Figure 6. The simulated result of the
complete radioactive pollution model of
RSKB
im
Figure 7. The simulated result of the
RPLA-Radioactive Pollution Level of AIR
“i
Tin
Figure 8. The simulated result of the
RPLL-Radioactive Pollution Level of
LAND
6200
NIRPEL
VERPB CPR ~SSRPKB
Figure5. System Dynamics Structural Model of the Radioactive Pollution Subsector of the
RSKB
*
Figure9. The simulated result of the RPLS Figure10. The simulated result of the
- Radioactive Pollution Level of the SEA RPLSB-Radioactive Pollution Level of the
SEABED
“ VPS
Figure 11. The simulated result of the
RIKB-Regional Income of the RSKB
Dail
fs } | A uu
Figur 12. The simulated sul ofthe SWG-Simulted Wind Generar
Figure 13. The simulated result ofthe SPG-Simulated Precipitation Generator
Figure 14. The simulated result of the SSCE -
Simulated Sea-Current Generator
3. A complete model of the ecological
subsystem of RSKB
The Ecological Regional Submodel of the
RSKB has more then three equations
because it has three “parallel” pollution
sectors: 1.-radioactive, 2.-other material
particles (heavy metals) and 3.-biological
cells. If a project found a precise and
simple way of identifying some other
pollutant, new “parallel” sectors could be
added.
Every level of the pollution is presented, in
this case, as a “first order non-linear
differential-integral equation system”. The
complete model of the Ecological Regional
Subsystem of RSKB is presented through a
12 non-linear differential equation system,
and each of the levels is presented, in this
case, with a differential equation in the
DYNAMO or POWERSIM program
language also, because DT was chosen to
be in accordance with the Sampling
Theorem (DT=0.0625 year). The non-
linear dynamic character of the complete
model is the result of using numerous
stochastically and tabular variables.
A number of different scenarios have also
been simulated and this model, as a
cause/consequence part of the global
model of RSKB, coincided well with a lot
of measure experiments. All scenarios are
based on the following criteria: 1.-the
means to reduce pollution, 2.-quality of
development, 3.-quality of environment.
4. Conclusion
The Computer Simulation Model of the
Ecological Continuous Subsystem of the
"Kastela Bay" is a discrete-digital and
continuous model, because DT was chosen
to be in accordance with the Sampling
Theorem. It is of a high order, non-linear,
stochastic, highly complex and relatively
simple-modular as a software. Also, it is
highly applicative, and adaptable to the
computer simulation modelling of other
tegional analogous systems.
All resultants of simulation gained through
the use of the ecological model of the
RSKB point to the universal fact that the
seabed is exposed to the highest level of
jeopardy by long-term pollution of
assimilation materials. This means that the
seabed fish and other seabed biological
organisms make the most dangerous food.
This ecological model of the RSKB has
been made as an important part of the
global model of RISK and it has been
conducted through the Mediterranean
Action Plan according to the Joint Venture
Agreement signed by national and
approved by the local authorities. This
entire Program has been defined within the
wider national project “Rational
management of the Kastela Bay Area’,
carried out by the University of Split, in
co-operation with numerous national and
intemational institutions. It has been
supported by both the European
Community and the Intemational bank.
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