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THE UNIVERSITY OF MELBOURNE
SCHOOL OF GEOGRAPHY, EARTH AND
ENVIRONMENTAL SCIENCES
SEMESTER 2 EXAMINATION, 2021
SUBJECT: MODELLING THE REAL WORLD, EVSC20007
Instructions to Students:
This assessment consists of four sections, Section A, Section B, Section C, Section
D. The exam has a total of 120 marks. Each Section has 2 questions, each worth
15 marks (30 marks in total) and it is suggested that you spend 30 minutes on
each Section. The marks available for each question are proportional to the
suggested completion times.
Please ensure that answer all Sections, photograph and upload your solutions
through gradescope – indicating the Section that each answer belongs to.
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SECTION A (30 marks in total as indicated)
A1. (15 marks)
a. Describe the steps you would follow when creating a model of a system.
(5 marks)
b. The following stock and flow diagram presents several complex
feedbacks. Describe two of the feedback loops, giving their sign and
describing their implications for the company and its decision making
processes. Demonstrate that the logic holds by a clear example.
(10 marks)
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A2. (15 marks)
a. The ozone hole forms every year in spring when the sunlight returns to the
Antarctic because of introduced chlorine to the stratosphere (10-50 km
altitude where the ozone layer exists). Chlorine has been introduced via
chlorofluorocarbons (CFCs) and halons (fire retardants) that have been
now banned for some years under the international Montreal protocol.
The reason that we are still experiencing Antarctic ozone holes every year
is because the CFCs are only destroyed very slowly in the stratosphere by
UV light. CFCs are also very effective greenhouse gases, and the Montreal
protocol banning CFCs remains the most significant climate action taken to
date.
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CFCs were replaced by HFCs, which were recently also banned due to
them having very high global warming potentials. HCFCs (another
replacement gas was proposed to be banned from 2020).
As policy makers are concerned with both ozone depletion and global
warming draw a conceptual model that captures the complexity of system
from emissions to impacts. Make sure it clearly captures how replacement
gases need to consider all possible impacts so that solving one issue
doesn’t result in another. (15 marks)
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SECTION B (30 marks in total as indicated)
B1. (15 marks)
You are interested in studying the dynamics of aquatic food chains. As a
starting point, you decide to make a simple model of a food chain involving
three species: algae, krill and small fish.
You know the following about how these species interact:
- Since algae are photosynthetic, they can grow and reproduce on their
own - Algae form the primary source of food for krill
- Small fish primarily feed on krill
Given that you are after a reasonably simple model, you decide to develop an
ordinary differential equation (ODE) model of this system.
a. Write down the state variables you are considering.
(2 marks)
b. List the processes you wish to consider. You may find it helpful to draw a
diagram of the system.
(4 marks)
c. Derive the ODEs for the system. You may assume that all interactions
follow the law of mass action. Define all your parameters and state any
additional assumptions you make.
(7 marks)
d. Briefly explain how you would modify the equations you derived in part c to
account for fishing, which removes small fish from the ecosystem.
(2 marks)
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B2. (15 marks)
You wish to make a model of how wounds heal to better predict how effective
certain treatments are. Over the days after a wound forms, the skin cells
surrounding the wound gradually close the wound through two processes: - Proliferation: the division of one cell into two identical cells
- Migration: the random movement of cells to nearby locations
a. You decide to make a cellular automata model of wound healing. What are
the advantages of using a cellular automata model in this context?
(5 marks)
b. Describe how you would make a cellular automata model of wound healing
that incorporates the processes of proliferation and migration. You may
assume that the wound is initially circular, with a radius R. Please discuss
the following in your answer: - What variables and parameters will you use?
- How will you set the initial conditions?
- What assumptions will you make?
- Briefly describe the rules and heuristics you would use for your
model. You may find it helpful to use diagrams to illustrate your
points.
(10 marks)
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SECTION C (30 marks in total as indicated)
C1. (15 marks)
You and a friend have stumbled upon a short film festival. Unfortunately, there
are only two hours remaining in the festival. Immediately you construct a
schedule containing all the remaining viewings.
Movie Start Time Finish Time Critic Review
Score
1 85 100 2
2 50 70 7
3 15 40 5
4 50 95 7
5 40 75 5
6 95 120 5
7 0 25 6
8 10 35 4
9 85 110 9
10 25 45 9
Note, each person has their own screen meaning you do not need to change
location between each movie.
For the questions below, present all steps and calculations required to obtain
the solution.
a. Your friend suggests that the best strategy is to view as many of the
movies as possible. What is the maximum number of movies that can
be attended? Also, which movies were suggested? (5 Marks):
b. Having recently attended Modelling the Real World at the University of
Melbourne, you instead suggest to your friend that it might be better
to maximise your viewing based on the critic review score of the
movies. What is the maximum value and which
movies are selected? (10 Marks)
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C2. (15 marks)
Consider the following rail network, connecting our source city, S, to our
destination city, T. This rail network passes through the satellite cities (nodes)
denoted 2, 3, 4, 5 and 6. Each arrow denotes the direction in which the cargo
can move, with the capacity of each route given by the number in the box.
a. What is the maximum amount of cargo that we can send through our
network? Show full working (10 marks)
What is the corresponding minimum cut to the network that we could make to
completely disrupt the flow of cargo?
b. ? (5 marks)
Remember to construct a residual graph and provide it as part of your
solution.
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SECTION D (30 marks in total as indicated)
D1. (15 marks)
The Department of Environment (DoE) are concerned about vegetation change
in public lands of the high plains. Forests are an important carbon sink. These
upland areas are also watersheds for major rivers supplying irrigation,
hydroelectric power and native animals and plants. Cattle are grazed in some
areas under licence, returning profit to some farmers. Cattle create bare ground
with their hooves and eating plants, allowing sediment to wash into streams.
DoE wish to know how to decide whether to renew cattle grazing licenses.
DoE have some aerial photographs that they think may help with assessing
how it has changed over time and some information about the history of land
use (was there a fire, was it grazed by cattle, was clearing visible). The air
photos can resolve three vegetation types, forest, grassland and shrubland.
They suspect that some areas of grassland become shrubland and particularly
after fires. They also think that cattle like to graze in fresh, young grasslands,
but surprisingly they eat shrubs. Forests were cleared from substantial areas,
resulting in grasslands. Trees have returned to some of those grasslands, and
it might be that cattle grazing influence this.
a. Describe a first-cut model for this system. Use a diagram. (5 marks)
b. Your DoE contact wants to collect more data (air photos) to help with the
modelling. But it is a lot of work and there aren’t that many air photos,
roughly once a decade since the 1940s. They ask whether they should
collect more data. One option is to have snapshot data from lots of
places. Another is to have high detail on a small number of places, for
one time period. Another option is to have several time slices with less
detail. From your modelling, which type of data collection would be most
useful and why? (5 marks)
c. Your contact at DoE explains that one section of the DoE is interested in
the long-term dynamics of the system for carbon sequestration and
quality and amount of water supply. Another section is concerned to
know when and where they should intervene to keep the high plains
‘healthy’. Would one model suffice for both uses? What model type
would you favour and why. Describe both, if you believe one would not
cover both uses. (5 marks)
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D2. (15 marks)
Land clearing of forest for agriculture, has resulted in 5 fragments of forest near
the Wet Tropics World Heritage Area Rainforests. These are isolated from the
main forest of 100 000 ha which supports 60 species of frogs. The frogs are
poor dispersers across farmland (what the forest has been transformed into).
The number of frog species each fragment contains is reported below, along
with some other information about the fragments.
Site Area
(hectares) species Distance
(km)
1 a 1.0 15 0.5
2 b 5.0 30 1.0
3 c 1.5 22 3.0
4 d 4.0 28 2.8
a. Your colleague, an ecologist, approaches you for help. They want to
conserve as many species as possible. They are concerned that those
fragments will lose more species. Which fragment do you expect may
lose the most species? Explain, drawing on an appropriate model.
(4 marks)
b. There are funds available to support conservation actions to minimise
the number of local extinctions. Actions including building corridors of
forest to connect areas, or to increase the size of individual forest
fragments. You have no data on the species composition of the
individual patches. Which of the forest fragments would be your priority
for action and why? (4 marks)
c. Explain how data on species composition could assist in the decision
process. (3 marks)
d. One species the cricket frog, Litoria smithii, occurs in the forest
fragments. Outline how one might use population ecological information
and modelling to justify decisions to best conserve this species.
(4 marks)
END OF EXAM
