Please add the annotated bibliography in the page of works cited.Xxx 1
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Professor xxx
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24 February 2020
Forest Fire and the Mathematical Model
Forests can be considered as the lungs of the earth because they absorb carbon dioxide and
produce large amounts of oxygen for life on earth. At the same time, forests provide human
beings with wood for human survival, which is used to make paper, houses, furniture and so on.
And forests are homes of countless creatures. Therefore, the forest is an indispensable part of the
earth, and it plays a vital role for human beings. However, forest loss has been dramatically
increasing every year. The expansion of agriculture, uncontrolled logging, mineral mining and so
on are all the reasons for the reduction of forests. However, the most important and urgent cause
is the forest fire. In recent years, the frequent occurrence of forest fires not only drastically
reduced the number of trees, but also brought irreparable damage to the environment.
Firefighters are often helpless in the face of such natural disasters but watch the fire burn and
pray for rain. Therefore, because of the seriousness of forest fire and the limitation of forest
firefighters, forest fire fighting needs to be combined with a mathematical model to effectively
prevent forest fire.
Impacts of Wildfires
Wildfires in Australia have been going on since September 2019, with nine people dead, about
1000 houses destroyed and more than 12 million acres lost (Paddison). Fire continues to engulf
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trees and lives, and it has brought serious consequences to human beings. Animals have nowhere
to run in a fire and can only be burned alive, which leads to the extinction of some species. It is
difficult for not only animals but also humans to escape from forest fires. The burning of the
forest produces a lot of smoke. The smoke contains poisonous gases such as carbon monoxide.
The polluted air can spread far away and endanger people’s health. Forest fires can also pollute
land and water, which is difficult to recover. Rob Nelson, an ecologist from the University of
Hawaii, mentions that forest fires can cause immediate and long-term damage to soil and water.
Soil becomes difficult to absorb water after a forest fire, and rivers or lakes are contaminated by
toxic chemicals and ashes produced by burning. Therefore, wildfires not only endanger lives and
property, but also cause great harm to the environment.
However, more and more forest fires have occurred recently, and they are becoming more and
more serious, such as wildfires in California, burning in the Amazon rainforest, and fires in
Siberian forests. “Siberia, one of the coldest places on Earth, is on fire. The Amazon, one of the
wettest places on Earth, is on fire.” (Goodman and Robinson). Wildfire is no longer a
coincidence, but a problem that people need to pay attention to and deal with at any time. The
frequent outbreaks of wildfires and their inestimable serious consequences will have a direct
impact on the human world and affect the life and death of human beings.
Background of Forest Fires
Large forests are generally composed of multiple forests, and there are relatively many surface
mulches, such as weeds, fallen leaves, dead branches and so on which are easy to catch fire in
extremely dry conditions. There are two main causes of forest fire: first, human factors. For
example, cigarette butts, matchboxes and other substances that are easy to cause fire are casually
discarded in the forest or on the dry surface of the surrounding area, thus causing a fire. Even
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intentional arson can cause a fire. The second is the factors of nature. For example, fire caused
by lightning hitting trees, fire caused by volcanic eruption, spontaneous combustion caused by
excessive dryness of the surface and so on.
Fires caused by human factors often gradually spread from the surface to the canopy and will
spread in different directions with different wind directions, which do great harm to the forest,
not only endanger older trees, but also damage younger seedlings. As the fire caused by lightning
often starts from the canopy, the canopy fire will rapidly expand outward under the action of the
wind, and even cause a new fire. Thus, when firefighters discovered the forest fire, the fire had
spread from a point in the beginning to an area. To make matters worse, there is no road in these
huge forests, and it is difficult for firefighters to get to the scene of the fire in the first place. As a
result, once a forest fire breaks out, it will become uncontrollable. But in some less serious
wildfires (when firefighters can get to the fire site quickly), firefighters still have some ways to
deal with the fire. The first way is to use control lines to prevent the spread of fire. Brooks Hays,
the writer of science news, states that “A rocky ridge or river can serve as a natural control
line, or firefighters can establish a manmade one by, for example, clearing out an
extended line of brush” (2). This method achieves the goal of reducing the loss from
forest fire by leaving the flame with nothing to burn. When the flame reaches the river, it
will not be able to burn any more. Similarly, when the flames reach the control line set in
advance by firefighters, it will have no way to continue to expand. Of course, this method
is only suitable for small wildfires because large forest fires require more firefighters a nd
trees are difficult to saw quickly to form control lines. Another way is to use aircraft to
sprinkle chemicals that prevent the fire from burning over the fire area. The advantage of
this method is that planes can reach places that firefighters cannot r each quickly, because
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the terrain of the forest is complex and there are no roads. The problem, however, is that
this method is difficult to cover all the burning places and put out the fire effectively, and
once a little fire is left, the forest fire will continue. As a result, firefighters are often
helpless and powerless in the face of forest fires, and their lives are in great danger when
they are surrounded by fire.
Conceptions of Mathematical Model
A mathematical model designed for forest fires is expected to make a prediction for the
next forest fire and calculate a spreading speed and contour when there is a fire going on.
There are several conceptions of such a mathematical model (Rothermel).
First, researchers need to calculate the heat for igniti on. By considering the amount of
fuel and the moisture content of the fuel, a temperature of ignition can be calculated. By
using equations, people can understand and predict the conditions and probability of
causing fire in different environments. Therefore, people can know when to prevent a fire
when there’s a fuel leak or under other situations.
Second, knowing the reaction intensity. When the researchers calculate the intensity of
the fire burning in the forest, they can simulate the speed and trend of the fire spread. The
calculation method is based on the combination of the density of tree distribution, the
average size of trees, moisture and chemical composition. Researchers can then
understand the energy release rate of fire, which can further help to understand the
development of the model.
Third, knowing the effect of slope and wind. First, different slopes will have an impact
on the way and speed of forest fire spread. The topography of the forest cannot be
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completely horizontal, some in the mountains and some in the valleys. The fire spreads
faster toward higher slopes and slows down when it spreads to lower slopes, because in
the absence of wind, the flame burns vertically upward. However, when it is windy, the
situation is completely different. The intensity and direction of the wind will guide the
direction and speed of the fire. Therefore, the researchers need to combine the factors of
slope and wind in order to calculate the combustion route of the fire.
According to these concepts, a mathematical model at the conceptual level can be
made and used to simulate and predict forest fires.
Application
The National Fire-Danger Rating System already started using the mathematical
models (35). These different mathematical models simulate the forest situation under
different environments and conditions respectively. “Eleven fuel models (table 1) have
been assembled that represent a large portion of the forests, brush fields, and grasslands
found in the temperate climates of North America” (35). These models can bring fire
warning and response measures to different forest areas of the United States. Assuming
that the temperature in an area will rise and reach a very high level in the next few days,
and the dryness of the area is likely to cause a fire, then the mathematical model of this
area will help the National Fire-Danger Rating System to give an early warning. In this
way, aircraft or firefighters can be sent to the area in advance to take precautions. The
plane can use a water tank to sprinkle water over the area.
When a fire breaks out, the mathematical model also plays a vital role. Because the
mathematical model effectively predicts the spread contours of the fire in the target area,
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firefighters can cut down the trees in the direction in which the flame is about to spread
in advance to form a control line. If there is no such model to tell firefighters where to
start deploying control lines, then they will have two possibilities. The first is that the
control line is arranged too far away from the fire area, causing the control line to be too
long, which will lead to a huge problem of understaffing and expenses. The second
problem was that the place chosen by firefighters was so close to the fire that the fire
spread before the control line was deployed. Then not only will the firefighters’ situation
become very dangerous, but their efforts will also be in vain. Therefore, fire losses can be
reduced more quickly, and manpower can be deployed more efficiently by using the
mathematical model.
Although such a mathematical model can help prevent forest fires, the number of
wildfires in California has increased rather than decreased in 2019. The reason is that this
model has obvious limitations because it cannot predict the factors that cause fir es by
humans, and unpredictable factors such as fires caused by thunder. This model is based
on theoretical support, but it cannot take all incalculable factors into account.
Suggestion for Improvement
Mathematical models designed to prevent forest fires should be applied internationally.
Forest managers in each region should find the closest model to the forest they are
responsible for, which can be used to solve the problem of forest fires in different areas.
At the same time, people need to continuously collect sample data and input them into the
mathematical model to ensure the effectiveness of the model. For forest fires that have
occurred and are occurring, scientists should record and refer to the relevant data
generated by the fire, which can be used to guide and improve the mathematical model.
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Conclusion
Forest fire has become a problem that cannot be ignored. In order to avoid the massive
reduction of trees, the extinction of species, the threat to human life, and the harm to the
environment, human beings need a scientific and effective solution. The strength of
firefighters alone is far from being able to put out frequent forest fires. Therefore, the
existence of mathematical model which can prevent forest fire to a certain extent plays a
vital role. However, how to apply this mathematical model more effectively and widely
will be a problem worthy of further discussion and study by mathematicians.
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Annotated Bibliography
Goodman, Jack and Robinson, Olga. “Forest Fires: Are They Worse than in Previou s
Years?” BBC, 19 Sep. 2019.
Jack Goodman is the scientist who studied about Plant and Soil Science. Olga
Robinson is an experienced Russian media analyst. They write the arti cle mainly
focus on showing that forest fires are happening in places that are not easy to
happen. Which means that the problem of wildfires is getting worse and worse.
Hays, Brooks. “10 Strategies Firefighters Use to Fight Wildfires.” Mental Floss, 31 Jul y.
2018.
Brooks Butler Hays is a freelance writer based out of Washington, DC. He
covers science news for United Press International. He writes 10 techniques that
firefighters use to fight against forest fires. He mentions that control lines are the
most important components of wildfire suppression.
Nelson, Rob. “The Environmental Impact of Forest Fires.” UntamedScience, April. 2019.
Rob Nelson is an ecologist from the University of Hawaii.
In his article, his main point is making people know the harmful effects of
wildfires. First, Wildfires can pollute rivers, lakes, and streams. Second, vegetation
can be significantly impacted. Third, wildfires can cause air pollution which is
harmful to human’s health.
Paddison, Laura. “2019 Was the Year the World Burned.” HuffPost, 2 Jan. 2020.
Xxx 9
Laura Paddison is an editor and a writer who writes about the topics of climate
change and biodiversity. In her article, she reports the loss in the great forest fires
happened in 2019. She used a lot of data to show readers how severe the problem is.
I used the data from her article in order to show that wildfires are destroying our
planet. People should consider the issue of wildfires as an urgent one.
Rothermel, Richard. A Mathematical Model for Predicting Fire Spread in Wildland Fuels.
Harris, 1972.
Richard C. Rothermel is the Research Project Leader for the Fire Physics
research work unit. He has been engaged in research on mechanisms of fire spread at
the Northern Forest Fire Laboratory. In the book, he shows the concepts and the
equations of the model designed for simulating the forest fire. On the basis of
science, he provides formulas for calculating the speed and ways of fire spread under
different conditions. Besides, the model has been put into use is mentioned in this
book.
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Professor xxx
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3 March 2020
Forest Fires and the Mathematical Model
Forests have a considerable contribution to the provision of the important requirements in
the modern-day communities. Through the forests, people are able to obtain most of the
necessary requirements and to ensure that they need (Hautier et al. .50-56). However, frequent
fires in the forests is a major problem facing most people who depend on forests. Forests play a
significant role in the provision of the important requirements for improving their survival
chances but forest fires have a negative influence on the lives of most people. Forest fires are a
fairly complex issue that needs more attention so that the application of the approach that may
lead to the reduction of the problems linked with forest fires is required (Moore, 210-245). To
arrive at this, the development of a mathematical model with an unique design to manage forest
fires and the effects associated with it is required. Since some forest fires occur naturally and
may be relatively challenging to achieve, the involved stakeholders must come up with a
mathematical model that may predict and calculate the rate at which the fire spreads. The use of
a mathematical model may also assist in the improvement of the knowledge that may be present
regarding the direction and the temperature of the fire. The mathematical model of evaluating the
rate at which the forest fire spreads.
Human actions have a significant contribution to the depletion of forests due to their
engagement in adverse responses that may cause more damage to the global environment. Forest
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fires may come as a result of activities that the users of the forest may put in place, while for
some cases, forest fires may come as a result of unpredictable and uncontrolled instances
(Lidskog et al., 148-155). Forest fires are caused by natural factors such as lightning, and in rare
cases, the combustion of leaves and sawdust may act as the fuel that may, in turn, result in forest
fires. The other cause of forest fires is the human-induced actions, and in this case, the activities
that humans may engage in may have a significant contribution towards the problem as
mentioned above.
Solving the problem
Over the past years, when a fire breaks out, it brings about significant losses to the
affected region and this is why there requires the creation of a critical method that may solve the
problem stated above. The effectiveness of the current models of the fighting fire has made it
necessary for the establishment of a tool that may predict the presence of fire and also create
effective measures that may manage the arising forest fire. The mathematical model required to
solve the problems linked with forest fires depends on the information gathered in relation to fire
and the effects that the failure to address the outcome may bring about to the environment. The
model can gather data regarding the possible disasters regarding fire and the level of impact that
the fire may have. For that reason, the mathematical model is responsible for the prediction of
the possible breakouts o fire through the analysis of current data.
The model will also evaluate the most influential strategy that needs more consideration
when addressing fire. In most cases, the slope at which the wind flows is a significant factor that
results in the rate at which the fire spreads. Having a significant knowledge regarding the spread
of wind concerning the slope at which the wind flows. Since in most cases, the topography of the
forest may not always be horizontal, learning about the effects that wind may have concerning
3
forest wind and the negative impact that it has on the general environment. The development of a
mathematical model, for that case, will lead towards the improvement of the knowledge that
people may have regarding the effects in which chemical compositions in the forest may have
about the spread. Besides, this knowledge regarding chemical composition, moisture as well as
the average size that trees have is essential for ensuring that the model needed to evaluate the
rate and the impact that the forest fires may have when they arise.
Application of the mathematical model
In the United States, the rate at which fire spreads in the cases that it occurs need more
attention to ensure that the challenges that are linked with the forest fires are managed in an
appropriate manner. The mathematical model proposed above is imperative since it may assist in
bringing warnings regarding the fire in the various forests within the US. Although this
mathematical model may not effectively predict the challenges in which the natural factors
regarding forest fire may occur, it will assist in the development of critical information in
reference to fire and outcome that may come in the case where fire may arise. Whenever the
mathematical model predicts about the occurrence of fire in the forest, the relevant stakeholders
in the management of fire can be easily deployed, and this may positively assist in the
management of forest fire whenever it occurs. Among the various approaches that can be put in
place to ensure that there is the effective management of forest fire include the deployment of
aircraft and firefighters in some instances that may need more attention.
In the instances where forest fire may break out, the mathematical model has a significant
task of predicting contours of fire in the vulnerable as well as target areas. As a result of the
information that the fire management team may get regarding the fire break out in the forest in
question, they may be able to cut down trees to cover the areas that are yet to be affected by the
4
fire in question. In the cases where there is no model as mentioned, the team involved in fighting
fire may not have the ability to address the possible causes of fire and at the same time reduce
the negative challenges linked with fire breakout. Although the above-mentioned model may
have a significant contribution towards the prediction as well as overall management of the
critical breakouts of fire in the first, training is required to ensure that users of the system have
high-level knowledge that may assist in ensuring that they come up with an appropriate decision
when solving the challenges as stated above.
Importance of the issue
There are several ways in which addressing forest fires is relatively essential (Barlow et
al., 144-147). One of the ways in which addressing the topic on forest fire is imperative is
because it assists in creating an insight regarding the effects associated with the matter in
question. Forest fires are related to significant losses in the areas where they may affect. The
problem in relation to forest fires occurs in many parts of the globe, and for that reason, it has a
significant impact on most areas where it occurs. Since forest fires have had a considerable effect
in most parts of the globe, it, therefore, has been considered as a critical condition that needs
more attention from all stakeholders and participants. The issue in question is mainly due to the
effects that it brings about as well as the minimal approaches of managing it that are put in place
by the relevant bodies. The Most of the animals living in the areas that may be affected by first
fires may lose lives, suffer from injustices, and at some instances, loss of their habitats may
significantly affect the interaction of wild animals that may live in areas that may experience
wildfires.
The creation of measures that address the high rate of forest fires, as well as the
frequency at which it occurs, is a significant measure that leads towards the control of the impact
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caused by the occurrence as mentioned above. There are multiple strategies used to address the
issue as mentioned above, and the different stakeholders that participate in its management
ensure that they work together to ensure that there is adequate control of the effects of the
mentioned environmental issue. Training more regarding the need to emphasize preparedness is
one of the well-known methods that is used to address the fires that may occur in the forest. In
this strategy, training people regarding the need to ensure that they remain vigilant and at the
same time, practice measures that may lead towards the low rate at which forest fires occurs and
spreads is imperative. The natural and unpredicted causes of wildfires, although relatively
challenging to address are also controlled through the prediction of the instances in which they
may occur as well as the influence that the natural factors likely to bring about forest fire are
managed. Multiple regulatory bodies help in controlling the effects of the issue as mentioned
above, as well as preventing its further occurrence (Marchi et al., 1385-1394).
The top environment conservation organization is one of the concerned stakeholders that
participate in ensuring that they offer adequate training to people to ensure that they have the
required knowledge that may assist in control lion the rate at which people engage in activities
that may contribute towards a high percentage of forest fires. Government-related bodies are
other stakeholders that participate in the reduction of the effects of the above mentioned
environmental issue. In this case, the government has special teams such as the fire department
that is equally equipped with materials as well as quality resources that may allow them to
overcome the high rate at which forest fires may occur and the impact that forest fires may
possess in the instances that they occur.
The creation of laws that helps to control the rate at which people engage in activities that
are at a high position of bringing about forest fire is essential in the reduction of the effects that
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are linked with the problem. The government has developed regulations that limit the rate at
which people access the forest area mostly during the dry weather. This regulation is meant to
ensure that the human-induced fires are regulated and that there is a reasonably low rate at which
the community suffers from the occurrence of this issue. Besides, the general population has
received training regarding the subject as well as the measures that they need to put in place to
ensure that the problem is addressed. The community is also taught more about the relationship
as well as the perception that they need to put inconsideration in the attempt of ensuring that they
are no longer involved in the creation of this harmful issue.
Forest fires are a critical issue that has required the development of qualitative methods
that may lead to the reduction of the problems associated with its occurrence (Hesslen, 178-190).
For that reason, there have been approaches that have enabled the community to learn more
about the effects linked with forest fires and at the same time allow people to practice measures
that may lead towards the reduction of the rate and number of casualties that may come as a
result of this occurrence. Since most of these activities involve the engagement of the community
in appropriate decision making to ensure that the problems are managed, the methods that are put
in place to ensure that forest fires are managed seems more useful. However, there requires the
improvement of the level of training and resources that are put in place to address the issue.
Through this measure, the government, environmental organizations, as well as other participants
involved in managing first fires, will succeed in the management of the negative issues
associated with the occurrence of forest fires. Due to the impact liked with the presence of forest
fires, the provision of training, preparedness and the implementation of high-level resources
necessary for the management of this issue are among the methods that will need to be put in
place to solve the mentioned problem. The other techniques that will need to be put in place are
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the engagement of the general community in decision making regarding the measures that need
to be put in place to ensure that the problems may not affect the community further.
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Works cited
Barlow, Jos, et al. “Anthropogenic disturbance in tropical forests can double biodiversity loss
from deforestation.” Nature 535.7610 (2016): 144-147.
Hautier, Yann, et al. “Local loss and spatial homogenization of plant diversity reduce ecosystem
multifunctionality.” Nature Ecology & Evolution 2.1 (2018): 50-56.
Hessen, Hayley. “Wildland fire prevention: a review.” Current Forestry Reports 4.4 (2018): 178190.
Lindskog, Rolf, and Daniel Sjödin. “Extreme events and climate change: the post-disaster
dynamics of forest fires and forest storms in Sweden.” Scandinavian Journal of Forest
Research 31.2 (2016): 148-155.
Marchi, Enrico, et al. “Sustainable Forest Operations (SFO): A new paradigm in a changing
world and climate.” Science of the Total Environment 634 (2018): 1385-1397.
Moore, Peter F. “Global Wildland Fire Management Research Needs.” Current Forestry
Reports 5.4 (2019): 210-225.

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