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Mathematical Models for Estimating Damages
Due to Natural Disasters in the Philippines

A thesis proposal
submitted to
in partial fulfillment of the requirement
in Fundamental of Research ( Edu 51)

Submitted by:

Perla V. Cruzada
Joe Rico B. Ducay
Ralph Laurence S. Manubay
Maribeth B. Maraya

March, 2014

The Problem and Its Background
Philippines is situated in the world’s hazard belts and are subject to floods, droughts, cyclones, earthquakes, windstorms, tidal waves and landslides, etc. The major natural disasters that occur periodically are largely due to climatic and seismic factors. Disasters can result from meteorological phenomena such as typhoons and hurricanes, sheet flooding and marine and river-based floods, geological processes such as volcanic eruptions, earthquakes and tsunami and climatic phenomenon such as the El Nino Southern Oscillation that results in a lowering of mean sea level in the east of the region, failure of the monsoon rains in India, and drought in Indonesia and Australia. The Philippines has a tropical marine climate dominated by a rainy season and a dry season. The summer monsoon brings heavy rains to most of the archipelago from May to October, whereas the winter monsoon brings cooler and drier air from December to February. Most of the lowland areas are hot and dusty from March to May. Annual rainfall measures as much as 5,000 millimeters in the mountainous east coast section of the country, but less than 1,000 millimeters in some of the sheltered valleys. Monsoon rains, although hard and drenching, are not normally associated with high winds and waves. But the Philippines do sit astride the typhoon belt, and it suffers an annual onslaught of dangerous storms from July through October. In the last decade, the Philippines have suffered severely from natural disasters. In 1990 alone, Central Luzon was hit by both a drought, which sharply curtailed hydroelectric power, and by a typhoon that flooded practically all of Manila's streets. Still more damaging was an earthquake that devastated a wide area in Luzon, including Baguio and other northern areas. The city of Cebu and nearby areas were struck by a typhoon that killed more than a hundred people, sank vessels, destroyed part of the sugar crop, and cut off water and electricity for several days. Natural disaster can cause considerable loss of lives, homes, livelihood and services. They also result in injuries, health problems, property damages, and socio-economic disruptions. From 2001 – 2012, natural disaster in the Philippines caused the death of 12,899 people, and injury to 138,166 individuals. These disasters also affected more than 71 million individuals and render almost 375,000 persons homeless. The risk from natural disasters is increasing all the time, more cyclones, and floods are predicted to result from global climate change. At the moment, on average, each year natural disasters leave countless people homeless and kill numerous people in the Philippines, and are not even taking into consideration the damage that they perform in the process, and the cost that this causes the economy. It is certain that natural disasters have a significant impact in the Philippines, the extent to of this effect will always determine how prepared the area that it occurs is, and so how bad the impact on the country is. This is the main concern of our study, Mathematical Models for Estimating Damages Due to Natural Disaster in the Philippines, in order to have at least reliable prediction of possible occurrence resulting to damages in the different field by constructing a model which will be useful in the study.

Theoretical Framework
Kerry Emanuel studied Theory and Modelling predict that hurricane intensity should increase with increasing global mean temperature, but work on the detection of trends in hurricane activity has focus mostly on their frequency. He defined an index of potential destructiveness of hurricanes based on total dissipation of power, integrated over the lifetime span of the cyclone, and showed that this index has increases markedly since the mid-1970s. This trend is due to both longer storm lifetimes and greater storm intensities. He found that the record of the net hurricane power dissipation is highly correlated with tropical sea surface temperature, reflecting well documented climate signals, including multi-decadal oscillation in the North Atlantic and North Pacific, and lead to an upward trend in tropical cyclone destructive potential, and taking into account an increasing coastal population, a substantial increase in hurricane related losses in twenty first century.

Fluctuations in tropical cyclone activity are of obvious importance to society, especially as populations of afflicted areas increase. Tropical cyclones account for a significant fraction of damage, injury and loss of life from natural hazards and are the costliest natural catastrophes in the US6. In addition, recent work suggests that global Tropical cyclone activity may play an important role in driving the oceans’ thermohaline circulation, which has an important influence on regional and global climate.

Conceptual Framework
The research paradigm illustrates the conceptual framework of the study that shows the relationships of the input, process and output of the topic. This framework embodies the specific direction by which the researcher will have to be undertaken by describing the relationship between the specific variables and identifies in the study. Furthermore, the process on how the researcher will develop a mathematical model for predicting damages of natural disaster will be based on the analyses of the variables to be used. Several statistical instruments will be applied to test the significant relationship among the variables. Multiple regression analyses will also be employed to come up with a model that will be predicted damages caused by natural disaster in the Philippines. The conceptual framework provides a merging lens to examine damages cause by the natural disasters in the Philippines.

Figure 1
Research Paradigm

Statement of the Problem
This study aims to develop a mathematical model to estimate damages caused by natural disaster in the Philippines. More specifically this study will answer the following questions: 1. How frequent is the occurrence of natural disasters in the Philippines in terms of: 1.1 landslide;

1.2 flooding; and
1.3 destructive cyclone?
2. How extent the damages caused by natural disaster in terms of: 2.1 casualties;
2.1.1 dead, and
2.1.2 injured?
2.2. properties;
2.2.1. infrastructure, and
2.2.2. agriculture?
3. What mathematical model will be appropriate in assessing the damages caused by the natural disaster in the Philippines in terms of: 3.1 landslide;
3.2 flooding; and
3.3 destructive cyclone?

Research Hypothesis
The Mathematical Model that will be proposed cannot assess the possible damages due to the occurrence of different natural calamities in the Philippines.

Scope and limitation of the Study
This study includes the cyclones, landslide and flooding that hit the Philippine Area of Responsibility within the period of 10 years (2003-2012).

Assumption of the Study
This study is anchored on the following assumptions:
1. That the Philippines experienced 20 typhoons every year.
2. That landslides happened on high level areas during continuous rain and destructive cyclones in the Philippines. 3. That the Philippines encountered flooding due to monsoon rain. 4. That during natural disaster in the Philippines there are significant number of damages on casualties and properties.

Significance of the Study
The findings of this study would be of great help to the different sectors of our government and to the community itself especially those concerning the different natural phenomenon occurring in the country and causing a serious damage in the different aspects most especially to us humans. To the different government agencies (PAGASA, NDRRMC). This study will help them gain additional understanding to the nature, occurrence and tendencies of the different natural calamities, its effects to us to be able for them to come up with a better resolution and forecasting plans.

Definition of Terms

Continuous rain - used with respect to a process that flows uninterrupted, i.e. there is no pause during the period
Cyclone – a storm or system of winds that rotates about a center of low atmospheric pressure, advances at a speed of 20 – 30 miles (about 30 – 50 kilometers) an hour, and often brings heavy rain. Earthquakes - a shaking, trembling, or concussion of the earth, due to subterranean causes, often accompanied by a rumbling noise. The wave of shock sometimes traverses half a hemisphere, destroying cities and many thousand lives.

Flash flood - a sudden, localized flood of great volume and short duration, typically caused by unusually heavy rain in a semiarid area, Flash floods can reach their peak volume in a matter of a few minutes and often carry large loads of mud and rock fragments.

Flooding - a temporary rise of the water level, as in a river or lake or along a seacoast, is resulting in its spilling over and out of its natural or artificial confines onto land that is normally dry. Floods are usually caused by excessive runoff from precipitation or snowmelt, or by coastal storm surges or other tidal phenomena. 

Landslide - is a type of "mass wasting." Mass wasting is down slope movement of soil and/or rock under the influence of gravity. A landslide is a movement of mass rock, debris, or earth down a slope. The failure of the slope happens when gravity exceeds the strength of the earth materials.

Mathematical Model – is an abstract model that uses mathematical language to describe the behavior of a system, representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form (Eykhoff, 1974). Method of simulating real-life situations with mathematical equations to forecast their future behavior uses tools such as decision-theory, queuing future behavior, and linear programming.

Natural Disasters - are major adverse events resulting from the natural process of the earth that are beyond the act of human being which cause widespread destructions on lives and properties.
Southwest monsoon - a system of winds that influences the climate of a large area and that reverses direction with the seasons. Monsoons are caused primarily by the much greater annual variation in temperature over large areas of land than over large areas of adjacent ocean water. This variation causes an excess of atmospheric pressure over the continents in the winter and a deficit in the summer. The disparity causes strong winds to blow between the ocean and the land, bringing heavy seasonal rainfall.

SPSS – (statistical package for the social sciences) is an integrated family of products that addresses the entire analytical process from planning to data collection to analysis, reporting and deployment. With more than a dozen fully integrated modules to choose from, you can find the specialized capabilities you need to increase revenue, outperform competitions, conduct research and make better decisions.

Review of Related Literature and Studies
This chapter presents the background readings undertaken by the researcher on the variables to be focused in this study. The researchers went to the library to search for related reading materials particularly books, articles, and magazines that has connection with the study. The researchers also searched for information in the internet. It starts with related foreign literature followed by local literature and related foreign studies followed by local studies. It also contains synthesis of the review.

Foreign Literature
Wageningen,(2013) Natural disasters and violent conflicts affect the lives of a great number of people across the world, especially in developing and unstable countries. The impact of conflicts and disasters on people’s security, livelihood and future prospects is often dramatic, and disproportionally hits those that are already poor and marginalized. Despite efforts to address these problems, these are likely to continue to mark global development in the decades to come. Disasters have become more frequent and intense, due to a combination of increasing social vulnerability (for instance through the formation of slum areas on steep slopes), environmental degradation and human-induced climate change. The spread and intensity of violent conflict has belied post-cold war optimism. Since the end of the Cold War, civil wars in post-colonial and transition countries and the global ‘war on terror’ have involved the uprooting and killing of large numbers of civilians. Leighton Walter Kille, (2013) Research shows that in recent years both the frequency and severity of extreme weather events have increased. As a consequence, mega-storms such as hurricane are likely to become regular visitors in the future, exacerbated by rising sea levels. While efforts are being made to reduce carbon-dioxide emissions, one of the root causes of human-caused climate change, there are acute risks ahead. Rising oce...

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