Task1: Fragility Model Construction

Framework Based on BBC.

After assesing many models, we decide to choose BBC Conceptual Frame work(Borgardi et al. 2004) as follows , and make a moderate adjustment to it.

BBC

It can solve the whole problem, on the left, the Fragility is defined by three spheres, Environmental, Social, Economic. And the framework define the risk, helping the government to take measures and prevent the state from being more fragile. What's more it exert a feedback to the intervention system, making a difference in mitigate the risk of climate change.

Model Construction

During our model construction, we make use of indicators from
FSI[1] to get Social and Environment sphere, Environmental sphere is from EPI[2]. Their data and analysis is scientific and we can use their data and variables.

Using FSI indicators

We define Social sphere as social fragmentation which make a difference in offering basic embodiment to population. Same as FSI, we make qualitative analysis and quantitative analysis.
Firstly, we think those variable related to economic and development denote more, such as: ED,FD, HF. And the left variables denotes less to the index.

Economic Sphere

Obviously, it could have a liner model between them, shows they are related.
We could sum them simply to calculate the Economic.

Economic=EC+UD+HF

Then, we apply the same method to Social spheer.

Social=SA+FE+GG+SL+PS+HR+RD+EX+0.1*DP

Where DP is a cohesion of Population，Public Health，Food and Nutrition，Environment，Resources. And it is related to Environment sphere, so we make its coefficient smaller than other indicators by qualitative analysis[3].

In the FSI model, all the variables have adequate explanations under scientific process.

Feature Egineering

However, the FSI pay little attention to environmental stress which comes from climate change whose effects include increased droughts, shrinking glaciers, changing
animal and plant ranges, and sea level rise. In FSI, only DP, that is Demographic Pressure, consider this in a small share.

Environmental Performance Index
Fragile State Index

The first heat maps is EPI maps executed by Yale University, and it has an authority to evaluate a government's environmental policy.[4]
Compare these two heat maps, we found there is high similarity lies in them. When the state has a high score in FSI indicating high fragility, it also gets a low score in EPI indicating worse environment.
For example, Burundi， get only 27.43 score of EPI, and get a high score in FSI and belong to Alert level of fragility. Swittherland, best environmental-friendly county, also is the third in stability.

Therefore, we introduce a new variable Environment sphere to optimize FSI model. Considering FSI and EPI have the same indicators, we make some feature engineering in EPI.

Construction of EPI

• We delete Water Resources, Agriculture, Forests, Fisheries, Biodiversity by qualitative analysis on account of those indicators are contained in FSI model.

• We remain the two portions that lies in Environmental health and Ecosystem vitality, Climate change and Air pollution.

Then, we update the EPI, and define the Environmental stress or sphere as follows:

Environment= 0.6* Environmental health+0.4* 0.75* Climate change + 0.4* 0.25* Air pollution

Ecosystem Vitality(40% in EPI)
Cohesion Indicators

Then we get our model, the fragility is a function of Economic, Social, Environment.

Fragibility = f(Economic, Social, Environment)

Data Processing

We operate on the data provided by FSI and EPI. We do data screening, deleting data he top 10 most fragile states as determined by the Fragile State Index, and merging different indicators using a multiple regression model. For climate change, we firstly reserve the original data from EPI. We will further optimize the model while applying the model to analyse a specific state in task2.

Our data train set as follows, we take top 10 state for example. And Environment has some missing values. There are totally 10 missing values in our data set, we’re ready to start exploring missing data and rectifying it through imputation. There are a number of different ways we could go about doing this. Given the small size of the dataset, we don't opt for deleting entire observations (rows) containing missing values. We’re left with the option of replacing missing values with a sensible values given the distribution of the data. We will create a model predicting Environment based on other variables. We could definitely use recursive partitioning for regression to predict missing ages, but we choose to use the mice package in R for this task. The multiple imputation using chained equations in r was widespread used in data imputation, and then we compare the results we get with the original distribution of passenger ages to ensure that nothing has gone completely awry.

Data imputation

And We divide those countries based on FSI, and we get the 3 kinds of country , they are fragile, vulnerable, and stable.

Train data
Then we get a completed data to determine our model.

BP Neural Network

Considering the significant interaction, we construct a new model to evaluate the fragility instead just get a simple linear model that sum them. In FSI, it has an assumption stating that the relationship between Sum score and indicators is additive, that is to say, the effect of changes in a predictor X on the response Y is independent of the values of the other predictors. 然而正如面的分析所说，经济落后的地区其社会结构也更加脆弱，它为民众提供基本需求的能力也大大下降，同时又会导致低于环境灾害的能力大大降低，因此我们采取神经网络模型，对其分类，而不是利用一个简单的线性模型。(However, as the qualitative analysis shows, the social fragmentation is more vulnerable in developing countries, its ability to provide basic embodiment to the public also drops drastically. Meanwhile, its ability to withstand natural disaster is less effctive. )

Interaction between three sphere

Weakness of F-S-I model:

1. Indicators cohesion and weight determination exist a subjectivity because of the scoring method is determined only by expert.
2. The calculation process is simple, the indicators are added directly, ignoring the correlation among those indicators
3. The impact of climate change on fragility is not considered.

BP neural network is a multilayer feedforward network for training according to the error back-propagation algorithm , its main advantage is the strong non-linear mapping ability. Therefore, it can solve the problem that there is a high correlation among Social, Environment, Economic.
Based on the train data defied before, we transfer the factor into numerical data, that is, Fragile=3, Vulnerable=2, Stable=1. Then we have a BP neural network train data as follows.

BP train data

BP neural network is composed of input layer, output layer and one or several hidden layers. Each layer contains several neurons. The layers and inter-layer neurons are connected by the connection weights and thresholds. Studies have shown that a three-layer BP network model can achieve any continuous mapping.[25]

Topology

The 3-layer BP network model is used to evaluate the national vulnerability.Three indexes of Social, Economic and Environment are used as input neurons of BP neural network, and Fragility as output neurons of BP neural network.

BP neural network training process will repeatedly adjust the network connection weights and thresholds so that the network model output value and known training sample output value of the error between the predetermined value. Training and Simulation of BP Neural Network Model Using Matlab Software.

Basic model of BP

The results shows the model have a good prediction. And climate change exert an indirect influence on fragility through Environment sphere in equation (2)

Results of Basic Model and Validation

略 后面补上

Application and Analysis

Task 1: Measuring the Impact of Climate Change Further

In our data train set and basic model, we just take the value of Climate change from the Climate and Energy in EPI, and simply amplify its weight to calculate the Environment indicator. Not surprisingly, we also get a good results. In this stage, we analyse the Climate change more sophisticated to measure the impact of it.

Climate change lies at the heart of some of the most pervasive and intractable environmental problems. These impacts are producing a strong cascade of effects that imperil existing social and economic structures.Social development and climate change must be seen as closely related. The costs of climate change are likely driven by alterations to hydrological systems, lower crop yields, species extinction, natural disasters, public health crises, increased conflict, and lowered economic productivity (Field et al., 2014).

indicators
Climate Change
Environment

Qualitative analysis: climate change could exert a great influence on the model, and influence Environment, Economic, Social. So we should pay more attention on climate change.
In out model, when climate change is high, then the environment get a lower score, and influence the fragility indirectly.
We can further to analyse it, as is shown in picture ,we can make sure that climate change exert great influence on Social and Economic. Especially in developing countries, they highly rely on natural resources.

Optimizing the BP network by Interaction Term

So, in order to optimize our model, we introduce a new interaction term, which is shown

Climate change* Social * Economic

And then, we update our model, that is plus the interaction term, and the model have a higher accuracy and a better performance in validating set.

Update model by interaction term

We make feature engineering again, and get a completed train data as follows:

BP train data

Where CSE is the interaction term Climate change* Social * Economic, and CCE is climate change which we don't use in optimizing our new model.
And the score is the same as FSI's sum score, showing the higher value, the more fragile the state.
And we apply the new interaction to the BP network.

The model has a great enhance compared with the former model which don't place the climate change on a high share. And it also measure the impact of climate change is definitive.

Analyzing the Central African Republic

During our model construction, we don't consider top 10 state in FSI. In this section, we select Central African Republic to analyse how climate change influence the fragility.
The model result is numerical data, and the state is stable when it is less than 1, while the state is fragile when it is more than 2. And, the higher value means the higher vulnerability to fragile.

Firstly, the environment is only 26.8, showing its bad performance in Environment, and its rank among 178 countries is 171th. Environment and interaction term are influenced by Climate change. So, we further analyse it from quantitative perspective.

WEIGHT AND INDICATORS

Climate change=0.5* DCT+0.2* DMT+0.05* DNT+0.05* DBT+0.2* DPT

Secondly, a report from the bloody, crumbling Central African Republic in 2014[4], trigger
a lot of problems, and the most severe is environment. Along a desolate stretch of the Avenue de France, the Red Cross has operated an on-demand, white-gloved sanitation service that, within an hour of being called, will show up to collect human bodies, whether chopped up or left intact. And these will denote the emission to CO2 intensity, and the war really do harm to the climate change and air pollution. In the country, we assume that the Central African Republic is less sever in Environment, and its ability to climate change rises.
So, we try to change the value of CEE in the model, and think it as only 1 value. Then, we apply our model to it.

Central African Republic

Climate change=17.55, showing that it has a bad environment, we use our BP network, and get its score, 2.88, meaning that it is a fragile country. And the impact of climate change exert a big influence.

We change the CCE, think the climate change don't have a high influence on Fragility, make it only CCE 1. Then Environment and CSE(Climate change *Social *Economic) also changed in the equations.

Environment=0.6 * 29.16+0.4* 0.75 * Climate change +0.4* 0.25 * 42.93
CSE= 86 * 26.8 * Climate change

Then we get a score is only 1.87, and the country becomes vulnerable. Again, the outcome confirms the impact of Climate change.

Analyzing the Bangladesh

Bangladesh is out of the top 10, and its climate change is only 49.8, under the average score--61. And we can analyse this country to find the tipping point.

Bangladesh

We change the climate change again and again

Environmet=0.6 * 11.96+0.4* 0.75* climate+0.4* 0.25* 4.12
Interaction=68.8 * 20.3 * climate

Tipping point
Tipping point