Assessing spatial vulnerability of Bangladesh to climate change and extremes: a geographic information system approach

Abstract 

Regarding climate change, the world’s most discussed issue for the last few decades, countries like Bangladesh are always noteworthy due to its susceptibility resulting from its geography, hazard proneness, and socioeconomic condition. Thus, this study aimed to justify the hypothesis that Bangladesh has spatial diversity in sectors of climate change vulnerability (CCV) by identifying the sectors of vulnerability and visualizing the spatial distribution of vulnerability through multivariate geospatial analysis in the GIS environment. For an integrated assessment of CCV, 38 indicators (socioeconomic and biophysical) have been incorporated in the IPCC framework in raster form. Test statistics have shown that Kaiser–Meyer–Olkin (KMO) value is 0.73 and the p-value of Bartlett’s sphericity is 0. The principal component analysis resulted in 6 principal components with 73.52% total explained variance. Sectors of CCV are the coastal vulnerability (PC1), meteorological shift vulnerability (PC2), infrastructure and demographic vulnerability (PC3), ecological vulnerability (PC4), pluvial vulnerability (PC5), and economic vulnerability (PC6) with Cronbach’s alpha 0.90, 0.81, 0.88, 0.72, 0.72, and 0.66, respectively. Among 3 clusters of weighted averaged indices, the highly vulnerable cluster has shown that the PC1 has the highest magnitude with a score of 0.53–0.87, while the PC5 has the highest spatial coverage with 24 districts. The present study however is a new edition in climate vulnerability assessment in Bangladesh since it encompasses multivariate spatial analysis to demonstrate countrywide CCV. This study should be an important tool for setting adaptation and mitigation strategies from the root level to policymaking platforms of Bangladesh.

Appendices

Appendix 1 Details of selected indicators

Initially, 42 indicators for climate change vulnerability (CCV) have been selected based on literature review and data availability. The list of all indicators has been mentioned in Table 5 with a description of units, sources of data, theme, and vulnerability components.

Table 5 Selected indicators with units, sources, and relation with vulnerability

Appendix 2. Rescaling of raster datasets: normalization

A maximum-minimum normalization technique (Eq. 2) has been used for all raster datasets using an iterative model (Fig. 

Fig. 7

Iterative model for normalization of raster datasets in a defined workspace

7) consisting raster calculator.

$$Normalization=\frac{x-minimum\;of\;x}{maximum\;of\;x-minimum\;of\;x}$$

(2)

The map algebra expression used in the above model, a modification of Eq. 2 for the raster calculator, is in the following (Eq. 3).

$$Normalized\,raster=\frac{"{\%Band_01\%" -}"{\%Band_01\%" .minimu}{m}}{{" \%Band_01\%" .maximum - " \%Band_01\%" .minimum}}$$

(3)

Appendix 3. Elimination of insignificant variables

As a common practice, the correlation coefficient between − 0.3 and 0.3 is considered insignificant. When a variable has no significant correlation with other variables, or the number of significantly correlated variables is negligible concerning the total number of variables in the dataset, it is considered unsuitable for exploratory factor analysis or principal component analysis (PCA). However, to examine the internal relation of the raster dataset, the following correlation table (Table 6) has been extracted from the “Band collection statistics” tool of ArcGIS.

Table 6 Correlation matrix of initially selected 42 indicators (absolute values). Highlighted cells indicate an insignificant relationship

Here, some variables have negligible or no relation with the rest of the variables in the dataset which are unfavorable for PCA. Hench, we have eliminated them from the dataset, (22) crop damage, (30) erosion-affected households, (34) drought prone areas, and (42) erosion prone areas. After the elimination of 4 insignificant variables, the remaining datasets of 38 variables has been considered for further procedures.

Appendix 4. Test statistics

Kaiser–Meyer–Olkin (KMO) test of sampling adequacy:

The Kaiser–Meyer–Olkin (KMO) test is a measure of how suited the dataset is for factor analysis or PCA. The test measures sampling adequacy for each variable in the dataset and the complete dataset. KMO returns values between 0 and 1. KMO values between 0.8 and 1 indicate that the sampling is adequate. KMO values less than 0.6 indicate that the sampling is not adequate and that remedial action should be taken. Some authors put this value at 0.5, and here we have used 0.5 as the lower limit. KMO values close to zero mean that there are large partial correlations compared to the sum of correlations. In other words, there are widespread correlations which are a large problem for factor analysis.

However, individual KMOs can be tested using the correlation and partial correlation (anti-image of correlation) matrices of the dataset with Eq. 4.

$$Individual\;KMO=\frac{\sum_{i\neq j}r_{ij}^2}{\sum_{i\neq j}r_{ij}^2+\sum_{i\neq j}u_{ij}^2}$$

(4)

where ${r}_{ij}$ = correlation coefficients of I with j and ${u}_{ij}$ = partial variance coefficients of I with j.

Individual KMOs for all variables have been shown in Table 7. Then, the overall KMO of the sample dataset has been tested using Eq. 5.

$$KMO= \frac{\sum_{i\ne j}{R}_{ij}^{2}}{\sum_{i\ne j}{R}_{ij}^{2}+ \sum_{i\ne j}{U}_{ij}^{2}}$$

(5)

where ${R}_{ij}$= correlation matrix and ${U}_{ij}$= partial covariance matrix.

The overall KMO is 0.73 (Table 7), which makes the datasets suitable in terms of sampling adequacy; thus, the datasets are suitable for PCA.

Table 7 Calculation of KMO values of individual indicators

Table 8

Table 8 Calculation of the over KMO of the sample datasets

Bartlett’s test of sphericity:

Bartlett’s test of sphericity compares an observed correlation matrix to the identity matrix. Essentially it checks to see if there is a certain redundancy between the variables that we can summarize with a few numbers of factors. The null hypothesis of the test is that the variables are orthogonal, i.e., not correlated. The alternative hypothesis is that the variables are not orthogonal, i.e., they are correlated enough to where the correlation matrix diverges significantly from the identity matrix.

This test is often performed before we use a data reduction technique such as principal component analysis or factor analysis to verify that a data reduction technique can compress the data in a meaningful way. If the p-value from Bartlett’s test of sphericity is lower than our chosen significance level (common choices are 0.10, 0.05, and 0.01), then our dataset is suitable for a data reduction technique.

To measure the overall relationship between the variables, the determinant of the correlation matrix |R| is calculated. Under H₀, |R|= 1, if the variables are highly correlated, then |R| ≈ 0. Bartlett’s sphericity is tested by chi-square statistic and level of significance. Equation 6 has been used for chi-square statistics.

$${\chi }^{2}=-\left(n-1- \frac{2p+5}{6}\right)\times \mathrm{ln}\left|R\right|$$

(6)

where $p$ = number of variables, $n$ = total sample size, and $R$ = correlation matrix.

A summary of Bartlett’s test of sphericity has been shown in Table 3. Since Bartlett’s test showed a p-value < 0.0001 (Table 9), the datasets have suitability for dimensionality reduction techniques like PCA.

Table 9 Summary of Bartlett’s test of sphericity

Appendix 5. Test of reliability: Cronbach’s alpha

Cronbach’s alpha usually ranges from 0.00 to 1.00, and values higher than 0.5 are generally considered indicative of a valid internal relation. Equation 7 has been used for calculating Cronbach’s alpha of each PC.

$$\alpha =\frac{k \times \overline{c} }{\overline{v }\times (k-1)\overline{c} }$$

(7)

where $k$ = the number of items in the components, $\overline{c }$ = the average of all covariances between items, and $\overline{v }$ = the average variance of each item.

An overview of the calculation of alpha has been given in Table 10.

Table 10 Calculation of Cronbach’s alpha