### Measures of the vulnerability index

The indicators used for measuring the vulnerability index in Theme 1–4 (Supplementary Table S2) were retrieved from the Census of Population and Housing via Table Builder Portal from the Australian Bureau of Statistics^{50}. The census data was retrieved at the Statistical Area level 1 (SA1) as the smallest census unit. SA1 areas generally have a population of 200 to 800 people, and an average population of about 400 people^{51}. SA1 areas in remote and rural regions generally have smaller populations than those in urban areas. There are 57,523 SA1 areas in total in Australia; amongst those, 1313 SA1 areas with population less than 50 were excluded in our analysis because these small population numbers were randomly assigned by ABS data privacy protection. The remaining 55,218 SA1 areas were used in the analysis.

The indicators in Theme 5 were derived from multiple data sources. First, Points of Interest (PoI) data originally retrieved via the Open Street Map were provided by Australian Urban Research Infrastructure Network^{52}. The PoI data contains the locations (X, Y coordinates) of + 100 types of places and we reclassified them to a total of 24 major types (Supplementary Table S14). They were used to calculate the nearest distance of a SA1 area (the centroid of a SA1) to a particular place using the ‘*nearest’* function in ArcGIS Pro 2.8. Second, the digital cadastral data from Department for Infrastructure and Transport contains the nationwide road and railway networks^{53}. We selected five types of drivable roads from the road network data—‘freeways/motor ways’, ‘high ways’, ‘secondary ways’, ‘local connector roads’ and ‘street/local roads’—used for measuring the distance from a place to the nearest road segment. Such distances were calculated in ArcGIS Pro 2.8 using the ‘*nearest’* function. Third, the Sentinel-2 satellite imagery retrieved via Google Earth Engine (2020) were used to calculate the normalized difference built-up index (NDBI) to indicate the coverage of built-up areas (code provided in Supplementary Note 6)^{54}. Sentinel-2 carries a multispectral imagery with a swath of 290 km. The imagery provides a versatile set of 13 spectral bands spanning from the visible and near infrared to the shortwave infrared, featuring four spectral bands at 10 m, six bands at 20 m and three bands at 60 m spatial resolution. NDBI highlights urban areas where there is typically a higher reflectance in the shortwave-infrared region, compared to the near-infrared region (Google Earth Engine, 2020). The NDBI value ranges from − 1 to + 1. Negative values represent water bodies whereas the higher positive values represent the bigger build-up areas. Fourth, the land use data from the Department of Agricultural, Water and the Environment contained ten types of land use, including commercial, education, hospital, industrial, parkland, primary production, residential, transport, water, and other land use^{55}. Then, we used Simpson’s index to measure land-use diversity as Eq. 1^{56}:

$$Simpson^{\prime}s Index = 1 – \sum \frac{{n_{i}^{2} }}{{N^{2} }}$$

(1)

where \({n}_{i}\) indicates the total number of areas in one SA1 for land use type i; N is the total area of all land use types, i is the types of land use classified into ten. Simpson’s Index ranges from 0 (minimum diversity) to 1 (maximum diversity). Equation 1 was also used to calculate the ethnicity diversity and housing diversity based on the census data (Supplementary Table S2). In the end, we derived a total of 41 indicators, including four indicators in four themes After normalizing some indicators via log-transformation, all 41 indicators were transferred to be normally distributed (Supplementary Table S2).

We then employed the principal component analysis (PCA) to generalize the underlying structure of the 41 indicators and extracted the principal components that were used to construct the overall vulnerability index. PCA allows for a robust and consistent set of variables that can be monitored over time to assess any changes in overall vulnerability^{57}. The PCA used to generate the standardising principal component scores is expressed as^{57}:

$${PC}_{SA1}=\sum_{i=1}^{j}\frac{{L}_{i}}{\sqrt{\mu }}\times {X}_{i, SA1}$$

(2)

where \({PC}_{SA1}\) denotes the raw principal component score for one SA1; \({X}_{i, SA1}\) denotes the standardized indicator of the \(i\)-th indicator for the SA1; \({L}_{i}\) is the loading for the \(i\)-th indicator; \(\mu\) denotes the engenvalue of the principal component; \(j\) is the total number of indicators in that principal component.

We conducted PCA for urban and rural areas, generating a total of 10 PCs and 11 PCs, respectively. The overall vulnerability index (\(VI\)) was calculated by using an evenly-weighted arithmetic (additive) aggregation procedure^{6}:

$$VI=\sum_{n=1}^{p}{PC}_{n,SA1}$$

(3)

where \({PC}_{n,SA1}\) is the eigenvalue of that PC in one SA1 and \(p\) is the total number of PCs extracted in that SA1.

### Validation and sensitivity analysis

We conducted a sensitivity analysis by running the PCA for urban space (eight capital cities) to extract different number of PCs and testing whether the outcome measure of vulnerability is sensitive to the selection of PCs. In addition to the first scenario (extracting 10 PCs) that we did previously, we generated two more scenarios with 12 and 17 PCs extracted to explain the 74.58 and 84.69% of data variance, respectively (Supplementary Table S15). We then compared these two scenarios with the first scenario (10 PCs) by conducting a pairwise Pearson’s correlation^{58} and the one-sample t-test^{59} to assess the sensitivity of PC selection on the construction of VI. The result of the Pearson’s correlation (Supplementary Table S16) shows that VI generated by three scenarios are highly correlated with the coefficient above 0.773 (*p* < 0.01). The result of the T statistics (Supplementary Table S17) indicates that the means of VI generated by three scenarios have insignificant differences (*p* > 0.1). It means that the VI generated by the first scenario (based on 10 PCs) is representative thus we select the first scenario to measure VI for the purpose of simplification. To validate our measures of VI, we also conducted a pairwise Pearson’s correlation analysis between VI and four indices of SEIFA developed by ABS, including Index of Relative Socio-Economic Disadvantage (IRSD), Index of Relative Socio-Economic Advantage and Disadvantage (IRSAD), Index of Education and Occupation (IEO), and Index of Economic Resources (IER)^{43}. The result shows that VI in Theme 1 (socioeconomic status) is highly correlated with the four indices of SEIFA (Supplementary Fig. 12) but VI in other themes are not. It means that our measures of VI capture multiple dimensions of vulnerability that SEIFA is not able to fully cover.

### Estimating natural hazards

#### Hazard 1: Earthquake

Earthquake data was retrieved from the National Seismic Hazard Assessment for Australia (NSHA18) developed by Geoscience Australia^{60}. This NSHA18 dataset contained time-independent, mean seismic design values which were calculated on rock sites (Standards Australia’s AS1170.4 Soil Class) for the geometric mean of the 5% damped response spectral accelerations, Sa(T), for different timespans (e.g., from 0.1 to 4.0 s)^{60}. The hazard values were estimated across the Australian continent using a uniformly-spaced 15 km grid. Hazard curves and uniform hazard spectra were also calculated for key localities at the 10 and 2% probability of exceedance in 50-year hazard levels. We selected the seismic map with Sa(T) of 0.2 s at the 2% probability of exceedance in 50-year hazard levels given that it had a wider range of estimated earthquake probabilities (originally ranging from 0 to 71%) compared to other seismic maps with different parametric settings. We then utilised the ‘reclassify’ function in ArcGIS Pro 2.8 to re-categorise the earthquake probability to three risk levels based on the equal interval (i.e., 0–23.7% as low risks coded as 1, 23.7–47.3% as medium risks coded as 2, and 47.3% to 71% as high risks coded as 3) (high (Fig. 6A-1).

#### Hazard 2: Wildfire

Fires in Australia’s forests 2011–16 (2018) dataset was collected from the Australian Bureau of Agricultural and Resource Economics and Sciences^{61}. It contains the extent and frequency of planned and unplanned fires that occurred in the five financial years between July 2011 and June 2016, and reported from multiple fire area datasets contributed by state and territory government agencies. This fire dataset is in raster format with a resolution of 100 m. It has a key attribute ‘TOTAL_X_BURNT’ indicating the number of times burnt in each cell (originally ranging from 0 to 5), which was reclassified to three levels of risks using ‘reclassify’ function in ArcGIS Pro 2.8 based on the equal interval method (i.e., 0–1.67 as low risks coded as 1, 1.67 to 3.34 as medium risks coded as 2, and 3.34 to 5 as high risks coded as 3) (high (Fig. 6A-2).

#### Hazard 3: Flood

Flood data at a global scale was retrieved as a collection of flood maps from Joint Research Centre (JRC) Data Catalogue, European Commission^{62}, depicting flood prone areas for river flood events of different magnitudes (e.g., from 1-in-10-year to 1-in-500-year). We did not use the historical flood map here as the extend of historical flood events was too small and sporadic to observe in the national scale. Instead, the JRC flood maps were estimated and simulated using hydrological and hydrodynamic models, driven by the climatological data of the Global Flood Awareness Systems (GloFAS). After tailoring to the Australian scale, they comprise most of the geographical Australia (excluding external territories such as Christmas Island) and all the river basins in the Australian mainland and the state of Tasmania. Flood maps are in raster format (GEOTIF) with a grid resolution of 30 arcseconds (approximately 245 m after projection). We selected three flood maps (i.e., 1-in-10-year, 1-in-100-year, and 1-in-500-year) and each map has binary attributes with 0 indicating no flood cells and 1 indicating flooded cells. We then overlapped these three maps by the *‘raster calculator’* function in ArcGIS Pro 2.8, generating the final flood risk map with attribute values ranging from 0 indicating no flood risk and 1–3 indicating flood risk levels from low to high (Fig. 6A-3).

### Inequity metrics

We utilised the inequity index developed by Gluschenko^{63} to evaluate the inequality of vulnerability in hazard-affected areas across urban and rural space. The inequity index has the advantage to characterise distributions of environmental hazards^{63}, as it allows the input variable (i.e., vulnerability) to be negative values and also it allows the adjustment of the parameter \(k\) in Eq. (4) to reflect the non-linearity of marginal damages caused by three types of natural hazards^{64}. The lower value of \(k\) corresponds to a higher marginal damage of the hazard \(x\), resulting in a higher inequality index value for a given unequal distribution. When \(k\) approaches zero, the inequality index would be close to zero. For the vector of VI, the inequality index can be expressed as^{63}:

$$I\left(x\right)= -\frac{1}{k}Ln\frac{1}{N}\sum_{n=1}^{N}{e}^{k\left[\overline{x }-{x}_{n}\right]}, for k<0$$

(4)

where \(\overline{x }\) is the mean of the vulnerability in each urban or rural SA1 area and \(k\) is a parameter indicating the degree to which inequality in the distribution is undesirable due to increasing marginal damage^{63}.

Since there is no consensus on the selection of \(k\)^{65,66,67}, the literature typically presents results for a range of values^{64}. Thus, we selected three possible values for \(k\)(0.25, 0.5 and 0.75) in the calculation of the inequality index. Existing studies use inequality measures for which the elasticity is a constant. For the measure of the inequality index, however, this elasticity, \({x}_{n}\), is a function of \(x\). To present results for a range of \(k\) that generates elasticities comparable to those in the existing literature, we first identify a value of \(k\) that is consistent with a given constant elasticity. To establish a correspondence between an elasticity and a vector of elasticities \(x\), we use the below approach of choosing the value of \(k\) that minimizes the sum of squared differences between the individual elasticities:

$$k\left(\beta \right)=-{\mathrm{arg}}_{\widehat{k}}\mathrm{min}\left\{{\left[\widehat{k}x-\beta \right]}^{^{\prime}}\left[\widehat{k}x-\beta \right]\right\}=-\frac{\beta \sum_{n=1}^{N}{x}_{n}}{\sum_{n=1}^{N}{x}_{n}^{2}}$$

(5)

where \(\beta\) denotes the given constant elasticity; \(N\) denotes the total number of SA1 areas; \({x}_{n}\) is the vulnerability score of a given SA1 area \(n\). Here we employed three levels of inequality aversion—low \(k\)(0.25), moderate \(k\)(0.50), and high \(k\)(0.75)—representing different inequality aversions to calculate the inequality index presented in Supplementary Table S13.

### Ethics statement

This study did not receive nor require ethics approval, as it does not involve human & animal participants.

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