We compiled the variables used in the Social Vulnerability Index (SoVI; Cutter et al. 2003) and the Heat Vulnerability Index (HVI; Harlan et al. 2013) from multiple sources for 358 census tracts that were either within or intersected with the City of Phoenix, Arizona boundary. The HVI we used was developed by Harlan et al. (2013) to best capture the variables known from extensive prior research to influence heat vulnerability in Phoenix. Harlan et al. (2013) adapted their index based on the nationwide HVI first created by Reid et al. (2009). We converted all variables, as needed, to summary values (means, medians, or percentages) rather than raw totals because of the variation in population size between census tracts. For comparability, all variables were from data collected in the year 2016 or ending in 2016.

To compute SoVI, we compiled 27 census tract level variables from the 2012-2016 5-year American Community Survey (ACS) using the tidycensus package (version 0.9) in R (version 3.5.1). Since initial publication by Cutter et al. (2003), the variables used in SoVI have been partially modified to reflect the evolution of researchers’ understanding of social vulnerability in the literature. In this study, we used variables identified in the most recent iteration (2010-2014) of SoVI, which can be found online at University of South Carolina’s Hazards & Vulnerability Research Institute (HVRI) webpage (HVRI, 2014). Because it was not available in the 2012-2016 ACS, we replaced the variable "percent of population living in a nursing facility" from the most recent SoVI iteration with the variable "percent of population with a disability".

To calculate HVI, we followed a version of HVI that was modified by Harlan et al. (2013) to capture heat vulnerability in Maricopa County (which encompasses Phoenix). Specifically, we obtained 10 census tract level variables related to heat vulnerability. In an identical fashion to the methods for obtaining ACS data in SoVI, we calculated seven variables from the 2012-2016 5-year ACS. We obtained one variable, residential central air conditioning prevalence, from the Maricopa County Assessor’s Office for the year 2016.

The remaining two HVI variables, vegetated area mean and standard deviation, we collected by calculating the normalized difference vegetation index (NDVI; Tucker, 1979) in Google Earth Engine (GEE). NDVI is an index that varies between -1 and 1 that depicts the greenness of vegetation which is often used to assess vegetation prevalence. NDVI is calculated by utilizing the light reflection from vegetation in the red and near-infrared wavelengths. We utilized the Landsat 8 Surface Reflectance Tier 1 data product accessed through GEE. This dataset is atmospherically corrected surface reflectance from Landsat 8 Operational Land Imager (OLI) and Thermal Infrared Sensor (TIRS). Landsat 8 Surface Reflectance Tier 1 is available at 30x30-meter spatial resolution available every 16 days. Band 4 and Band 5 represent the red and near-infrared spectral bands for Landsat 8. Images with zero percent cloud cover, as identified in the image metadata, taken between the months of June through September from 2014 – 2016 were collected in GEE. These years closely align with the 2016 5-year American Community Survey (ACS) Dataset. While the 2016 5-year ACS covers the years of 2012 and 2013, the Landsat 8 Surface Reflectance Tier 1 data does not exist prior to 2014. A median composite image was created from the set of filtered images. The resulting composite image represents the median pixel values from the filtered collection. NDVI was calculated for the composite image calculated using the "normalizedDifference" function in GEE. Finally, the average and standard deviation of NDVI were calculated for each census tract in the Phoenix study area.

Once the variables were obtained for each respective index, both SoVI and HVI were calculated using the same methodology. Using the psych package (version 1.8.3.3) in R, we performed a principal components analysis (PCA) on the Pearson product-moment correlation matrices of the vulnerability variables. Many of the variables used in each index are highly correlated; PCA eliminates issues with multicollinearity by recombining total variance among the variables so that each resulting component is uncorrelated with the other components. In an effort to calculate SoVI and HVI in a manner that is most similar to how SoVI and HVI are calculated and used by practitioners, we did not utilize the interpretability of each component in our decision to retain or not retain a given component. Instead, to determine the appropriate number of components to extract, we primarily used the simple Kaiser criterion of eigenvalues greater than one—as used by Cutter et al. (2003) for SoVI and Harlan et al. (2013) for HVI. We then rotated the retained components using varimax rotation to maintain independence between components (orthogonality), distribute variance as evenly as possible between components (the first components are still extracted to retain maximal variance), and aid in interpretation.

Separately, for each index, we examined the variables that loaded most highly on each component to determine the predominant directionality of vulnerability (e.g. higher vulnerability vs. lower vulnerability) captured by the component, using knowledge of how certain variables influence vulnerability as identified in vulnerability and hazards literature. The overall goal was to ensure that the cardinality of each component was capturing the same phenomena, such that more positive loadings represent higher vulnerability, and more negative loadings represent lower vulnerability. In general, only component loadings greater than .700 or less than -.700 were considered when determining the directionality of vulnerability. However, when a component only had smaller loadings, we considered variables with loadings greater than .400 or less than -.400 to identify the direction of vulnerability. For components that required a cardinality correction, we multiplied the component scores by -1.

PCA of the 27 SoVI social vulnerability variables for Phoenix census tracts yielded six components that accounted for 72% of the variance. All but one of the components had multiple loadings greater than .700 or less than -.700 that agreed internally on the directionality of vulnerability (e.g., variables loading highly on one component that increase/decrease vulnerability all had the same cardinality within that component). Incidentally, those same components were all output with the correct cardinality, where positive loadings increase vulnerability and negative loadings decrease vulnerability. Component RC5 did not have any loadings greater than .700 or less than -.700 so we used the smaller loadings to determine the direction of vulnerability for RC5. The positive loadings for median dollar value of owner-occupied housing units and percent of families earning more than $200,000 per year, and the negative loadings for percent African American indicated that RC5 should be adjusted for cardinality.

PCA of the 10 HVI heat vulnerability variables for Phoenix census tracts yielded three components that accounted for 84% of the variance. All three components had multiple loadings greater than .700 or less than -.700 that agreed internally on the directionality of vulnerability. Component RC2 had positive loadings for vegetated area mean and standard deviation, which required a cardinality adjustment because increased vegetation is known to decrease heat vulnerability (Harlan et al., 2013; Jenerette et al., 2016).

Lastly, we summed the indices’ component scores for each census tract to produce a SoVI value that represents social vulnerability and an HVI value that represents heat vulnerability of each census tract relative to all other census tracts in Phoenix. We spatially joined the SoVI and HVI index values to their respective census tract shapefile using the tigris (version 0.7) and sf (version 0.7.2) packages in R.

References:

Cutter, S. L., Boruff, B. J., & Shirley, W. L. (2003). Social vulnerability to environmental hazards. Social Science Quarterly, 84(2), 242–261. https://doi.org/10.1111/1540-6237.8402002

Harlan, S. L., Declet-Barreto, J. H., Stefanov, W. L., & Petitti, D. B. (2013). Neighborhood effects on heat deaths: Social and environmental predictors of vulnerability in Maricopa County, Arizona. Environmental Health Perspectives, 121(2), 197–204. https://doi.org/10.1289/ehp.1104625

Hazards & Vulnerability Research Institute (HVRI). (2014). SoVI®. Retrieved December 5, 2018, from http://artsandsciences.sc.edu/geog/hvri/sovi%C2%AE-0

Jenerette, G. D., Harlan, S. L., Buyantuev, A., Stefanov, W. L., Declet-Barreto, J., Ruddell, B. L., … Li, X. (2016). Micro-scale urban surface temperatures are related to land-cover features and residential heat related health impacts in Phoenix, AZ USA. Landscape Ecology, 31(4), 745–760. https://doi.org/10.1007/s10980-015-0284-3

Reid, C. E., O’Neill, M. S., Gronlund, C. J., Brines, S. J., Brown, D. G., Diez-Roux, A. V., & Schwartz, J. (2009). Mapping community determinants of heat vulnerability. Environmental Health Perspectives, 117(11), 1730–1736. https://doi.org/10.1289/ehp.0900683

Tucker, C. J. (1979). Red and photographic infrared linear combinations for monitoring vegetation. Remote Sensing of Environment, 8(2), 127–150. https://doi.org/10.1016/0034-4257(79)90013-0