**5. Methods**

The methodology was conducted in two phases. For this study, the first phase included the state-of-the-art bottom-up approach we selected as the most appropriate with respect to the study's objective. The alternative approach of quantifying material stocks that has been widely used in previous studies is a top-down method, that accounts for total quantities of stocked materials in a given system. This approach lacks information on the location of these stocks and their uses [59–61]. As our purpose is to highlight the vulnerabilities inherent in material stock patterns across the island, we opted for the bottom-up approach as the only other alternative. Alternative GIS datasets allowed us to quantify and map the spatial distribution and uses of the building material stock in A&B. In the second phase, a vulnerability assessment estimates the quantity of MSs threatened by various sea level rise scenarios.

#### *5.1. Material Stock Analysis (MSA) of Buildings*

The building shapefile for A&B provided by the Department of Environment (DOE) consisted of 60,000 building footprints (BFs). The first step involved the creation of a classification system to categorize the BFs for the entire island into their respective building use type classes. It consisted of two main components: the interpretation and analysis of remote sensing satellite imagery and local knowledge of the physical infrastructure in A&B. Image interpretation included the analysis of basic elements, such as the shape, size, pattern (spatial distribution), and association of the BFs on external mapping platforms, such as OpenStreetMap (OSM) and Google Maps, as shown in Figure 1. The distinctive shapes of specific building typologies such as cathedrals and stadiums enabled for clear identification of buildings from the OSM data layers to the DOE data layer. Buildings within residential and commercial areas usually follow distinctive spatial patterns that can be identified by their size and layout. Understanding the contrast in sizes amongs<sup>t</sup> different classes of buildings introduces a scale factor that allows for the recognition of buildings that are less easily identified than others. Association involved the observation that the presence of specific building use type classes influences the presence of others. Each village or parish in A&B has present their group of churches, healthcare clinics, and small shops.

**Figure 1.** Schematic of the building footprint classification process adopted for Antigua and Barbuda. Image interpretation required the use of a base map provided by the Department of Environment (DOE) which was compared and contrasted to a reference map from OpenStreetMap. The four main characteristics guiding the classification process included: shape, pattern, size, and association.

The 2004 BF layer was sourced from the DOE in A&B [62] and used as a base map during the building classification process. The original BFs dataset only provided information on the area, perimeter, and feature attributes of each building footprint, resulting in all BFs to be considered as "unclassified" in the absence of assigned categories describing their specific use type role. To accurately compare and analyze the base map, a reference map was provided by OSM that provided greater details (e.g., supplementary geographic data at more defined scales, road networks, location tags of basic areas and other points of interest) during the classification process. Physical data were collected during empirical evaluations of a sample size of 303 building footprints, which were randomly selected within each of the seven parishes in A&B. These data included height measurements and the study of local construction styles for the material intensity typologies (MITs). The generation of material intensity typologies (MITs) is based on the local construction styles practiced within the country under the varying building use type classes. The MIT separates the material intensities (MIs) into four main categories of construction materials (aggregates, wood, concrete, steel). The adoption of GIS tools facilitated the calculation of the total estimated material stock within the island and generated maps of its spatial distribution.

In the absence of actual height measurements of the BFs, the number of stories or floors within each building was used as a proxy. A sensitivity analysis of the original floor estimates of +/− floor change in each building use type shows the fluctuations in the material stock (MS) estimates in Table S4 of the Supporting Information.

To calculate the gross floor area (*GFA*) for each building footprint (represented by *b*), the equation is as follows:

$$\text{GFA}\_{(b)} = \text{Building Footprint Area}\_{(b)} \times \text{ The number of floor stories} \tag{1}$$

*MS*, measured per material category *m* (aggregate, timber, concrete, or steel), for a building footprint *b* is calculated as follows:

$$MS\_{\left(b,m\right)} = GFA\_{\left(b\right)} \times MI\_{\left(m\right)}\tag{2}$$

Total *MS* (*MSsum*) for the GFA of a building footprint *b* is calculated by the sum of the material stock measured per material category *m* (aggregate, timber, concrete, and steel):

$$MS\_{\text{sum}} = \Sigma \cdot MS\_{(b,m)} = MS\_{\text{\"Aggregate\"}} \cdot \_{(b,m)} + MS \cdot Time \, \_{(b,m)} + MS \, \_{\text{Concrete}} + MS \, \text{Stel\\_(b,m)} \tag{3}$$

To calculate the total MSs for all the BFs from the 2004 BF layer, the *MSsum* is summed for each BF.

#### *5.2. Residential Material Intensity Distribution*

The residential sector accounts for the majority of the material stock estimate, as after classifying the BFs of the entire island, residential dwellings constitute 90% of the BFs in A&B. As a result, the MITs distributed within the residential sector were determined using housing statistics in the 2001 National Census [63]. The ratio of the outer wall materials of household dwellings stated in the census was the determining factor in distributing the corresponding MITs. In the absence of on-site empirical evaluations, material intensities were assigned by a Monte Carlo simulation coded in R. To evaluate the level of uncertainty, the margin of error was assessed through running multiple iterations of the code. This step illustrates how the material stock estimates are affected by the random assignment of MITs that may result in the potential overestimation or underestimation of material stock estimates.

#### *5.3. Estimating Vulnerable Building Stocks*

Sea level rise (SLR) assessments in the study were based on 1 m and 2 m scenarios. These values were derived from four scenarios presented by Parris et al. [64], including an intermediate–low scenario measured at 0.5 m, and the highest scenario measured at 2 m. A triangulated irregular network (TIN) file containing elevation data for Antigua was sourced from the DOE [62] and converted into a 1 m resolution raster file. The 0–2 m elevation levels were extracted, while the resulting raster layer contained areas measured at 1 m or less in elevation. An overlay analysis of the elevation polygon file and the BF data layer identified buildings falling within the 1 m and 2 m boundary. These steps were repeated for the 2 m level rise analysis. This methodology was adopted in the absence of shoreline data and accounting for hydrological connectivity to the sea, as utilized in previous research [65–67].
