*2.1. Building Modelling*

The West Midlands region has a population of 5.6 million [26], and contains Birmingham, the second-most populous urban area in the UK. During the 2003 heatwave, the region had an estimated 130 excess deaths due to hot weather [2].

The baseline housing stock and population model is the 2010–2011 English Housing Survey (EHS), which contains regionally-representative housing and occupant data for 1558 dwellings in the West Midlands [27]. Resident age data is available within the database for each dwelling occupant. Data within the EHS is used to inform the geometry, floor area, glazing area, construction type, and insulation levels of each dwelling, while the energy efficiency and airtightness of each dwelling has been estimated using standardised methods [28].

Readers are referred to Symonds et al. (2016) for further information on the indoor temperature model. Briefly, indoor temperatures and energy use for space heating in the West Midlands housing stock were estimated using a series of metamodels derived from the results of simulation studies [29,30] using the building physics model EnergyPlus. Previous studies have compared the underlying EnergyPlus model outputs against a large dataset of monitored indoor temperatures, showing that the model is able to capture the trends in overheating risk between dwelling variants [30]. Here, the model is adapted to model dwellings with and without energy efficiency, occupant behavior, and passive overheating interventions. Air conditioners (A/C) were not modelled due to their rarity in English housing stock—estimated at 3% of dwellings [31]—and because of their high energy demands.

Metamodels were developed for each combination of dwelling geometry (end terrace, mid-terrace, semidetached, detached, bungalow, converted flats, low-rise flats, and high-rise flats), wall type (cavity or solid), and heat adaptation (shutters or no shutters). For each combination of the above, EnergyPlus models were developed with fabric energy efficiency levels, permeability, floor area, glazing area, and local wind exposure randomly sampled from distributions available from representative samples [27,32] of English dwellings. For this study, roof and wall absorptance was also randomly selected in the range of 0.1–0.6, representing the painting of external surfaces with a low absorptance paint; the indoor temperature threshold above which windows are opened were also randomly selected (18 ◦C–35 ◦C) to represent extreme ranges in occupant behaviour. Archetypes, used to represent dwelling geometries, can be seen in Appendix A. Models were run using Test Reference Year weather data, representing the "average" climate for 2030 under a medium emission scenario (A1B-50th percentile) [33], assumed to be representative for the region.

From the results of these simulations, we computed the mean maximum daytime living room temperature at different two-day rolling mean maximum outdoor summer temperatures, as well as annual energy use (kWh) for space heating. A metamodel was then generated using artificial neural networks [34] to determine energy use and indoor temperatures from dwelling characteristics across the West Midlands housing stock. The metamodel was applied to obtain indoor temperature and energy use estimates for individual dwellings in the West Midlands under the adaptation scenarios in Table 1, using weather data that describes "average" Birmingham summers in 2030s, 2050s, and 2080s (A1B-medium emissions scenario, 90% probability [4,33]).

**Table 1.** The adaptations and underlying assumptions modelled. The reduction in fabric U-value is based on the UK Government's Standard Assessment Procedure (SAP) for Energy Rating of Dwellings, with the lowest possible U-value for the fabric component selected based on the fabric type and dwelling age [35]. The change in permeability is estimated based on the work by <sup>a</sup> Hong et al. [36] or <sup>b</sup> UK SAP, following the methods described by Hamilton et al. [37].


