2.1 Research design

The methods used to generate simulation models for this study are summarised below. Further details of the auto-generation process are presented in Section 2.3.1.

• An analysis of the PDSP national database of school building stock level data was carried out to quantify the propensity for different geographical locations and building typologies within non-mechanically ventilated classrooms from the English stock of 9629 primary schools. Building form, fenestration and building fabric characteristics associated with various construction eras were defined for each of these combinations at the stock level and used as the basis for auto-generating individual thermal classroom models representing sectors of the stock.
• Base-case classroom simulation models were constructed with the EnergyPlus (US Department of Energy 2021) dynamic building simulation software using the Data dRiven Engine for Archetype Models of Schools (DREAMS) modelling framework (Schwartz et al. 2021a). This method uses 168 building archetypes to represent the primary school building stock in England for energy modelling purposes. Omitting 57 mechanically ventilated school archetypes for the current project, 111 similar archetypes containing four different classroom orientations were auto-generated from geometric seed models to incorporate 12 geographical locations, five different construction era archetypes and modification status of the original building. Classroom models were set up to provide specific metrics for overheating, three separate contaminants (CO₂, NO₂, PM_2.5) and space heating demand over a simulation year.
• EnergyPlus base-case models were updated to reflect an additional retrofit scenario, comprising future structural adaptations in the building fabric to improve energy efficiency and reduce carbon emissions.
• Both the EnergyPlus base-case and retrofit scenario were updated to include a programme of measures, including increasing flow through windows and internal shading, for the purposes of mitigating overheating risk.
• Simulations were carried out to investigate the variation of overheating, air quality and carbon emissions metrics reflecting the two objectives, first, across the entire stock under current conditions, before following up with modelling current and future retrofit and overheating mitigation scenarios for a smaller subset of buildings under different climate change scenarios.

2.2 Analysis of building stock-level data

A statistical analysis previously carried out on an English school dataset (Schwartz et al. 2021a) was recently updated to include additional operational characteristics (Hong et al. 2022) by linking the following two national datasets:

• Property Data Survey Programme (PDSP) dataset (EFA 2012), containing physical properties of more than 18,000 establishments, or 85% of the English school stock.
• Display Energy Certificate (DEC) dataset based on the Chartered Institution of Building Services’ (CIBSE) (2008) benchmarking of annual measured energy use.

The combined dataset was used to classify the stock of 9629 primary schools, after removing secondary schools and other establishments (Hong et al. 2022), by the following criteria:

• Geographical location: weather files are available for 10 locations across England (CIBSE 2016), with differing uses for the purpose of overheating described in further detail in Section 2.6. These were allocated to the 12 degree-day regions given by CIBSE in TM46 (CIBSE 2008), used to split schools into geographical regions, as shown in Figure S1 in the supplemental data online.
• Building construction era: five archetypes were defined based on construction age, as detailed in Section 2.3.1. While different eras, particularly post-1976, contain a variety of contrasting construction types (Pegg et al. 2007), to characterise these further would require data on propensity of construction types, which are unavailable in the existing PDSP dataset, but potentially derivable from the more recent Condition Data Collection (CDC) (ESFA 2017).
• Modification status: whether the building has been modified previously (e.g. through the addition of an extension) or remains in its original form.

Fenestration size was accounted for by averaging the window-to-wall ratios (WWR), detailed within the PDSP, of each primary school building within each separate classification of the school stock.

2.3 Construction of base-case simulation models

2.3.1 Building geometry and fabric

EnergyPlus (US Department of Energy 2021), a widely tested and validated software, has been used to simulate energy demand and annual exposures to overheating and air contaminants by calculating heating loads and ventilation requirements based upon external conditions. It has the advantages of not only being widely used and open source, allowing access for a wide range of stakeholders, but also has the ability to introduce modules, such as airflow networks and contaminant models described below, to add increased complexity where required for a particular application.

Geometric classroom models were constructed for the English primary school stock within EnergyPlus version 9.5, with geometries as shown in Figure 2 using the OpenStudio graphical user interface (GUI) (Guglielmetti et al. 2011), based on an approach devised previously (Schwartz et al. 2021b). These consist of north-, south-, west- and east-facing classrooms, each with three adiabatic walls, an adiabatic floor and ceiling, representing adjacent classrooms with similar heating loads and occupancies, and a single external wall customised for different construction eras and fenestration areas. For their construction details, see Table S1 in the supplemental data online.

Figure 2 

Geometry of the classroom model.

For each external wall, five different construction eras were allocated the features and U-values given in Table 2 based on a previous analysis of the PDSP dataset (Schwartz et al. 2021a). Despite identical external walls, the same era archetypes from different geographical regions will still have different thermal properties since the glazing ratios as described in Section 2.2 will vary. Although an identical classroom geometry has been assigned to each era, this is a base assumption and differentiation of geometry by era may be updated based on future iterations of the PDSP analysis, as was done previously for buildings themselves in an energy context (Schwartz et al. 2021a).

Table 2

Composition of external walls for different eras.

ERA	PRE-1919	INTER-WAR	1945–66	1967–76	POST-1976
U-value (W/m2K)	1.916	1.916	1.370	1.370	0.735
Outer layers	Brick 225 mm	Brick 225 mm	Plaster	Plaster	Brick 125 mm
			Brick 125 mm	Brick 125 mm	Air gap 10 mm
			Air gap 10 mm	Air gap 10 mm	Brick 100 mm
			Brick 100 mm	Brick 100 mm	Stone wool 25 mm
Inner layers	Plasterboard	Plasterboard	Plasterboard	Plasterboard	Plasterboard
	Plaster	Plaster	Plaster	Plaster	Plaster

Across the entire stock, primary school classroom models were auto-generated for each individual set of classification of geographical region, era and modification status across England using the EPPY 0.5.56 scripting package (EPPY 2021) in Python 3.9.2 programming language (Python 2021). After excluding 19 combinations that had no schools allocated to them in the PDSP database, 111 EnergyPlus models were constructed in total. As part of pre-processing, 6 mm thickness single-glazed windows were auto-generated on each external surface in each model with the following characteristics:

• Window sill at 1.05 m above the floor, 1.4 m in height for <30% WWR, 2 m for ≥30% WWR.
• Width calculated for each archetype to maintain symmetry of the window on the surface while achieving the WWR defined for each category.

EnergyPlus requires the user to specify a terrain type, which can be ‘city’, ‘suburbs’ or ‘country’, although a suitable means of defining this for each school included in the PDSP has not yet been identified. Table S2 in the supplemental data online lists the variables used to adjust wind speed measured at a weather station for different terrain types, based on model terrain type. Since the definition of terrain affects airflow and therefore natural ventilation, each of the three options was included in the analysis, as described in Section 2.1.

2.3.3. Air-flow modelling

The following pollutant sources were simulated in this study:

• Internal transfer of NO₂ and PM_2.5 contaminants in the classroom from external sources.
• Concentrations of CO₂ in the classroom from internal and external sources.

To facilitate this, the following systems were modelled within EnergyPlus:

• Ventilation was modelled using the air flow network (AFN) model to allow demand-controlled window opening in response to high internal temperatures. Previously these models have been run using a fixed ventilation rate.
• Air pollutant transfer was modelled using the generic contaminant model to calculate the subsequent influx of external contaminants through ventilation and infiltration, and their removal through deposition on internal surfaces.

2.3.3.1. Ventilation modelling

While previous iterations of the UK school stock model (Schwartz et al. 2021b) have used fixed ventilation rates based on a design allowance of 8 l/s/person (Bakó-Biró et al. 2012), AFN modelling was adopted as in the housing stock model (Taylor et al. 2014) to demonstrate weather-driven ventilation behaviour in practice. An advantage of the AFN model is that wind speeds and directions from different regions are accounted for when windows are opened for ventilation, hence ventilation as well as heat gain from illumination are dependent on classroom orientation. Although double-sided, stack or more complex ventilation arrangements could also be modelled, within the scope of this research the AFN model was set up for single-sided ventilation, approximating a classroom surrounded by an access corridor opposite the external wall and adjacent classrooms on the two other sides, using the layout on the external facade shown in Figure 3.

Figure 3 

Description of the external facade.

Table S4 in the supplemental data online describes the ventilation parameters for window openings and trickle vents at 3.3–3.4 m, and the infiltration system represented by cracks at 0–0.1 m, and 3.4–3.5 m height. EnergyPlus calculates airflows using these parameters coupled with the internal pressure based on wind velocity, v_z at height z, dependent on the orientation of the classroom and wind direction. Infiltration surfaces were placed at the top and bottom of the external surface to model airflow based on differences in wind pressure at different heights rather than assume a single height. Although trickle vents are mostly features of modern school buildings, they were included in the base case as well. Setting air permeability at 9 m³/h/m² @ 50 Pa indicative of a ‘typical school’ (ATTMA 2010) is a key base-case assumption that has been updated in the retrofit cases to improve airtightness. Methods employed in previous work on residential buildings (Taylor et al. 2014) were followed with respect to inputs of flow coefficients and leakage areas, with the discharge coefficient of the window of 0.5 and opening schedules as the key parameters, which are adjusted for the IEQ mitigation scenario in Section 2.5.

2.3.3.2. Air pollutant modelling within EnergyPlus

The role of the EnergyPlus generic contaminant model, previously verified against a CONTAM model (Taylor et al. 2014), was to model internal air temperatures, CO₂ concentration levels and indoor/outdoor (I/O) ratios of NO₂ and PM_2.5 contaminants at hourly intervals based on internal loads and ventilation for an entire year.

External CO₂ concentration was set at 415 ppm, based on 2021 atmospheric measurements (NASA 2021), static over the 2020s, 2050s and 2080s climate scenarios, while recognising that this figure is increasing to different extents under different climate scenarios. As detailed in Table S3 in the supplemental data online, occupants provide an internal source of CO₂, based upon a density of 0.55 children/m² (Communities and Local Government 2013), metabolic rate per child of 110 W (representing 80% of the 145 W attributed to secondary age children in a classroom environment; Communities and Local Government 2013) and CO₂ generation rate of 3.82/e⁸ m³/s/W (Schwartz et al. 2021b).

There were no assumed internal sources of NO₂ and PM_2.5, which is a necessary stock modelling oversimplification, since it is unknown if there are catering activities adjacent to or carpets installed within the classrooms. In addition, external concentrations are location dependent, hence I/O ratios were exported from the model and internal concentrations were calculated in the post-processing of EnergyPlus outputs described in Section 2.3.3.3.

Within EnergyPlus, external contaminants are modelled using experimental deposition rates of 0.87/h (Emmerich & Persily 1996) and 0.19/h (Long et al. 2001) for NO₂ and PM_2.5, respectively, applied to each available surface comprising the building envelope to give a deposition velocity. A penetration factor of 80% was then applied for PM_2.5 contaminants from October to April inclusive in post-processing to account for the building fabric, potentially filtering out one-fifth of particles because they infiltrate the classroom in the absence of ventilation. The significant degree of uncertainty of these values due to the need to estimate values empirically is acknowledged. The I/O ratio (C_in/C_out) of both NO₂ and PM_2.5 contaminants is calculated based on inputted deposition velocity, k, penetration factor, P, and air exchange rate, a (/h) (Long et al. 2001):

$\frac{C_{\text{in}}}{C_{\text{out}}}=\frac{Pa}{a+k}$

M1 \documentclass[10pt]{article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ \frac{{{C_{{\rm{in}}}}}}{{{C_{{\rm{out}}}}}} = \frac{{Pa}}{{a + k}} \] \end{document}

2.3.3.3. Processing of EnergyPlus outputs

A Python script was used to process time-series output from the EnergyPlus classroom stock model to allow the relative comparison of different typologies and geographical location through the following metrics:

• Prediction of overheating: the most recent criteria available for overheating in UK schools comes from BB101 (ESFA 2018), following on from CIBSE Guide A (CIBSE 2015). Hence, three overheating metrics, detailed in Section 2 in the supplemental data online, were defined for each model based on total hours and degree of exceedance (rounded) derived from hourly internal temperature and daily external dry bulb temperatures during occupied hours. For clarity, the first metric (number of hours exceeding the threshold temperature based on a weighted average of daily external temperatures) was used in the plots in Section 3.
• Reduction in heating demand: the benchmarking of measured fossil fuel energy demand of individual schools (CIBSE 2008) has been an annual requirement for most English school buildings through the DEC scheme. In the classroom models it was assumed that all heating comes from fossil fuels and the energy intensity (kWh/m²) was calculated for each classroom by normalising annual space heating demand in kWh by the available floorspace of 52 m². It is important to note that since such modelling necessarily omits the heating of hot water and other uses of fossil fuels, the calculated values cannot be compared against total benchmark energy consumption values from other databases.
• Prediction of indoor contaminant concentrations: the World Health Organisation (WHO) has recently updated its recommended annual targets for exposure to NO₂ and PM_2.5 (WHO 2021) from 2005 figures (WHO 2005) to:
  • 10 μg/m³ annual mean for exposure to NO₂ (down from 40 μg/m³); and
  • 5 μg/m³ annual mean for exposure to PM_2.5 (down from 10 μg/m³).
• CO₂ concentration guidelines were derived from BB101 (ESFA 2018), which suggests high, normal and acceptable moderate levels of 1765, 1215 and 965 ppm internal CO₂ given an outdoor concentration of 415 ppm, maintained for all three climate scenarios.

Indoor concentrations of CO₂ (ppm) and I/O ratios of NO₂ and PM_2.5 were averaged over an entire year at hourly intervals during occupied periods. To convert NO₂ and PM_2.5 into indoor concentrations (μg/m³), annual figures of NO₂ and monthly figures of PM_2.5 concentration were previously extrapolated for the London, West Pennines and Portsmouth regions (Schwartz et al. 2021b), as shown in Table S5 in the supplemental data online. These figures were also used in this study, with the Portsmouth figures used as an analogue for East Anglia in terms of being a similar region with an urban/rural setting. Converse to external CO₂, it is expected that the external contaminants will decrease in future 2050s and 2080s scenarios (WHO 2021). However, since this has not been quantified, the current contaminant levels were maintained for the future scenarios.

2.4 Creation of an energy efficiency retrofit scenario

The ClimaCare study on overheating prevention in care homes (Oikonomou et al. 2020) presented a combination of ‘hard’ and ‘soft’ strategies, defined in the study as structural alterations to the fabric and non-structural occupant behavioural measures, respectively. Climate resilience can encompass both substantial upgrades in the building fabric and services covered in this section as well as adaptive capacity through options available to occupants to maintain reasonable IEQ covered in the following section. A retrofit scenario combining three separate potential improvements to the building envelope is presented in Table 3, which supplements the base-case scenario described in Sections 2.2 and 2.3.

The positioning of the additional insulation for the wall insulation measure has an impact on the thermal mass and hence the thermal capacitance and heating requirements of the classroom. In this case, the insulation was placed on the outside of the building to minimise the additional heating load required and to prevent overheating due to the decoupling of the wall thermal mass with the interior.

2.5 Creation of an IEQ behavioural measures scenario

As described in the previous section, both base and retrofit cases were additionally simulated for ‘soft’ behavioural measures, such as night-time cooling, which could be provided in a complementary fashion to more intensive changes in fabric to improve IEQ. Table 4 contains details of the ‘soft’ overheating mitigation measures applied to both base and retrofit cases to create four different combinations for the three metrics of overheating, contaminant concentration and heating demand.

2.6 Climate scenarios

Test Reference Year (TRY) and Design Summer Year (DSY) annual weather data files (CIBSE 2009), representing typical weather conditions and warmer conditions for the purposes of overheating assessment calculations, respectively, were updated by CIBSE (2016) for both current and future climates. These include high, medium and low ranges (10th, 50th and 90th percentile scenarios) of climate change prediction for the 2020s, 2050s and 2080s (CIBSE 2016) based on the UK’s Climate Projections from 2009 (UKCP09) (The Met Office 2009). For the initial analysis of impact of typology and location on overheating and indoor CO₂ across the entire stock, the unaltered current TRY files were used to represent a typical year. However, for the determination of resilience to future scenarios, hybrid weather files were created combining the following:

• From 1 October to 30 April, the 50th percentile TRY for 2020s high and 2050s and 2080s medium climate change scenarios representing a typical heating season.
• For 1 May to 30 September, the 50th percentile DSY1 for 2020s high and 2050s and 2080s medium climate change scenarios representing a ‘moderately warm summer’ (CIBSE 2016).

2.7 Model validation

Energy data generated by the DREAMS building stock were validated against DEC data (Schwartz et al. 2021a) and showed agreement within 4–12% by construction era. IAQ predictions for classroom models were also validated (Schwartz et al. 2021b), falling within the range of PM_2.5 (5.2–11.4 μg/m³) and on the high side of NO₂ (7.3–23.3 μg/m³) of internal concentrations provided by residential models (Taylor et al. 2014). The addition of AFN modelling to these fixed ventilation models offers similar ranges for the three separate contaminants, although slightly more dispersed due to the additional simulation of scenarios (see Table S6 in the supplemental data online for more details). For overheating prediction, the use of BB101 with hybrid DSY/TRY weather files prevents a direct comparison with previous uses of the DREAMS stock modelling, which used CIBSE (2015).

Further validation is possible by comparing the ventilation rates and internal temperatures predicted by modelling with monitored data and recommended rates. Figure 4 shows the modelled ventilation rates and internal temperatures for all four scenarios simulated of a west-facing London classroom run with the 2020s hybrid weather file, for the warmest week with respect to overheating-hours. The two scenarios containing the IEQ overheating mitigation use night ventilation, available overnight during weekdays, to reduce temperatures to the threshold of 22°C given in Table S4 in the supplemental data online.

The peak temperature experienced for the base case while occupied of 30–33°C is consistent with measured peak temperatures of 30°C previously measured in Western European classrooms from the Schools Indoor Pollution and Health Observatory Network in Europe (SINPHONIE) (Csobod et al. 2014). The natural ventilation rate of 15–20 l/s/person while occupied represents a high calculated airflow when compared with recommendations of 8–9 l/s/person for maintaining internal CO₂ around 1000 ppm (ESFA 2018) and measured rates of 13.33 l/s/person (Csobod et al. 2014). However, it is consistent with evidence that ventilation rates up to 15 l/s/person could be beneficial due to incremental improvements in attainment (Chatzidiakou et al. 2014).

3.1 Analysis of the modelling approach and impact of typology across the entire school building stock

3.1.1 Database analysis

Figure 5 shows the number of primary schools for each category within each geographical region by typology. Fewer than 3% of primary schools have mechanical ventilation (omitted from the modelling study), even within post-1976 primary schools, where it is slightly more prevalent. A total of 83% of schools contain multiple-age buildings, highlighting the complexity of assuming a building fabric based on construction era, with London, Midlands (Birmingham) and West Pennines (Manchester) containing, by far, the largest concentrations of all eras of schools. In terms of trends between construction era and geographical regions, there are above-average proportions of East Anglian schools, which are post-1976 buildings (30%) compared with all other geographical regions (18%), with pre-1919 London schools (22%) and 1967–76 Midlands schools (28%) also reasonably prevalent.

Figure 5 

Number of primary schools in each geographical region for various categories.

Note: Green shading denotes number of schools within each archetype category.

3.1.2 Definition of terrain

The relationship between orientation and CO₂ and overheating was examined by clustering points of the same orientation indicated by shaded zones in Figure 6, which includes all three terrain types. The widest contrast is between south-facing orientations, experiencing the greatest range of overheating due to direct sunlight but the lowest CO₂ concentration due to increased ventilation and north-facing orientations, with a wider range of CO₂ concentration, but markedly cooler conditions. However, there is some reasonably visible overlapping west and east clustering of points between both these groups.

Figure 6 

Cross-plot of average indoor CO₂ concentration versus overheating-hours for different terrains and orientations across all region and era archetypes.

Figure 6 also contains a single indicative line plot of overheating CO₂ concentration results for each orientation, using the same archetype, but spanning the three different terrains. In all cases, the city sites experience greater overheating but lower CO₂ than the suburbs site and then countryside site, respectively, due to a larger reduction to the windspeed incident on the external surface. However, the impact of terrain on overheating varies significantly between each trend line, as indicated by the slope, possibly since overheating-hours are determined by exceeding thresholds, with terrain having a higher impact on overheating closer to the acceptable limit of 40 h. In the case of the east example, lack of data of the school’s surroundings introduces an uncertainty range of 32–39 h, which for warmer future climates could be the difference between passing or failing the BB101 overheating criteria.

3.1.3 Comparison of geographical location/era archetypes

Figures 7 and 8 demonstrate the variation across geographical regions and archetypes for average indoor CO₂ concentration and overheating-hours, respectively, for west-facing classrooms in suburban terrain. The following trends can be observed:

• Geographical: south-eastern locations appear more susceptible to higher degrees of overheating throughout the year. Northern locations tend to have higher average CO₂ concentrations, possibly as a result of less hours when the window opening setpoint of 22°C.
• Construction eras: overheating is considerably more prevalent for the post-1976 archetype than for other eras, indicating the potential for conflict between the need to better insulate classrooms to reduce heating demand, and overheating prevention.

Figure 7 

Indoor CO₂ concentration for west-facing suburban classrooms.

Figure 8 

Overheating-hours for west-facing suburban classrooms.

3.2 Analysis of overheating, heating demand and IEQ for three examples

3.2.1 Effect of individual retrofit and IEQ measures

Figure 9 demonstrates, for example A (London pre-1919) under the current climate, the incremental effect of changes to the base case to create the retrofit scenario and then includes overheating mitigation across the five performance metrics. Not one individual change has wholly positive or negative effects across the range of metrics, indicating that changes in internal temperatures through altering insulative properties can have a complex relationship with IEQ practices through ventilation and heating constraints. For example, adding external wall insulation (and decreasing air permeability) in the model requires window-opening throughout the year to reduce overheating, lowering average indoor CO₂ but increasing ingress of external contaminant of PM_2.5 and NO₂ slightly, and reducing the benefit of greater energy efficiency on lower heating demand. This result is indicative of a need to optimise opening size and heating load to prevent heating overshoot when applying ventilation and space heating in models balancing IEQ and energy efficiency.

Figure 9 

Change in heating demand, overheating and contaminant concentration for incremental retrofit and indoor environmental quality (IEQ) measures.

3.2.2 Performance of three examples under different scenarios

Figure 10 summarises each scenario run on each case by averaging the results over all four orientations. Table S7 in the supplemental data online is an expanded version showing orientations with the minimum and maximum for each metric. Figure 10 demonstrates that no single case performs entirely satisfactorily under all five metrics, as indicated by colour coding, requiring a trade-off, for example:

• Scenarios without retrofit or IEQ mitigation, particularly in London and East Anglia, demonstrate significant overheating issues, exceeding the BB101 target of 40 h for the 2020s, 2050s and 2080s by increasing extents, for all but 2020s north orientations.
• Shading and insulation measures reduce the number of overheating-hours, while still breaching the target of 40 h for the 2050s and 2080s scenarios and non-north orientations. Additionally, elevated internal concentrations of PM_2.5 and NO₂ arise through increased demand for ventilation due to improved airtightness of the fabric, although these are very small and are within the error margins of the external data in Table S5 in the supplemental data online. However, naturally ventilated classrooms will increasingly become constrained in addressing overheating due to the tightening of WHO targets as external climate warms, unless I/O ratios are reduced by other means or reduction of ambient air pollution is achieved. For example, wider adoption of electric vehicles, leading to a reduction in NO₂.
• Where IEQ mitigation measures were added, overheating-hours were reduced below the 40 h threshold for most orientations, even for the Midlands and East Anglia 2080s scenario. However, there is a large subsequent increase in heating demand of around 60–120% depending on if retrofitting has also been applied.
• Geographically, the more northernly Midlands school experiences greater issues with CO₂, exceeding BB101 guidelines, which could be improved by IEQ measures, again with the penalty of increasing heating demand.
• While the vulnerability of north-facing classrooms to high CO₂ concentrations and south-facing to higher NO₂ and PM_2.5 is again seen respectively, there is no discernible annual trend between orientation and high and low heating demand and overheating.

Figure 10 

Summary of annual overheating hours, heating use and average contaminant concentration for three cases under various retrofit and climate scenarios, averaged over four orientations.

Note: IEQ = indoor environmental quality.

4.1 Policy implications of findings

The differing degrees of conflict between simultaneously meeting space heating demand reduction measures, indoor overheating risk mitigation and IAQ targets have been demonstrated for three separate cases in Figure 10. Overheating above the BB101 threshold of 40 h in the current school stock can be reduced through a range of retrofit and overheating mitigation strategies to a certain extent.

In terms of the practicality of the measures suggested, while cost-effectiveness is outside the scope of this research, it is clear that night ventilation for overheating mitigation and overhangs for windows in retrofitting represent examples of lower cost measures alongside more intensive fabric insulation and fenestration upgrades. This study has shown both to be somewhat effective at lowering the hours of overheating, if practical barriers to implementing this, such as security concerns, can be overcome. However, to reduce overheating below 40 h without exceeding WHO-recommended guidelines thresholds of NO₂ and PM_2.5 will not be possible for any of the climate scenarios modelled. Hence either a significant improvement in external NO₂ and PM_2.5 concentrations through the successful implementation of Clean Air policies and strategies is required, or the widespread use of mechanical ventilation to reduce internal temperatures (Jenkins et al. 2009) or the use of air purifiers (WHO 2021).

Current school ventilation guidance (ESFA 2018) acknowledges that schools ‘in London […] and polluted areas’ will be required to minimise the ingress of external air and employ mechanical ventilation, although this is not a specific requirement for retrofitted school buildings within the building regulations (HM Government 2013). However, this research indicates without further intervention that a large number of schools throughout England, including the rural and semi-rural locations given in Table 5, will fail to meet the updated WHO guidelines both now and in the future.

More generally, it is important to note that building stock models are not designed to model a single variable in isolation. This study illustrates that a focus on a single goal such as space heating demand reduction through building fabric improvement may miss important implications for IEQ. It may be necessary to revise such models, used in regulatory energy benchmarking calculations through TM46 (CIBSE 2008), to account for whether overheating and air quality targets are met with the recorded regime of energy use.

4.2 Model uncertainty, limitations and future work

An inherent risk of stock modelling is failing to appreciate the narrow margins of internal temperature predictions and I/O ratios within modelling error between meeting or failing overheating and air quality targets, respectively. This is present due to the necessary approximation of features such as glazing and building service operation within archetypes. Since the key output of the stock model is the success or failure of meeting these targets, rather than the raw model data themselves, uncertainties in internal temperature prediction and the effect of ventilation could be amplified when internal temperature approaches the threshold.

In terms of the point of onset of overheating, Figure 4 demonstrates that due to night-time ventilation, the internal temperature of the classroom is 3–4°C lower at the start of the school day (indicated by shading) for IEQ mitigation scenarios. This leads to temperatures that are around 1–2°C lower later in the day, delaying the predicted onset of overheating, as defined by BB101. These cumulative small differences in the onset of overheating lead to a 23% reduction in annual hours of overheating, from 103 to 79 h, and a further 80% reduction to 16 h once retrofitting and IEQ mitigation are added, respectively. The same reasoning applies, given the closeness of revised WHO guidelines to external contaminant levels (see Table S5 in the supplemental data online). Uncertainties in I/O ratio become amplified as internal concentrations approach the target. Hence, the rate of heating dictated by internal gains from humans and equipment is also critical to this prediction, since the rate of heating dictates the rate of temperature increase and requirement for ventilation throughout the day.

AFN modelling, while providing a beneficial linkage of hours of overheating to weather-driven ventilation, dependent on internal and external pressure and temperature differences rather than assumed ventilation, adds additional model uncertainty in the use of a discharge coefficient, adjusted for the IEQ mitigation scenarios. While this could be adjusted for different window types and geometries in the future, this assumption of ventilation performance means that such models will require validation against monitored ventilation data.

There is ample scope to improve the data available on critical elements of the system, within the novel methodology of combining previous work on school stock modelling with airflow network modelling and scenario modelling. In terms of archetypes, greater disaggregation of the post-1976 archetype into smaller groupings such as low carbon schools should be possible based on the next iteration of the PDSP, the CDC (ESFA 2017), providing more detail on construction types, including air permeability. It is also acknowledged that school classrooms are not uniform geometrically, and this should be adapted into future archetypes as for variations in floor area/occupant density which could be critical determinants of overheating and CO₂, and hence heating demand and PM_2.5 and NO₂ concentrations.

Hence, significant improvements can be made to this methodology in the next decade with the increasing availability of data through future iterations of the PDSP on additional items such as terrain, demonstrated to be an important consideration in Figure 6, and classroom geometry, as well as improving existing items such as investigating the variance of WWR across the stock, as well as the mean.

A key data availability limitation is the granularity of weather and PM_2.5 and NO₂ concentration data across the UK, making it impossible to correct the performance of the AFN for local weather effects. Lack of model calibration means that models cannot yet be considered predictive of IEQ; however, increased CO₂ and internal temperature monitoring in classrooms could allow these models to be corrected for local conditions.

The next step of this study involves a survey of a wide range of school building professionals to determine the most appropriate use of performance metrics, including the possibility of modelling additional air contaminants. Optimisation of specific details such as window-opening sizes and schedules will be required to meet overheating requirements while minimising the ingress of pollutants and heating energy demand. Additional measures not investigated here, such as internal heat management, thermal mass and increased albedo, may also be useful tools in preventing overheating without resorting to air-conditioning methods; testing these additional scenarios forms part of ongoing work.