A Generalisable Bottom-up Methodology for Deriving a Residential Stock Model From Large Empirical Databases

Average reference dwellings representing a predominant housing typology are defined in this work. Specifying such reference buildings is a prerequisite for (i) calculating cost-optimal energy performance requirements for buildings and building elements and (ii) ensuring valid calculations of national building energy consumption. In the EU, an Energy Performance Certificate (EPC) rating is an assessment of the energy consumption of a dwelling. The use of inappropriate default-values for the building envelope thermal transmittance coefficients (U-values) and standardised thermal bridging transmittance coefficients (Y-values) in the production of EPCs leads to an over-estimation of potential energy savings from interventions in the existing dwelling stock. A methodology is presented for the derivation of simplified default-free inputs to a bottom-up residential cost-optimality energy consumption model from an EPC dataset. 35 reference dwellings (RDs) are employed to appropriately characterise 406,918 dwellings. Use of these RDs enable quantification of (i) the energy saving potential of a predominant housing typology, (ii) the effect of default U-value and standardised Y-value use on the prebound effect in dwellings (iii) overall national building energy consumption.

Thanks -we have changed the text to read as follows and introduced a new reference (see Page 9) i) 70% of Irish detached dwellings were constructed before the mid 1970's when wide adoption building thermal regulations prompted by the first oil crisis in 1973 required increased levels of thermal insulation 1 [30,35,[70][71][72][73].
We have also included a new reference for this - [70]  Footnote added to explain construction period…see Page 13 and as below; To ascertain whether the segmented sample population (N s ) of 50,236 detached is representative of the entire population (N p ) of 406,910, the margin of error at a 99 % confidence level (z-score 2.58) for each construction period 2 was calculated using Equation (1) with results shown in Table 1 f) Page 15: Can the default U-value selection be biased in some way?
It is a deterministic value rather than a measured value, so the simple answer is no g) Page 16: You show a U-value distribution by number of buildings, but it will be more interesting to see the same distribution distributed on construction areas instead. Is that information available in the Irish EPC, and if so, why did you not use it for a more valid description of the thermo-physical properties of the RBs?
This figure is used to demonstrate the systematic default effect/error only. It is shown to demonstrate that the default U-value does not form part of the frequency distribution so is therefore a statistical outlier h) Table 4: Is it only faulty e.g. walls and roofs that are removed from the dataset (Ahern [87]), or the whole building that contained the faults? Section 2.1 was slightly revised to make this clearer -See Page 15 (and below text) As more retrofit interventions are carried out in the housing sector, current base-default U-values become less relevant to the real statistical distribution over time especially with respect to Mode 1 dwellings [35,81]. The use of outmoded default U-Values to necessarily maintain the costeffectiveness of EPC decreases the accuracy and hence credibility of both the EPC and the EPC database [35]. Unlike walls and roofs, dwelling floor U-values have a normal distribution as there are fewer retrofits of floors due to the high replacement cost of floor coverings [91] together with the impracticality of retrofitting floor insulation. To eliminate the systemic error associated with outmoded base-thermal-default values [35] so data better meets accuracy, coherency, compatibly and clarity requirements; it is thus appropriate to remove default wall and roof U-values from the database [97].
If not removing the whole building, it might disturb the whole picture of the analysed buildings. Please elaborate on this issue! See Page 12 -"Based on the statistical analysis of a large building sample the "Synthetical Average Building" (SyAv) approach identifies an "archetype" defined as "a statistical composite of the features found within a category of buildings in the stock" [83]. The archetype is a notional building characterised by a set of properties detected statistically in a category of buildings [23,29,[84][85][86]." Therefore it is not necessary to remove the entire dwelling as other ideally non-default information recorded in the dwelling is relevant for characterizing other elements i) Table 5 is not referenced in the text.
Apologies this was a typo - Table 5 correctly referenced on Page 18 j) Page 21: Miss information on how you patch the unreliable data in the database with "other available data and expert enquiries" Table 16 added to limitations of the study -Page 54 k) Table 8: the distribution losses in this table seems very low compared to the same losses in table 7please check.
Yes this is a fair point the following text has been added -see Page 30 Building energy assessors measure the roof 'at the thermal envelope' where the insulation is located. As shown in Figure 8 (a), a typical single storey Irish house with a pitched roof has insulation laid between (and possibly above) the ceiling joists, resulting in a flat 'roof' on the reference dwelling [179]. Figure 8 (b) and (c) depict two-storey dwellings. Figure 8 (c) depicts a single-storey dwelling where the attic is converted into a habitable space, recorded in DEAP as a separate storey. In two-storey dwellings and referring to Table 10, the roof area is larger than the floor area suggesting that the typical location of roof insulation in this dwelling type is in the rafters of the roof. The data relating to roofs in Table  10 behaves rationally and correlates with ground floor areas. To facilitate better the characterisation of the RD, it is recommended that two-storey dwellings be classified by type (1) or (2) in the EPC database.

Figure 8 (a, b & c) Typical location of insulation in single and two-storey case study dwellings
p) Table 11: Values are probably only valid for the heating season -especially in high latitudes, which includes Ireland. This is ok for the current study, but not for a study on the summer comfort. if correct, make a note about this to avoid misuse of the information in the future.
We take your point on summer/winter seasons differing. Text added to make this clearer -is the note still required? q) Figures 9 and 10: Not easy to grasp the idea. Consider other alternatives. Explanation of approach detailed in Figure 11 It is not easy to represent this data visually -a lot of alternatives were tried but this is the best way. This graph presents proportion of retrofitted dwellings and non retrofitted dwelling proportional along with the U-values of the building envelope components. r) Tables 12 and 13: radar diagrams are difficult to read due to size and quality, and contains little information. They tells the same story -that windows are the source for the highest heat loss in all models. Consider other colouring for the numbers in the tables.
A better quality image will be submitted separately with the paper -this was inserted into text as a jpg for coherency. It doesn't stay formatted on conversion to pdf. The following text has been added -see Page 38 The radial graphs elucidate the relative weighting of the RDs thermal characteristics resulting in a unique shape for each classification. There is notable difference in the profile of pre and post thermal regulation dwellings with thermally poor dwellings displaying a 'short and fat' diamond shape and well insulated dwellings exhibiting a 'long and thin' triangular shape. The graphs visualise opportunities for targeted policies for each RD by quantity. s) Table 14: What is the unit for "Occupancy".
Unit for occupancy is people, derived from the census. t) Air permeability seems VERY high, equal to approx. 10 air changes per hour -is that measures or estimated, and is it correct?
The values are measured values. Air permeability is discussed Section 3.2 -see Figure 17 -Applying q 50 /20 rule of thumb Ac/hr averages 0.35 ac/hr to 0.4 ac/hr. The EPBD reporting mechanism requires air tightness reported as air permeability (m 2 /(h.m 2 )) so this is how it is reported in this work u) Ψ Linear thermal transmittance coefficient (W/K) z-score Dimensionless quantity indicating how many standard deviations (σ) a random variable (x) is from the mean (µ)

Policy Context
Households consume 27% of end-use energy in the EU 28 [1]. The extent and duration of the dominance of the thermal characteristics of pre-existing houses depends on the construction rate, floor areas and specifications of new dwellings [2]. As average replacement rates for existing housing stocks in the EU are less than 0.1% [3], the majority of Europe's existing dwellings will remain in place in 2050 [4]. In the United Kingdom, for example, around 75% of dwellings that will exist in 2050 have already been constructed [5]. Accordingly, achieving less overall energy use requires energy refurbishment of existing dwellings [2,[6][7][8][9]; but as suboptimal or partial refurbishments can render future energy performance improvements more difficult or expensive [10], understanding existing dwellings stocks is a prerequisite before making energy efficiency, policy or market interventions. However, there are few large-scale building monitoring projects [11][12][13], in the small samples of buildings studied [9,11], evidence of patterns in energy demand in buildings by population and stock segmentations are limited [9,11,12,14,15], with little common [9,16], transparent or prescribed data reported [9,11,12]. This absence of robust data inhibits the effectiveness of policy frameworks [11,17,18]. Evidence-based policies are a prerequisite to achieving targets for reduced building energy demand [11][12][13][14][19][20][21][22].
The calculation of the total energy consumption of a dwelling stock combines stock and energy models [10]. A stock model describes the stock's size, composition and renovation status, whereas an energy model describes the average energy intensities of the various stock segments and assumed energy savings from renovation [10]. A paucity of observed data, together with a lack of documented transparency around energy performance model inputs have hindered agreement on the validity of building stock energy consumption models [11,12,14,19]. P a g e | 6 The development and use of dwelling stocks energy consumption models [12,23] is now driven by policies [24] to; a) reduce domestic energy use, b) lower greenhouse gas emissions, c) reduce dependence on imported fuels, d) reduce the cost of energy, and e) alleviate fuel poverty.

Energy analysis of a building stock
The average change in energy intensity of a total dwelling stock changes [28] over time due to different construction techniques and materials [29], material and labour costs [30], architectural forms [29], heating systems [31], occupant comfort expectations [29], occupant behaviour [32], patterns of use of space within dwellings [33], appliance use [34], economic drivers [30], regulations [29], and the scope and prevalence of refurbishments [35]. Multicollinearity between these factors complicate isolating each of the influences on dwelling energy consumption [36,37] with one study finding half the variability in energy consumption to be unexplainable [36]. The interaction of thermophysics of a building with its local climate [32,36,38] and occupant behaviour [32] underlie energy consumption with heat energy consumption often dominated by building fabric characteristics [11,[39][40][41][42][43]. For similar buildings, heating system efficiencies, primary fuel types and heat sources cause large differences in energy consumption [44,45] and carbon emissions [46]. Understanding residential energy consumption drivers thus requires disaggregated thermophysical characteristics [28,36].
Modelling residential energy consumption can be; a) Top-down; where historic cumulative energy assessments are regressed, as a function of national energy statistics, gross domestic product, population and climate, to determine dwelling stock energy consumption. As this approach cannot distinguish energy consumptions of individual end-uses it is unable to predict the effect of specific interventions. To do this, bottom-up models are required [43,[47][48][49]. P a g e | 7 b) Bottom-up models estimate energy consumption of a representative set of individual houses which are extrapolated to determine regional and national relationships between dwelling characteristics and energy use [43,50]. Bottom-up approaches are referred to as "statistical", "engineering" or a hybrid of both [51]. "Statistical" approaches use historical data to correlate relationships between energy end-uses and total energy demand. "Engineering" approaches, determine end-use energy based on building geometry and thermophysical relationships. As bottom-up engineering models address explicitly the effect of occupant behaviour and passive solar gains, they thus can assess the effect of thermal retrofit measures on residential housing stock energy consumption [15,43,48,49,51].
EPBD energy refurbishments are assessed against cost-optimal criterion to [2,52]; i) ensure coherent and well-planned refurbishment standards that avoid low-cost but suboptimal improvements, and ii) invest in interventions that will recoup their life-cycle costs.
As shown in Figure 1, a building stock is more accurately reported by a larger number of RBs [54], so the effectiveness of RBs depends on the; i) number of building subcategories employed [62], ii) level of detail in defining each RB [56], P a g e | 8 iii) validity of information used to characterise each RB [56,60,63], iv) selection of default data [35,53,63,64]. Certificates" (EPCs), be issued for buildings constructed, sold or leased in the EU [65,66].
EPC's provide empirical national dwelling stock information that can inform characterisation of contemporaneous RBs [35,67].
Single-family dwellings constitute 49.4% of the total building floor area in the EU [68] while households consume 27% of end-use energy in the EU 28 [1]. 34% of the EU 28 population lived in detached single-family houses in 2013 [35]. More generally, energy efficiency retrofits remain important as 67% of European housing was built prior to 1980 [69], before the introduction of thermal building regulations for the housing sector.
ii) Ireland has the highest proportion, circa 90%, of single-family dwellings in Europe.
Though as shown in Figure 3, the UK, Greece, Norway and the Netherlands have similar profiles [35].
iii) Detached dwellings have relatively high surface area to volume ratios so generally exhibit larger heat losses than semi-detached or terraced houses of the same construction [53], with higher cost of heating to a given comfort level [74]. Detached dwellings are therefore targeted in energy-efficiency retrofit programmes [59,75,76].
iv) At 149m 2 , the mean-weighted-average heated floor area 2 of an Irish detached dwelling is approximately twice the average European floor area [69].
v) Detached dwellings in Ireland have a stronger association with fuel poverty than other dwelling types due to; a) a higher cost of heating them to a given comfort level [74], b) being classified as 'hard to treat 3 '' [77] and, c) having a higher proportion (88%) of middle-aged (50 -64 year olds) and older adults (aged 75 and over) compared to those living in and around Dublin (16%) or other towns or cities (38%) [76]. Older adults [76]; To ensure realistic RDs are created, data is assessed at each stage, for consistency before proceeding to the next stage [82].
There are three approaches [55] to defining reference buildings that are representative of climatic area, construction age and building size: 1. In the "Real Example Building" (ReEx) approach, a building type is selected by a panel of experts as the most representative of specific building size by construction period and climate location. This approach is applied when statistical data is unavailable.
2. The "Real Average Building" (ReAv) approach identifies a representative building type through statistical analysis of a large building sample to find a real building mirroring the characteristics exemplifying mean geometrical and construction features of buildings in the statistical sample.
3. Based on the statistical analysis of a large building sample the "Synthetical Average Building" (SyAv) approach identifies an "archetype" defined as "a statistical composite of the features found within a category of buildings in the stock" [83]. The archetype is a notional building characterised by a set of properties detected statistically in a category of buildings [23,29,[84][85][86]. P a g e | 12 The third approach is adopted in this work. A large, empirical and contemporaneous sample EPC dataset is used to create SyAv reference dwellings representative of a dwelling typology at stock level.

Segmentation
EPCs are generated in Ireland through a methodology embodied in the national Dwelling  [72,88]. 97% of detached dwelling are either single or two-storey, 98% are naturally ventilated [88].
As shown in Figure 2, rural, single and two-storey, oil centrally-heated and naturally-ventilated dwellings are the predominant dwelling type in Ireland accounting for 18% of the national dwelling stock and 63% of all detached dwellings. Dwellings with these characteristics were isolated from the larger dataset. To avoid inconsistencies, dwellings carrying a 'provisional' certificate were removed from the dataset. As shown in Table 1, this gave a sample of 50,236 dwellings, representing 12.35% of the detached dwelling typology nationally. The margin of error of a sample dataset (N s ) of a given population (N p ) is given by Equation (1) [89]; "Acceptable" margins of error fall between 4% and 8% at a 95% confidence interval [90]. To ascertain whether the segmented sample population (N s ) of 50,236 detached is representative P a g e | 13 of the entire population (N p ) of 406,910, the margin of error at a 99% confidence level (z-score 2.58) for each construction period 6 was calculated using Equation (1) with results shown in Table 1 for standard deviation (σ) of 0.5 (50%). Because older dwellings change ownership less often there are fewer EPCs for older dwellings than newer dwellings. Older dwellings are thus somewhat less represented in Table 1 than newer dwellings. Notwithstanding, in all cases, Table 1 shows acceptable margins of error indicating a statistically representative sample while the sample number and proportion of detached dwellings in the empirical dataset is coherent with the actual number and proportion of detached dwellings nationally, so verifying intradataset consistency.

Analysis of microscopic data within EPC Dataset
Extracted from the Irish national EPC dataset [88], Figure 4 illustrates a typical U-value frequency distribution for dwelling walls and roofs by construction period revealing the thermal characteristics of Ireland's walls and roofs to be bi-modally distributed. Referring to  'Mode 1' dwellings are thermally-upgraded building elements with lower U-value ranging between 0.1 to 0.59W/m 2 K.
As more thermal retrofits are carried out more building elements U-values will fall within Mode 2 than Mode 1.The standard deviation 7 for Mode 2 is greater than that of Mode 1 demonstrating that retrofits harmonise levels of thermal insulation. Figure 4 highlights statistically anomalous spikes in the data split-across time-periods in both pre and post-regulation dwellings; in the tail of the Mode 2 empirical U-value distribution for exposed building elements such as walls and roofs. Analysis revealed that these result from default U-value selection [35,81].
Where acquiring data would be prohibitively costly, nationally applicable default U-values for the building envelope are employed [73]. Use of such worst case default U-values ensure that a poor dwelling does not attain a better energy rating than is merited [35]. In the absence of empirical data in Ireland default U-values, as in many other EU member states, are determined by the type and date of construction and then prevailing building codes as shown in Table 2 [35, 91].  [97].

Figure 4 Illustrative typical frequency distribution of wall and roof U-values [88]
P a g e | 16

Validation of EPC Dataset
An analysis of dwelling element U-value distributions by construction period is summarised in Peaks observed consistently in distributions for upgraded dwellings relate to state-funded energy refurbishment grants to homeowners available through the SEAI [100] for insulated buildings elements as shown in Table 3. Table 3 U-values required to meet state-funded thermal refurbishment grants in Ireland P a g e | 17 Data quality checks and measures taken to ensure final data quality corresponding to Eurostat validation levels ranging from 0 (lowest) to 5 (highest) summarised in Table 4 are shown in Figure 5 [97,101]. The data was checked for internal consistency within the elements of the dataset to Eurostat validation level 1, intra-datasets time-series checks via differing periods of construction found data behaved consistently to validation level 2, while also confirming requirement to remove base-thermal wall and roof default U-values [81]. Using other data together with intra-domain consistency checks confirmed the quality of the data in the refined EPC dataset to data validation level 5 [97,101].  Table 5 are based on (i) outmoded base or as-built thermal default characteristics (see Table 2), (ii) smaller sample sizes, or (iii) indeterminate data. P a g e | 19

Figure 5 Methodological and validation process flowchart [81]
Methodological Flowchart Data Validation

Overarching approach
Adapting the methodology established by Corgnati et al. [56] for office buildings in Italy to apply to existing RDs under the relevant EPBD directives [54,57], SyAv reference dwellings where characterised as shown in Figure 6. Unreliable information within the database is replaced by other available data and expert enquiries.
EPC energy performance assessment procedures generally provide all the detailed information pertaining to the building form, system and envelope as defined in Figure 6. The methodology ignores aggregated EPC data such as energy consumption in favour of establishing disaggregated thermophysical data by period of construction [29,51,55,118,119]. A study carried out in the UK using data for 12,500 gas centrally heated houses in 2009 [120], found approximately 75% of the observed variance in the energy performance rating of the home was determined by heating system efficiency, external wall U-value and dwelling geometry. The RD are thus defined initially by these factors.

Heating and Hot Water Systems
As shown in Figure 1, for Irish dwellings 63% use oil and 31% use solid-fuel. As Central Statistics Office (CSO) data on fuel-use in Ireland is more comprehensive than within the EPC database, CSO data relating to solid-fuel use was reclassified by DEAP construction period as shown in Table 6. Table 6 Table 6 Central heating fuel source by construction period [79] pre 1900 1900 -1929 1930 -1949 1950 -1966 1967 -1977 1978 -1982 1983 -1993 1994 -1999 2000 -2004  Where dwellings are heated by solid-fuel, the characteristics of solid-multi-fuel were employed.
Characteristics of oil-fired and solid-multi-fuel systems are shown in Tables 7 and 8 respectively.
Solid-fuel and oil boilers serve a radiator system [88]. Of those using solid-fuel, two-thirds use a stove and/or cooker while a third use an open-fire with a back-boiler [72]. Standardising heating and DHW system characteristics meant the dominant parameters determining dwelling energy P a g e | 23 consumption are dwelling envelope thermal characteristics, surface area, heating duration and set point temperature.

Heat loss through the building fabric
The overall heat loss comprises heat transfer through the building envelope, linear thermal bridges and air infiltration. Using a sample of RDs 'BS EN 12831:2003 Heating Systems' was used to calculate relative percentage steady-state heat losses. 80 to 90% of the overall heat loss from dwellings is by planar heat losses through the building fabric; 8 to 16% is heat loss through air infiltration through the dwelling fabric and 4 to 16% is heat loss through linear thermal bridges P a g e | 25 [81]. The length of thermal bridges have increased as dwelling size and associated window ratios become larger with the progress of time [71]. The length of its linear thermal bridges in the RDs is captured initially via the classification of a dwelling by its construction period.

Climatic Location
The International Weather for Energy Calculations (IWEC) contains "typical" hourly weather parameters for building energy simulation [122].  [126] the whole dwelling is assumed to be heated only for specific time periods with the living area heated to a 3°C higher temperature than the rest of the home during these periods [126]. BREDEM differentiates weekdays and weekend heating schedules. Table 9 details the set-point temperatures and heating durations standardised in BREDEM and DEAP. As a wide variety of heating patterns exist [59,[126][127][128], neither BREDEM and DEAP reflect the heat consumption demand and duration characteristics of dwellings in the UK and Ireland accurately [45,59,[126][127][128]. In England, an average dwelling is heated for 8.4 hours/day with that increasing to 8.7 hrs per day in the average detached dwelling [59]. In Ireland, the average rest-of-home temperature is 17 o C [127]. The average temperatures P a g e | 26 and heating duration of dwellings are generally independent of year of construction and day of the week [128]. Living room temperatures are typically lower in the mornings than in the evenings [128] with temperatures of 21 o C rarely reached [128]. SyAv heating schedules and mean temperatures for an average year are required to produce a onefits-all model of space heating energy consumption in detached dwellings. To include increased comfort temperatures, an energy consumption model should ideally reflect empirical mean housing stock temperatures [64]. To account for longer heating duration associated in detached houses [59], the assumed demand temperatures and heating schedules for the RD are based on available empirical evidence [127,128] as detailed in Table 9.
P a g e | 27

Level of occupancy
Typical levels of occupancy by are based on national census statistics [72] for Ireland corrected to apply to DEAP construction periods [30]. SyAv occupancies established were subsequently weighted against the dominant dominant planar element U-value classifications established in Tables 12 and 13 in section 2.4.4, as shown in the summary results in Table 14 in section 3.0.

Form
SyAv dwelling geometries were determined from the refined empirical database [88]. Dwellings geometries display a normal distribution. The thermal performance of single storey and two-storey dwellings with the same thermal fabric characteristics differ due to their different volume-tosurface-area ratios. Single and two-storey geometries were therefore established. Typical geometries by construction period depicted in Figure 7 are described in Table 10.   Building energy assessors measure the roof 'at the thermal envelope' where the insulation is located. As shown in Figure 8 (a), a typical single storey Irish house with a pitched roof has insulation laid between (and possibly above) the ceiling joists, resulting in a flat 'roof' on the reference dwelling [129]. Figure 8 (b) and (c) depict two-storey dwellings. Figure 8 (c) depicts a single-storey dwelling where the attic is converted into a habitable space, recorded in DEAP as a separate storey. In two-storey dwellings and referring to Table 10, the roof area is larger than the floor area suggesting that the typical location of roof insulation in this dwelling type is in the rafters of the roof. The data relating to roofs in Table 10 thus behaves rationally, correlating with ground floor areas. To facilitate better the characterisation of the RD, it is recommended that two-storey dwellings be classified by type (1) or (2) in the EPC database.

Orientation and proportion of windows with no direct solar access
As they are used for aggregated thermal modelling, an RD has to be representative of the orientation of that dwelling type. EU commission delegated regulation 244/2012 [57] requires proportion of windows with no direct solar access to be reported. Solar access is the ability of a building to receive direct sunlight without obstruction from other buildings or impediments, not including trees [130]. Figure 9 shows a simplified sun-path indicating solar radiation is available in Ireland from approximately 5am to 10pm on the longest day of the year and from 8:30am to 4:30pm on the shortest day of the year. P a g e | 32 Houses in rural Ireland typically parallel the road [81]. It is not possible, to determine readily, a typical orientation representative of a dwelling stock. A study carried out in 2014 [133], in respect of 36 local authority urban housing schemes in Ireland, comprising 10,449 housing units, found the percentage orientations to be 29%, 27%, 23% and 21% north, south, west and east facing respectively. The results of that study suggest that houses developed traditionally, without solar orientation as a key design criterion, distribute reasonably uniformly.
The method for establishing percentage façade window area, applying to entire area of the window opening, including both frame and glass, with no solar access is shown in Figures 11 and 12 and as described below: P a g e | 34 a) SyAv geometries established (see Table 10) and shown in Assuming no solar access 50 o east and west of north and at each of the orientations the % of windows with no solar access was estimated as described in Table 11. P a g e | 35 Figure 11 Method for establishing percentage of windows with no solar access for single storey and two-storey dwelling type 2 P a g e | 36 Figure 12 Method for establishing percentage of windows with no solar access two-storey dwelling type 1 P a g e | 37  Table 11 and benefiting this characterisation there is no substantive difference in the share of windows with no solar access for single storey and two-storey dwellings Type 2 and twostorey dwellings Type 1 (reference Figure 8).

Typical thermal transmittance coefficients by construction period
A bimodal distribution was fitted to the empirical data to; a) establish the proportion of Mode 1 and Mode 2 dwellings by period of construction (see Figure 13) to indicate refurbishments, b) ascertain the means for Mode 1 and Mode 2 dwellings, (i.e. 'Mean 1' and 'Mean 2') by period of construction (see Figure 13).
Statistical means for Mode (1) [73] is adopted for the RD as shown in summary results in Table 15, Section 3.0.
To establish thermal envelope characteristics for the RDs, each characterisation by construction period (shown on the horizontal axis in Figures 14 and 15) is subcategorised vertically by common thermal characteristics in Figure 16. A minimum of 4 to a maximum of 5 categorisations per age category, [(a) to (d) or (e)] was required to reflect accurately the reference sample dataset by construction period as shown in Figure 16. This resulted in a grouping of 45 single and 45 twostorey dwellings by construction period as shown in Tables 12 and 13 respectively. Due to thermal upgrades there was commonality in thermal characterisations across construction periods. P a g e | 39 [88] Commonalities are grouped under the column 'category' in Tables 12 and 13 with the same colour and number; 1S, x for single storey dwellings where x varies between 1 and 21, and 2S, x for twostorey dwellings were x varies between 1 and 14. The number of categories was reduced from 45 to 21 for single-storey dwellings and from 45 to 14 two-storey dwellings. The validity of these classifications were confirmed via use of radial graphs shown in Tables 12 and 13. Each radial graph is denoted with the number in the 'category' column. For instance single-storey category 3

Figure 13 (a & b) Illustrative typical frequency distribution and of wall and roof U-value's
is denoted "Category 1S, 3" and two-storey category 9 is denoted "Category 2S, 9" and so on.
Singular or unique classifications are not depicted in radial graphs as there is obviously no commonality. The radial graphs elucidate the relative weighting of the RDs thermal characteristics resulting in a unique shape for each classification. There is notable difference in the profile of pre and post thermal regulation dwellings with thermally poor dwellings displaying a 'short and fat' diamond shape and well insulated dwellings exhibiting a 'long and thin' triangular shape. The graphs visualise opportunities for targeted policies for each RD by quantity. P a g e | 40

Fig. 13 Mean (1) and (2) and default U-values (W/m 2o C) for two-storey detached dwellings proportional to dwelling quantities by period of construction
Legend

Period of Construction
. P a g e | 42

Figure 16 Segmentation of synthetically averaged bi-modal exposed thermal characteristics for dwelling elements by period of construction
Statistical average thermal characteristics by period of construction subcategorised by common thermal characteristics by period of construction Segmentation proportional to dwelling quantity by period of construction P a g e | 43    1930-1949 1950-1966 1983-1993 1967-1977

Air Tightness
The reasonable upper limit of dwelling air infiltration prescribed in the 2011 Irish building regulations is 7m 3 /hm 2 . At 3.05m 3 /hm 2 at 50Pa or less, infiltration rates returned by the EPC dataset are much lower than expected. Dwellings in the dataset in which an air permeability test was carried out, typically had other measures installed that reduced the calculated overall energy consumption to below average. This indicates that end-users motivated to test for air tightness already had air-tight low-energy dwellings [134]. The infiltration rates in the empirical dataset were thus unrepresentative of the overall dwelling typology. There are few published air-tightness charateristics of existing dwellings in UK and Ireland [135,136]. A statistically small (  were slightly better for post-thermal regulation dwelling than pre-thermal regulation dwellings.
The GreenBuild dataset is shown in Figure 17 to compare well with the 417 dwelling UK dataset.
It was therefore employed in the characterisation of the case study RDs. Average air infiltration limit' 7m 3 /(hm 2 ) GreenBuild values used in the characterisation of reference dwelling P a g e | 48

Thermal Bridging
The Y-value is the sum of all the non-repeating thermal bridging heat transfer coefficients divided by the total exposed area of the building envelope. The Y-value is added to the average U-value to account for thermal bridges [140,141]. In DEAP a global default Y-value of 0.15W/m 2 K is applied for all existing dwellings [142], irrespective of dwelling type, that can either overestimate [143,144] or underestimate [145] the heat loss due to thermal bridging. The linear thermal transmittance values in this study were sourced from UK SAP guidelines [146] as corresponding values in Irish regulations are linked to unrepresentative U-values [81].
The SyAv geometries by construction period listed in Table 10 were reclassified according to thermal classifications, established in Table 12 and Table 13. To calculate the Y-Values shown in Table 14. To determine the likely length of thermal bridges junctions it was assumed that; The adopted Y-values in Table 14, are 40% to 47% lower than those the DEAP [73] global default Y-value of 0.15W/m 2 K.

Internal heat capacity
The dynamic effects of solar and internal heat gains are taken into account by introducing coefficients that account for thermal mass [31,73,147]. The thermal mass of Ireland's predominant housing typology is categorised "medium" giving utilisation and intermittent heating factors of 0.2 and 0.11MJ/m 2 K respectively [88]. P a g e | 49

Reference Dwelling definition process
The following steps were used to define the reference dwelling; 1) Common heating duration, set-point temperatures and climatic conditions for the reference dwellings were established (as described in Section 2.4.2.1.2).
2) Synthetically average occupancies by DEAP period of construction were established (as described in Section 2.4. 2.1.3).
3) Synthetically average dwelling forms, by DEAP construction period, were ascertained using maximum likelihood estimation of the microscopic data in the EPC dataset (as

Statistical model validation and generalisability
For internal validation of the model's performance repeated data-splitting was used [148]. In the refined EPC dataset detached dwellings were isolated from the larger dataset, rural detached dwellings were then isolated. The dwellings were then classified by number of stories, then by construction period (10 No.) then by dwelling element (wall, roof, floor etc.). The MLE statistical model developed (as described in Section 2.4.4.1) was applied repeatedly to each split dataset.
The robustness of the method was demonstrated by consistent goodness-of-fit of the cumulative distribution function to the real data [81].
To externally validate the methodology, an independent sample for a different housing typology from the same population was isolated from the original EPC dataset [88] used. The method has been shown to be valid by the goodness-of-fit of the fitted curve to the real curve for a different housing typology [81]. The recommended default U-values for walls and roofs for a different dwelling typology correlate with those recommended for the dwelling typology examined originally; corroborating the expectation that retrofit measures would be applied proportionately across single-family dwelling stock-at-large. P a g e | 51

Results
Overall reference dwelling characterisations are summarised in Table 14. Results are reported as detailed in Commission Delegated Regulation (EU) No. 224/2012 [57] in Table 15. P a g e | 52    Table 14 living area as a % of total floor area 16 [88] total length (m) See  Table 14 4

.0 Limitations of this Study
The EPC database employed [88] may present a favourable characterisation of the dwelling stock as homeowners must obtain an EPC to qualify for a state-led grant schemes. The estimated percentage of state-grant aided thermally refurbished dwellings in the database is 24% [81]; reduced from 50% in 2010 [93].
Applying a single weather file to the island of Ireland does not capture that temperatures tend to be higher in the south-western areas of the country and lower in the midlands and the northeast, however the average range of temperature is modest [150] ranging from 7 to 11 o C [124,151].
As elucidated throughout this work and summarised in Table 16, where information within the database was found to be questionable or unreliable, the composition of the reference dwelling was informed instead through other available data and expert enquiries. Thus the quality of the characterisation relies on subjective expert judgment [119]. Due to lack of information on the composition of dwelling stocks, this has been a common approach [23,56,57,71,86,119]. Realistic internal temperatures for UK housing adopted for RD [128] "Rest of the house" temperature adopted from Irish study that had a relatively small sample size. [127] Level Use of these RDs as inputs to national residential energy consumption enables models to better predict the energy saving potential of a predominant housing typology.

Policy Context
Households consume 27% of end-use energy in the EU 28 [1]. The extent and duration of the dominance of the thermal characteristics of pre-existing houses depends on the construction rate, floor areas and specifications of new dwellings [2]. As average replacement rates for existing housing stocks in the EU are less than 0.1% [3], the majority of Europe's existing dwellings will remain in place in 2050 [4]. In the United Kingdom, for example, around 75% of dwellings that will exist in 2050 have already been constructed [5]. Accordingly, achieving less overall energy use requires energy refurbishment of existing dwellings [2, 6-9]; but as suboptimal or partial refurbishments can render future energy performance improvements more difficult or expensive [10], understanding existing dwellings stocks is a prerequisite before making energy efficiency, policy or market interventions. However, there are few large-scale building monitoring projects [11][12][13], in the small samples of buildings studied [9,11], evidence of patterns in energy demand in buildings by population and stock segmentations are limited [9,11,12,14,15], with little common [9,16], transparent or prescribed data reported [9,11,12]. This absence of robust data inhibits the effectiveness of policy frameworks [11,17,18]. Evidence-based policies are a prerequisite to achieving targets for reduced building energy demand [11][12][13][14][19][20][21][22].
The calculation of the total energy consumption of a dwelling stock combines stock and energy models [10]. A stock model describes the stock's size, composition and renovation status, whereas an energy model describes the average energy intensities of the various stock segments and assumed energy savings from renovation [10]. A paucity of observed data, together with a lack of documented transparency around energy performance model inputs have hindered agreement on the validity of building stock energy consumption models [11,12,14,19]. P a g e | 6 The development and use of dwelling stocks energy consumption models [12,23] is now driven by policies [24] to; a) reduce domestic energy use, b) lower greenhouse gas emissions, c) reduce dependence on imported fuels, d) reduce the cost of energy, and e) alleviate fuel poverty.

Energy analysis of a building stock
The average change in energy intensity of a total dwelling stock changes [28] over time due to different construction techniques and materials [29], material and labour costs [30], architectural forms [29], heating systems [31], occupant comfort expectations [29], occupant behaviour [32], patterns of use of space within dwellings [33], appliance use [34], economic drivers [30], regulations [29], and the scope and prevalence of refurbishments [35]. Multicollinearity between these factors complicate isolating each of the influences on dwelling energy consumption [36,37] with one study finding half the variability in energy consumption to be unexplainable [36]. The interaction of thermophysics of a building with its local climate [32,36,38] and occupant behaviour [32] underlie energy consumption with heat energy consumption often dominated by building fabric characteristics [11,[39][40][41][42][43]. For similar buildings, heating system efficiencies, primary fuel types and heat sources cause large differences in energy consumption [44,45] and carbon emissions [46]. Understanding residential energy consumption drivers thus requires disaggregated thermophysical characteristics [28,36].
Modelling residential energy consumption can be; a) Top-down; where historic cumulative energy assessments are regressed, as a function of national energy statistics, gross domestic product, population and climate, to determine dwelling stock energy consumption. As this approach cannot distinguish energy consumptions of individual end-uses it is unable to predict the effect of specific interventions. To do this, bottom-up models are required [43,[47][48][49]. P a g e | 7 b) Bottom-up models estimate energy consumption of a representative set of individual houses which are extrapolated to determine regional and national relationships between dwelling characteristics and energy use [43,50]. Bottom-up approaches are referred to as "statistical", "engineering" or a hybrid of both [51]. "Statistical" approaches use historical data to correlate relationships between energy end-uses and total energy demand. "Engineering" approaches, determine end-use energy based on building geometry and thermophysical relationships. As bottom-up engineering models address explicitly the effect of occupant behaviour and passive solar gains, they thus can assess the effect of thermal retrofit measures on residential housing stock energy consumption [15,43,48,49,51].
EPBD energy refurbishments are assessed against cost-optimal criterion to [2,52]; i) ensure coherent and well-planned refurbishment standards that avoid low-cost but suboptimal improvements, and ii) invest in interventions that will recoup their life-cycle costs.
The all-encompassing disaggregated thermophysical input data required to effectively inform bottom-up cost-optimality models is computationally intensive [53]. Rather than calculate the cost-optimal interventions for every single building [53], in EPBD guidelines [54] a set of reference buildings (RBs) are defined for each EU member state representative of national building stocks [35,55,56]. A common EU-wide reporting methodology (EU Regulation No 244/2012) for RBs; (i) provides more transparent reporting, (ii) enables comparison of building stocks across the EU, and (ii) enables cost-optimal building stock refurbishment interventions to be developed [15,35,55,57].
As shown in Figure 1, a building stock is more accurately reported by a larger number of RBs [54], so the effectiveness of RBs depends on the; i) number of building subcategories employed [62], ii) level of detail in defining each RB [56], P a g e | 8 iii) validity of information used to characterise each RB [56,60,63], iv) selection of default data [35,53,63,64]. Certificates" (EPCs), be issued for buildings constructed, sold or leased in the EU [65,66].

Figure 1 Illustrative indication of variation of energy consumption prediction accuracy of a stock model with the number of reference buildings considered
EPC's provide empirical national dwelling stock information that can inform characterisation of contemporaneous RBs [35,67].
Single-family dwellings constitute 49.4% of the total building floor area in the EU [68] while households consume 27% of end-use energy in the EU 28 [1]. 34% of the EU 28 population lived in detached single-family houses in 2013 [35]. More generally, energy efficiency retrofits remain important as 67% of European housing was built prior to 1980 [69], before the introduction of thermal building regulations for the housing sector.
ii) Ireland has the highest proportion, circa 90%, of single-family dwellings in Europe.
Though as shown in Figure 3, the UK, Greece, Norway and the Netherlands have similar profiles [35].
iii) Detached dwellings have relatively high surface area to volume ratios so generally exhibit larger heat losses than semi-detached or terraced houses of the same construction [53], with higher cost of heating to a given comfort level [74]. Detached dwellings are therefore targeted in energy-efficiency retrofit programmes [59,75,76].
iv) At 149m 2 , the mean-weighted-average heated floor area 2 of an Irish detached dwelling is approximately twice the average European floor area [69].
v) Detached dwellings in Ireland have a stronger association with fuel poverty than other dwelling types due to; a) a higher cost of heating them to a given comfort level [74], b) being classified as 'hard to treat 3 '' [77] and, c) having a higher proportion (88%) of middle-aged (50 -64 year olds) and older adults (aged 75 and over) compared to those living in and around Dublin (16%) or other towns or cities (38%) [76]. Older adults [76];

Figure 3 Distribution of single-family and apartment buildings in Europe [18]
5 To allow quantification of default effect by comparison to previous study [71]

Methodology
The methodology to describe a total building stock through RDs follows distinct stages [23,80,81]: 1. Segmentation by common characteristics such as housing typology, heating type and construction period etc.).
2. Analysis of single field empirical building data.

Aggregation of RDs to stock level.
To ensure realistic RDs are created, data is assessed at each stage, for consistency before proceeding to the next stage [82].
There are three approaches [55] to defining reference buildings that are representative of climatic area, construction age and building size: 1. In the "Real Example Building" (ReEx) approach, a building type is selected by a panel of experts as the most representative of specific building size by construction period and climate location. This approach is applied when statistical data is unavailable.
2. The "Real Average Building" (ReAv) approach identifies a representative building type through statistical analysis of a large building sample to find a real building mirroring the characteristics exemplifying mean geometrical and construction features of buildings in the statistical sample.

Based on the statistical analysis of a large building sample the "Synthetical Average
Building" (SyAv) approach identifies an "archetype" defined as "a statistical composite of the features found within a category of buildings in the stock" [83]. The archetype is a notional building characterised by a set of properties detected statistically in a category of buildings [23,29,[84][85][86].

P a g e | 12
The third approach is adopted in this work. A large, empirical and contemporaneous sample EPC dataset is used to create SyAv reference dwellings representative of a dwelling typology at stock level.

Segmentation
EPCs are generated in Ireland through a methodology embodied in the national Dwelling  Figure 2. 60% of detached dwellings within the EPC database are rurally located while an average of 76% of rural homes were oil-heated equating to 19% nationally [88]. 18% of detached homes were recorded as oil heated in the 2006 national census [72]. The relative sample sizes in the EPC dataset used are thus consistent with the national distribution of detached dwellings by construction period published by Ireland's national statistics office [72,88]. 97% of detached dwelling are either single or two-storey, 98% are naturally ventilated [88].
As shown in Figure 2, rural, single and two-storey, oil centrally-heated and naturally-ventilated dwellings are the predominant dwelling type in Ireland accounting for 18% of the national dwelling stock and 63% of all detached dwellings. Dwellings with these characteristics were isolated from the larger dataset. To avoid inconsistencies, dwellings carrying a 'provisional' certificate were removed from the dataset. As shown in Table 1 (1) = "Acceptable" margins of error fall between 4% and 8% at a 95% confidence interval [90]. To ascertain whether the segmented sample population (N s ) of 50,236 detached is representative P a g e | 13 of the entire population (N p ) of 406,910, the margin of error at a 99% confidence level (z-score 2.58) for each construction period 6 was calculated using Equation (1) with results shown in Table 1 for standard deviation (σ) of 0.5 (50%). Because older dwellings change ownership less often there are fewer EPCs for older dwellings than newer dwellings. Older dwellings are thus somewhat less represented in Table 1 than newer dwellings. Notwithstanding, in all cases, Table 1 shows acceptable margins of error indicating a statistically representative sample while the sample number and proportion of detached dwellings in the empirical dataset is coherent with the actual number and proportion of detached dwellings nationally, so verifying intradataset consistency.

Analysis of microscopic data within EPC Dataset
Extracted from the Irish national EPC dataset [88], Figure 4 illustrates a typical U-value frequency distribution for dwelling walls and roofs by construction period revealing the thermal characteristics of Ireland's walls and roofs to be bi-modally distributed. Referring to  'Mode 1' dwellings are thermally-upgraded building elements with lower U-value ranging between 0.1 to 0.59W/m 2 K.
As more thermal retrofits are carried out more building elements U-values will fall within Mode 2 than Mode 1.The standard deviation 7 for Mode 2 is greater than that of Mode 1 demonstrating that retrofits harmonise levels of thermal insulation. Figure 4 highlights statistically anomalous spikes in the data split-across time-periods in both pre and post-regulation dwellings; in the tail of the Mode 2 empirical U-value distribution for exposed building elements such as walls and roofs. Analysis revealed that these result from default U-value selection [35,81].
Where acquiring data would be prohibitively costly, nationally applicable default U-values for the building envelope are employed [73]. Use of such worst case default U-values ensure that a poor dwelling does not attain a better energy rating than is merited [35]. In the absence of empirical data in Ireland default U-values, as in many other EU member states, are determined by the type and date of construction and then prevailing building codes as shown in Table 2 [35, 91]. * 0.45 = ground floor and 0.6 = exposed/semi-exposed floor The frequency of default U-value selection across construction period, together with the independence of default U-value selection to building element type, implies that building assessors often select thermal-default U-values by construction period in preference to calculating actual elemental U-values.
Current default U-Values in Ireland under rank 100% of walls and 82% of roofs [35].
Procedures used in Ireland [71,93] along those in Italy [29], Spain [94] and Austria [95] use stock-aggregation methodologies to calculate residential stock energy consumption using asbuilt or base-default U-values applied to equally default dwelling typologies classified by construction period.
As more retrofit interventions are carried out in the housing sector, current base-default Uvalues become less relevant to the real statistical distribution over time especially with respect to Mode 1 dwellings [35,81]. The use of outmoded default U-Values to necessarily maintain the cost-effectiveness of EPC decreases the accuracy and hence credibility of both the EPC and the EPC database [35]. Unlike walls and roofs, dwelling floor U-values have a normal distribution as there are fewer retrofits of floors due to the high replacement cost of floor coverings [96] together with the impracticality of retrofitting floor insulation. To eliminate the systemic error associated with outmoded base-thermal-default values [35] so data better meets accuracy, coherency, compatibly and clarity requirements; it is thus appropriate to remove default wall and roof U-values from the database [97].

Figure 4 Illustrative typical frequency distribution of wall and roof U-values [88]
P a g e | 16

Validation of EPC Dataset
An analysis of dwelling element U-value distributions by construction period is summarised in Peaks observed consistently in distributions for upgraded dwellings relate to state-funded energy refurbishment grants to homeowners available through the SEAI [100] for insulated buildings elements as shown in Table 3.

Table 3 U-values required to meet state-funded thermal refurbishment grants in Ireland
P a g e | 17 Data quality checks and measures taken to ensure final data quality corresponding to Eurostat validation levels ranging from 0 (lowest) to 5 (highest) summarised in Table 4 are shown in Figure 5 [97,101]. The data was checked for internal consistency within the elements of the dataset to Eurostat validation level 1, intra-datasets time-series checks via differing periods of construction found data behaved consistently to validation level 2, while also confirming requirement to remove base-thermal wall and roof default U-values [81]. Using other data together with intra-domain consistency checks confirmed the quality of the data in the refined EPC dataset to data validation level 5 [97,101]. Check in respect of wall, roof and floor insulation levels Base-thermal-defaults (as described in Table 2) removed as inconsistent with other data sources  Table 5 are based on (i) outmoded base or as-built thermal default characteristics (see Table 2), (ii) smaller sample sizes, or (iii) indeterminate data. P a g e | 19

Figure 5 Methodological and validation process flowchart [81]
Methodological Flowchart Data Validation

Overarching approach
Adapting the methodology established by Corgnati et al. [56] for office buildings in Italy to apply to existing RDs under the relevant EPBD directives [54,57], SyAv reference dwellings where characterised as shown in Figure 6. Figure 6 Categorisation of characteristic data required to define reference dwelling for existing dwellings [54,56,57,121] P a g e | 22 Unreliable information within the database is replaced by other available data and expert enquiries.
EPC energy performance assessment procedures generally provide all the detailed information pertaining to the building form, system and envelope as defined in Figure 6. The methodology ignores aggregated EPC data such as energy consumption in favour of establishing disaggregated thermophysical data by period of construction [29,51,55,118,119]. A study carried out in the UK using data for 12,500 gas centrally heated houses in 2009 [120], found approximately 75% of the observed variance in the energy performance rating of the home was determined by heating system efficiency, external wall U-value and dwelling geometry. The RD are thus defined initially by these factors.

Heating and Hot Water Systems
As shown in Figure 1, for Irish dwellings 63% use oil and 31% use solid-fuel. As Central Statistics Office (CSO) data on fuel-use in Ireland is more comprehensive than within the EPC database, CSO data relating to solid-fuel use was reclassified by DEAP construction period as shown in Table 6. Table 6 Table 6 Central heating fuel source by construction period [79] pre 1900 1900 -1929 1930 -1949 1950 -1966 1967 -1977 1978 -1982 1983 -1993 1994 -1999 2000 -2004 2005 -2006  Where dwellings are heated by solid-fuel, the characteristics of solid-multi-fuel were employed.
Characteristics of oil-fired and solid-multi-fuel systems are shown in Tables 7 and 8 respectively.
Solid-fuel and oil boilers serve a radiator system [88]. Of those using solid-fuel, two-thirds use a stove and/or cooker while a third use an open-fire with a back-boiler [72]. Standardising heating and DHW system characteristics meant the dominant parameters determining dwelling energy P a g e | 23 consumption are dwelling envelope thermal characteristics, surface area, heating duration and set point temperature.

Heat loss through the building fabric
The overall heat loss comprises heat transfer through the building envelope, linear thermal bridges and air infiltration. Using a sample of RDs 'BS EN 12831:2003 Heating Systems' was used to calculate relative percentage steady-state heat losses. 80 to 90% of the overall heat loss from dwellings is by planar heat losses through the building fabric; 8 to 16% is heat loss through air infiltration through the dwelling fabric and 4 to 16% is heat loss through linear thermal bridges P a g e | 25 [81]. The length of thermal bridges have increased as dwelling size and associated window ratios become larger with the progress of time [71]. The length of its linear thermal bridges in the RDs is captured initially via the classification of a dwelling by its construction period.

Climatic Location
The International Weather for Energy Calculations (IWEC) contains "typical" hourly weather parameters for building energy simulation [122].  [36,59,60,125,126]. In Ireland, DEAP has a total heating period of 56 hours per week or 8 hrs/day of a 243-day heating season with no delineation between weekends and weekdays [127]. In both DEAP and the UK Building Research Establishment Domestic Energy Model (BREDEM) [126] the whole dwelling is assumed to be heated only for specific time periods with the living area heated to a 3°C higher temperature than the rest of the home during these periods [126]. BREDEM differentiates weekdays and weekend heating schedules. Table 9 details the set-point temperatures and heating durations standardised in BREDEM and DEAP. As a wide variety of heating patterns exist [59,[126][127][128], neither BREDEM and DEAP reflect the heat consumption demand and duration characteristics of dwellings in the UK and Ireland accurately [45,59,[126][127][128]. In England, an average dwelling is heated for 8.4 hours/day with that increasing to 8.7 hrs per day in the average detached dwelling [59]. In Ireland, the average rest-of-home temperature is 17 o C [127]. The average temperatures P a g e | 26 and heating duration of dwellings are generally independent of year of construction and day of the week [128]. Living room temperatures are typically lower in the mornings than in the evenings [128] with temperatures of 21 o C rarely reached [128]. SyAv heating schedules and mean temperatures for an average year are required to produce a onefits-all model of space heating energy consumption in detached dwellings. To include increased comfort temperatures, an energy consumption model should ideally reflect empirical mean housing stock temperatures [64]. To account for longer heating duration associated in detached houses [59], the assumed demand temperatures and heating schedules for the RD are based on available empirical evidence [127,128] as detailed in Table 9.
P a g e | 27

Level of occupancy
Typical levels of occupancy by are based on national census statistics [72] for Ireland corrected to apply to DEAP construction periods [30].  Table 14 in section 3.0.

Form
SyAv dwelling geometries were determined from the refined empirical database [88]. Dwellings geometries display a normal distribution. The thermal performance of single storey and two-storey dwellings with the same thermal fabric characteristics differ due to their different volume-tosurface-area ratios. Single and two-storey geometries were therefore established. Typical geometries by construction period depicted in Figure 7 are described in Table 10.  Building energy assessors measure the roof 'at the thermal envelope' where the insulation is located. As shown in Figure 8 (a), a typical single storey Irish house with a pitched roof has insulation laid between (and possibly above) the ceiling joists, resulting in a flat 'roof' on the reference dwelling [129]. Figure 8 (b) and (c) depict two-storey dwellings. Figure 8 (c) depicts a single-storey dwelling where the attic is converted into a habitable space, recorded in DEAP as a separate storey. In two-storey dwellings and referring to Table 10, the roof area is larger than the floor area suggesting that the typical location of roof insulation in this dwelling type is in the rafters of the roof. The data relating to roofs in Table 10 thus behaves rationally, correlating with ground floor areas. To facilitate better the characterisation of the RD, it is recommended that two-storey dwellings be classified by type (1) or (2) in the EPC database.

Orientation and proportion of windows with no direct solar access
As they are used for aggregated thermal modelling, an RD has to be representative of the orientation of that dwelling type. EU commission delegated regulation 244/2012 [57] requires proportion of windows with no direct solar access to be reported. Solar access is the ability of a building to receive direct sunlight without obstruction from other buildings or impediments, not including trees [130]. Figure 9 shows a simplified sun-path indicating solar radiation is available in Ireland from approximately 5am to 10pm on the longest day of the year and from 8:30am to 4:30pm on the shortest day of the year. P a g e | 32 Houses in rural Ireland typically parallel the road [81]. It is not possible, to determine readily, a typical orientation representative of a dwelling stock. A study carried out in 2014 [133], in respect of 36 local authority urban housing schemes in Ireland, comprising 10,449 housing units, found the percentage orientations to be 29%, 27%, 23% and 21% north, south, west and east facing respectively. The results of that study suggest that houses developed traditionally, without solar orientation as a key design criterion, distribute reasonably uniformly.
The method for establishing percentage façade window area, applying to entire area of the window opening, including both frame and glass, with no solar access is shown in Figures 11 and 12 and as described below: P a g e | 34 a) SyAv geometries established (see Table 10) and shown in Figures 7 (b) for single and two storey (type 2) and Figure 7 (d) for two-storey dwellings (Type 1) were oriented (distributed) uniformly through the cardinal axes (N-S), (NE-SW), (E-W), and (NW-SE).
Assuming no solar access 50 o east and west of north and at each of the orientations the % of windows with no solar access was estimated as described in Table 11. P a g e | 35 Figure 11 Method for establishing percentage of windows with no solar access for single storey and two-storey dwelling type 2 P a g e | 36 Figure 12 Method for establishing percentage of windows with no solar access two-storey dwelling type 1 P a g e | 37  Table 11 and benefiting this characterisation there is no substantive difference in the share of windows with no solar access for single storey and two-storey dwellings Type 2 and twostorey dwellings Type 1 (reference Figure 8).

Typical thermal transmittance coefficients by construction period
A bimodal distribution was fitted to the empirical data to; a) establish the proportion of Mode 1 and Mode 2 dwellings by period of construction (see Figure 13) to indicate refurbishments, b) ascertain the means for Mode 1 and Mode 2 dwellings, (i.e. 'Mean 1' and 'Mean 2') by period of construction (see Figure 13). (1) [73] is adopted for the RD as shown in summary results in Table 15, Section 3.0.

Statistical means for Mode
To establish thermal envelope characteristics for the RDs, each characterisation by construction period (shown on the horizontal axis in Figures 14 and 15) is subcategorised vertically by common thermal characteristics in Figure 16. A minimum of 4 to a maximum of 5 categorisations per age category, [(a) to (d) or (e)] was required to reflect accurately the reference sample dataset by construction period as shown in Figure 16. This resulted in a grouping of 45 single and 45 twostorey dwellings by construction period as shown in Tables 12 and 13 respectively. Due to thermal upgrades there was commonality in thermal characterisations across construction periods. P a g e | 39 Figure 13 (a & b) Illustrative typical frequency distribution and of wall and roof U-value's [88] Commonalities are grouped under the column 'category' in Tables 12 and 13 with the same colour and number; 1S, x for single storey dwellings where x varies between 1 and 21, and 2S, x for twostorey dwellings were x varies between 1 and 14. The number of categories was reduced from 45 to 21 for single-storey dwellings and from 45 to 14 two-storey dwellings. The validity of these classifications were confirmed via use of radial graphs shown in Tables 12 and 13. Each radial graph is denoted with the number in the 'category' column. For instance single-storey category 3 is denoted "Category 1S, 3" and two-storey category 9 is denoted "Category 2S, 9" and so on.
Singular or unique classifications are not depicted in radial graphs as there is obviously no commonality. The radial graphs elucidate the relative weighting of the RDs thermal characteristics resulting in a unique shape for each classification. There is notable difference in the profile of pre and post thermal regulation dwellings with thermally poor dwellings displaying a 'short and fat' diamond shape and well insulated dwellings exhibiting a 'long and thin' triangular shape. The graphs visualise opportunities for targeted policies for each RD by quantity.   [138] across DEAP age bands as shown in Figure 17.
GreenBuild Energy Rating and Building Information Services Ltd. have been conducting airtightness tests in Ireland since mid-2007, amassing air-tightness test data [139] relating to 187 refurbished as well as as-built Irish dwellings. Using this database, 118 detached dwellings representing 63% of sample set, were isolated from the larger dataset. Air-tightness results for similar dwellings constructed within the same period;  varied widely, even for dwellings with similar construction characteristics,  were not necessarily lower for refurbished dwellings than for as-built dwellings,  did not relate to wall-construction type (solid concrete, cavity block etc.),  were slightly better for post-thermal regulation dwelling than pre-thermal regulation dwellings.
The GreenBuild dataset is shown in Figure 17 to compare well with the 417 dwelling UK dataset.
It was therefore employed in the characterisation of the case study RDs. Average air infiltration The Y-value is the sum of all the non-repeating thermal bridging heat transfer coefficients divided by the total exposed area of the building envelope. The Y-value is added to the average U-value to account for thermal bridges [140,141]. In DEAP a global default Y-value of 0.15W/m 2 K is applied for all existing dwellings [142], irrespective of dwelling type, that can either overestimate [143,144] or underestimate [145] the heat loss due to thermal bridging. The linear thermal transmittance values in this study were sourced from UK SAP guidelines [146] as corresponding values in Irish regulations are linked to unrepresentative U-values [81].
The SyAv geometries by construction period listed in Table 10 were reclassified according to thermal classifications, established in Table 12 and Table 13. To calculate the Y-Values shown in Table 14. To determine the likely length of thermal bridges junctions it was assumed that; (i) single-storey houses have a length twice the width while two-storey dwellings are square The adopted Y-values in Table 14, are 40% to 47% lower than those the DEAP [73] global default Y-value of 0.15W/m 2 K.

Internal heat capacity
The dynamic effects of solar and internal heat gains are taken into account by introducing coefficients that account for thermal mass [31,73,147]. The thermal mass of Ireland's predominant housing typology is categorised "medium" giving utilisation and intermittent heating factors of 0.2 and 0.11MJ/m 2 K respectively [88]. P a g e | 49

Reference Dwelling definition process
The following steps were used to define the reference dwelling; 1) Common heating duration, set-point temperatures and climatic conditions for the reference dwellings were established (as described in Section 2.4.2.1.2).
3) Synthetically average dwelling forms, by DEAP construction period, were ascertained using maximum likelihood estimation of the microscopic data in the EPC dataset (as  Tables 14 and 15. P a g e | 50

Statistical model validation and generalisability
For internal validation of the model's performance repeated data-splitting was used [148]. In the refined EPC dataset detached dwellings were isolated from the larger dataset, rural detached dwellings were then isolated. The dwellings were then classified by number of stories, then by construction period (10 No.) then by dwelling element (wall, roof, floor etc.). The MLE statistical model developed (as described in Section 2.4.4.1) was applied repeatedly to each split dataset.
The robustness of the method was demonstrated by consistent goodness-of-fit of the cumulative distribution function to the real data [81].
To externally validate the methodology, an independent sample for a different housing typology from the same population was isolated from the original EPC dataset [88] used. The method has been shown to be valid by the goodness-of-fit of the fitted curve to the real curve for a different housing typology [81]. The recommended default U-values for walls and roofs for a different dwelling typology correlate with those recommended for the dwelling typology examined originally; corroborating the expectation that retrofit measures would be applied proportionately across single-family dwelling stock-at-large. P a g e | 51

Results
Overall reference dwelling characterisations are summarised in Table 14. Results are reported as detailed in Commission Delegated Regulation (EU) No. 224/2012 [57] in Table 15.
P a g e | 52    Table 14 living area as a % of total floor area 16 [88] total length (m) See  Table 14 4

.0 Limitations of this Study
The EPC database employed [88] may present a favourable characterisation of the dwelling stock as homeowners must obtain an EPC to qualify for a state-led grant schemes. The estimated percentage of state-grant aided thermally refurbished dwellings in the database is 24% [81]; reduced from 50% in 2010 [93].
Applying a single weather file to the island of Ireland does not capture that temperatures tend to be higher in the south-western areas of the country and lower in the midlands and the northeast, however the average range of temperature is modest [150] ranging from 7 to 11 o C [124,151].
As elucidated throughout this work and summarised in Table 16, where information within the database was found to be questionable or unreliable, the composition of the reference dwelling was informed instead through other available data and expert enquiries. Thus the quality of the characterisation relies on subjective expert judgment [119]. Due to lack of information on the composition of dwelling stocks, this has been a common approach [23,56,57,71,86,119]. Realistic internal temperatures for UK housing adopted for RD [128] "Rest of the house" temperature adopted from Irish study that had a relatively small sample size. [127] Level Use of these RDs as inputs to national residential energy consumption enables models to better predict the energy saving potential of a predominant housing typology.