Impact of building envelope design parameters on diurnal building anthropogenic heat emission

Anthropogenic heat fluxes from buildings ( Q F,B ) are a major source of additional heating in cities, but vary both spatially and temporally. Knowledge of temporal variations of Q F,B is critical to modulate urban climate through appropriate building design. Based on a new method to determine Q F,B [1], this study investigates the influences of building envelope design parameters on both magnitude and diurnal pattern of Q F,B by season through parametric building energy modelling in Beijing. Using K-mean clustering, the distinctly representative diurnal patterns of Q F,B in each season are identified. With classification-based analysis, we rank building parameters to understand their roles in causing these distinct Q F,B patterns. We conclude that: (1) the most important building parameters influencing Q F,B are U-value and thermal mass. (2) U-values effectively modulate both diurnal pattern and daily magnitude in all seasons. Buildings with small U-value (e.g., U-0.2) have lower daily energy consumption, resulting in an up to 73% reduction in Q F,B daily mean in winter. (3) Thermal mass is more important in autumn/spring Q F,B. It can both reduce the daily peak by up to 68% and shift the diurnal pattern dominated by mechanical cooling (peak during 15:00 – 17:00) into natural ventilation (peak during 01:00 – 06:00) with an 8 – 15 h lag. (4) Combined with natural ventilation, appropriate building envelope designs (e


Nomenclature
Hourly outdoor air temperature ( • C) x i data point belonging to cluster P x i

Introduction
With decades of rapid urbanization, 69% of the global population is predicted to live in cities by 2050 [2], leading to more attention being directed to better understand the thermal characteristics of cities. Cities often experience higher nocturnal canopy layer air temperatures than surrounding rural areas (referred to as the canopy layer urban heat island, CL-UHI) [3].This is regarded as the most apparent climate manifestation of urbanization [4].Warmer temperatures impact building cooling energy needs, thermal comfort and human health [5][6][7].
The anthropogenic heat flux (Q F ) is defined as the heat converted from the consumption of biological, chemical and electrical energy and released to the atmosphere due to human activities [8].As in dense parts of US and East Asian cities Q F can be order of 100-500 W m − 2 (at spatial resolutions of 30 arc-seconds), it can be an important source term in the urban energy balance (Dong et al., 2017).There is consensus from urban climate modelling studies that Q F can elevate near-surface air temperatures and strengthen the nocturnal urban heat island (e.g., Refs.[9][10][11][12]).At night (cf.daytime) the boundary layer can be relatively shallower and all energy balance fluxes, including Q F are smaller (e.g., Refs.[10,13,14]), but its release can warm the smaller near-surface volume of air at night.For example, Fan and Sailor [4] and Bohnenstengel et al. [14] used energy consumption (Q EC ) as a Q F proxy in their modelling studies and found the increases in nocturnal near-surface air temperatures of 2-3 • C (Philadelphia) and 1.5 • C (London), respectively.Hence, both the quantity of Q F released into the atmosphere and the diurnal timing of emission are important.
Buildings (Q F,B ) account for the majority of anthropogenic heat emissions in the cities (e.g., 89-96% globally in Ref. [15]).Building occupants use energy for different activities including space heating and cooling for thermal comfort, and daily living such as lighting and other electrical appliances.The consumed energy from these activities (Q EC ) is eventually released from the building volume into the surroundings through convection, longwave radiation, air exchange and waste heat from HVAC system [16].
Liu et al. [1] propose a new method to estimate Q F,B that considers the energy fluxes that arise because of a building being 'occupied' (o) relative to an 'unoccupied' (uo) baseline when the building is assumed to be only the physical structure with both a Q EC and a Q F,B of 0 W m − 2 [1].The Q F B emission from an occupied building (i.e., from human activities, Q EC > 0 W m − 2 ) can arise from four heat exchange mechanisms (Fig. 1): longwave radiation (ΔL ↑,o-uo ), convection (ΔH o-uo ), air exchange (ΔBAE o-uo ), and waste heat from heating/cooling system (Q waste ).Alternatively, Q F,B can be expressed in terms of the consumed energy (Q EC ) and changes in storage heat flux resulting from human activities (ΔS o-uo ) being released (absorbed) into outdoors (buildings) [1]: Although Q EC and Q F,B have similar magnitude for long-periods (e.g., annual, ΔS o-uo ≈ 0 W m − 2 ), their temporal pattern can be quite different over short time scales (e.g., sub-daily, ΔS o-uo ∕ = 0 W m − 2 ).This indicates that using the diurnal profile of Q EC (e.g., obtained from inventory methods) in urban climate modelling may cause bias to evaluating the Q F,B impact.Thus, understanding the temporal variation of Q F,B is crucial so that effective measures to modulate Q F,B and its impact on urban climate.
In the context of achieving the goal of net zero carbon, numerous studies attempt to optimize building designs to minimize annual building energy consumption [17][18][19].Theoretically, appropriate building design with minimal energy use across a year also results in the smallest magnitude of annual Q F,B .However, these studies did not consider the variation of energy use and heat release over the time at a higher temporal resolution.The influence of different building designs on Q F,B at sub-daily scale has not been explained and understood yet, despite it being important in predicting variability in local-scale urban weather.Therefore, our work aims to explore and understand how typical building dparameters affect the diurnal profile of Q F,B through parametric building energy modelling.Our results could help building and urban designers to understand how to modulate Q F,B in terms of magnitude and diurnal pattern through amending building parameters.
Our objectives are: • To identify the representative seasonal diurnal patterns of Q F,B and to provide a method for doing this.• To understand which building parameters are important in controlling the seasonal Q F,B pattern • To provide insight on how the important building parameters cause different Q F,B profiles.

Methods
This study is based on the Liu et al. [1] method to estimate Q F,B that considers the difference in energy balance fluxes between occupied (o) and unoccupied (uo) building (Eq.( 1), Fig. 1).Building energy simulations are undertaken for one-year for both the o and uo states (i.e. with the same building fabric) allowing 365 Q F,B diurnal profiles to be calculated for 600 building cases (i.e.unique combination of building parameter value in Table 1).Clustering is used to identify the main representative diurnal patterns of Q F,B in each season and help understand the relation between pattern distribution and building parameters.

Parametric building energy simulation
The multi-parametric building energy simulations use the Liu et al. [1] ov3 simplified residential building case, assuming continuous occupation (i.e.24-h per day) with thermal comfort achieved by Fig. 1.Schematic of principles used to derive anthropogenic heat emission from buildings (Q F,B ) by considering the differences in heat fluxes between an 'occupied' (o) and 'unoccupied' building (uo).Adapted from Ref. [1].[20]), for simplicity we assume all energy associated with the heating system is released indoors, and waste heat due to boiler efficiency and pipe heat loss are not considered.The waste heat from cooling system (e.g., including cooling load and cooling energy consumption) is assumed to be emitted to the outdoors immediately.
The unoccupied building (uo) baseline is assumed to be ideally sealed but with the same building envelope parameter values as the occupied building (o).The explored building parameters (Table 1) are selected to represent both those used in early building design decisions, and whose impact on building performance have been widely explored, such as energy usage index [17][18][19] and overheating risk [21][22][23].
Thermal mass, thermal resistance, and position of insulation layer are the three most crucial factors for the dynamic thermal behaviour of multi-layer building fabrics [24,25].Here three thermal mass levels are considered whose surface areal heat capacity (e.g., wall) ranges from 96.0 to 404.5 kJ m − 2 K − 1 .Different thermal mass levels are achieved by modulating the thickness of massive material (detailed information for building components characteristics given in supplementary material Table S.1-3).Note, the specified thermal mass (Table 1) is the average area heat capacity for all layers of construction material, independent of insulation position.The impact of thermal mass and insulation position (i.e., insulation layer external or internal to massive material for wall and roof) is analysed separately (Table 1).
As the U-value and solar heat gain coefficient (SHGC, i.e., fraction of solar radiation transmitted through windows) of thermal properties are treated together (i.e.opaque components and windows) in the local building code in China [26][27][28], we combine them to create five thermal properties levels that satisfy the requirement of improving energy efficiency.The U-value variations are achieved by modifying the thickness of insulation layer in external wall and roof (Table S.1, S.2).The two extreme cases (U-0.2 and U-2.1) have the best and poorest insulation (no insulation for heavyweight construction) respectively.Values assigned (Table 1) span the physically reasonable to ensure appropriate variation in simulation cases.
With the aim of having a theoretical understanding of how the fundamental parameters affect the diurnal variation of Q F,B , each value assigned to a parameter is discrete and has equal probability.Hence, 600 cases are simulated for one-year with Beijing climate forcing [29] by using the jEPlus [30] parametric tool to execute EnergyPlus [31].Beijing is chosen for its climate with distinct seasons (Fig. 2), with both cold winters (T median diurnal range: − 6.3 to 3.1 • C) requiring heating and hot summers (T median diurnal range: 21.5-30.5 • C) requiring cooling.The milder shoulder seasons (spring and autumn) has larger day-to-day variation (IQR shading, Fig. 2).This study can be extended easily to other climates.

K-mean clustering
The diurnal temporal pattern of Q F,B indicates when, and how, it may impact the urban environment.The patterns vary with building parameters and weather conditions, and has a direct influence on building energy use and storage heat flux.Pattern identification commonly involves an algorithm that clusters from a data into several groups with high similarity [32].Here the simulation results dataset (section 2.1) is used to identify the Q F,B representative diurnal patterns.
Although no agreement exists in the literature to the 'best' clustering algorithm, studies indicate K-mean clustering provides both good performance for pattern identification and a stable cluster result [33,34].Furthermore, it is one of the most widely applied algorithms for identifying electricity load patterns or building energy use profile [35][36][37].Hence, we select it for this study.
Given a dataset with a large number of diurnal profiles, K-mean clustering algorithm classifies all the profiles into pre-defined number (K) of clusters.The classified profiles are 'similar' within a cluster but 'dissimilar' to other clusters.
An iterative process is used with the objective to minimize the intracluster inertia [36]: where P k = (P 1 , P 2 , …… P k ) is the set of clusters, μ = (μ 1 , μ 2 , ……, μ k ) is the centroid of each cluster, x i is the data point belonging to P k .The main steps are to (e.g., [34]): Since the impacts from the building parameters could differ between seasons, the Q F,B diurnal profiles (section 2.1) are sub-divided into three periods groups: winter (December, January and February, DJF), summer (JJA) and shoulder season (MAM-SON).Every 10th Q F,B diurnal profiles is selected for all building cases, which reduces the day-to-day variability but retains the intra-season synoptic variability.This results in 5400 profiles for both winter and summer, and 10800 profiles in the shoulder season, to be analysed (i.e., 3 groups) with K-mean clustering.
Prior to analysis, the diurnal profile are normalised to capture pattern shapes and avoid negative influence of absolute magnitude [38] (using the Z-score method [37]): As the number of clusters needs to be pre-defined, but the truth is no agreed method to determine the optimal number.Some metrics are used (e.g., silhouette score [39], and Calinski-Harabasz (CH) Score [40]) balance the intra-cluster similarity and inter-cluster differences.However, we want to find the most representative patterns and understand the impact of building parameters on pattern variance.The clustering derived patterns are expected to be sufficiently distinct and the separation between clusters could be more important.To select the suitable value for K we use the 'clustergram' algorithm [41], which plots a wide range of K values alongside the weighted mean of the first component of a principal component analysis (PCA) in each cluster which indicates the Fig. 2. Seasonal diurnal median (line, T median ) and interquartile range (IQR, shading) outdoor air temperature in Beijing [29].Shoulder season refers to spring and autumn.Seasons are defined by months (e.g., Summer: JJA (June, July, August), Winter: DJF).
Y. Liu et al. variance of cluster performance.This method demonstrates how the dataset could be split between clusters by changing K (Fig. 3).Analysis of winter data indicates the optimal K is 3, gives a clear separation between clusters (Fig. 3).When K increases from 4 to 6, some points are rather close or overlap (i.e., clusters have similar diurnal patterns), making analysing the effect of building parameters on their difference more difficult.The same analysis is repeated for other seasons.The appropriate K are selected in Table 2.The K-mean clustering and relevant data processing step are summarised in Fig. 4.

Decision tree classification
The classification and regression tree (CART) algorithm is used [42] to understand the relative importance of building parameters on diurnal patterns of Q F,B .Binary splitting of input features space (i.e.building parameters values, Table 1) the algorithm disaggregates the target feature (i.e.diurnal patterns of Q F,B from clustering) into smaller subsets with higher similarity.The partitioning roles are constructed by minimizing the impurity of subsets (i.e.Gini index [43]) after the binary split at each node.This helps to build understanding of how selected building parameters values affect diurnal patterns and output a rank of relative importance.

Winter
From clustergram analysis in winter (Fig. 3) an optimal value for K of 3 is chosen.The three sets of data have distinct diurnal variations (Fig. 5a-c).The cluster with the most profiles (60%) is winter0.For this cluster the peak of the normalised Q F,B is typically in the early morning (07:00), after which it decreases to a valley in the afternoon (16:00).For winter1 the peak is about 2 h later than winter0, but it stays positive (i.e., hourly Q F,B > daily mean) until 16:00 (i.e., around sunset).Whilst winter2 has bimodal daytime peaks (07:00 and 15:00), the nocturnal and mid-day values are small (Fig. 5c).The human behaviours for modulating indoor thermal comfort have negligible difference among three clusters as mechanical heating systems are warming the building most of time (orange, Fig. 5d-f).
To identify the relative importance of the building parameters on the cluster Q F,B diurnal patterns the CART [42] algorithm is used (section 2.3).The U-value and thermal mass are found to be the most critical parameters (cf.others, Fig. 6) in determining the Q F,B diurnal patterns in winter (red, Fig. 6), accounting for 68.4% and 21.4% of feature importance respectively.
Small U-values (0.2, 0.3) cause winter0 to be the dominant Q F,B pattern (Fig. 7a).With better insulation, heat loss through conduction is reduced and in return less heating is required (median peak Q EC winter0 = 41 W m − 2 ; cf.winter1 = 87 W m − 2 ; winter2 = 77 W m − 2 ).Smaller Q EC throughout the day results in a small change in heat storage flux (ΔS o-uo ) (winter0 median peak = 4.4 W m − 2 ; Fig. 7e).Consequently, Q F,B (=Q EC -ΔS o-uo ) keeps the same temporal phase as Q EC but with less fluctuation.Small U-values are linked to small daily mean Q F,B (Fig. 7b), suggesting buildings with more insulation (e.g., new construction), not only consume less Q EC but also release less Q F,B .The winter Q F,B diurnal cycle is out-of-phase with typical outdoor air temperature (Fig, 7c).
With high U values (2.1), Q F,B and Q EC patterns differ and thermal mass impacts the diurnal shape.Winter2 is linked to heavy thermal mass (Table 1), while medium and light weight are more likely winter1 (Fig. 7a).No (or little) insulation leads to considerably higher heating energy demand resulting in larger variability of ΔS o-uo .The difference between winter2 and winter1 patterns is explained by the influence of thermal mass on Q EC and ΔS o-uo .
With warmer daytime outdoor air temperatures and solar radiation, heavyweight fabric absorbs more heat (cf.lightweight), consequently more heating energy is required to maintain the indoor air temperature.Conversely, the release of stored heat can reduce heating demand at night when outdoor air and external surface temperatures decrease.This is consistent with winter2 (heavyweight) Q EC being greater than winter1 (light/medium weight) between 12:00 and 19:00 (Fig. 7d).Winter2 allows a continuous increase of ΔS o-uo with increasing Q EC at night, while ΔS o-uo in winter1 stops increasing at 03:00 then decreases to become negative 3 h earlier than winter2 due to limited heat capacity.The earlier release of stored heat causes a higher Q F,B from 09:00 in winter1.While winter2 starts to release stored heat after 13:00, causing the second peak Q F,B in the afternoon.
Winter1 and winter2 could represent buildings constructed many

Summer
In summer, K is set to four, creating four clusters of diurnal patterns (Fig. 8).They can be categorised into two groups based on human behaviour for thermal comfort.Summer0, summer1 and summer2 are mainly dominated by mechanical cooling, therefore they have similar diurnal cycles but different time phases.Their peak values occur between 15:00-18:00 linked to timing of the largest cooling demand and waste heat release.These days have peak outdoor air temperature (T max ) of 29.8-34.4• C.
Whereas summer3 occurs only on 5 th June when the outdoor temperatures are mild (T max = 24.4• C) and suitable for natural ventilation (Fig. 8h).At night Q F,B peaks due to high indoor and outdoor heat exchange by natural ventilation, whereas, the minima occur midafternoon when the warm outdoor temperature limits natural ventilation but some cases yet needs mechanical cooling.The summer3 have small U-values or heavyweight fabric (Fig. 9a), suggesting buildings with these attributes can be cooled by natural ventilation when the outdoor air temperature is not very high.Whereas buildings with larger U-values (also larger solar heat gain coefficient (SHGC, i.e., fraction of solar radiation transmitted through windows)) and less massive fabric, receive more solar gain through windows but lack sufficient heat capacity to dampen indoor air temperature.Mechanical cooling is used despite mild weather, leading to other summer patterns.
To maintain indoor air temperature throughout the day in summer0-2, space cooling dominates, leading to similar Q F,B patterns among them, which follow the corresponding Q EC shapes (varying with cooling energy) (Fig. 9c and d).Summer1 peaks earliest (15:00), whilst summer0( 2) is delayed by 23) hours.Change in cluster proportions reveals how Uvalue and thermal mass alter the time phase (Fig. 9a).Unlike in winter, the effect of thermal mass can be the opposite for the two extreme U-values.For U-2.1, the dominant pattern changes from summer1 to summer2 with increasing thermal mass, indicating the peak Q F,B can be lagged if there is a higher heat capacity.It is consistent with the general expectation that larger heat capacity fabric stores more heat during the daytime, therefore delays the peak of cooling demand and Q F,B .Whereas, summer1 cases increase is linked to heavier fabric when the U-value is small (0.3 and 0.2) (Fig. 9a), suggesting an earlier peak will occur with increasing thermal mass.Heavyweight fabric stores more heat than lightweight fabric during the daytime.At night, such stored heat is trapped by high-level insulation, and cannot be dissipated by convection and longwave radiation until it is at the external surface.On the next day, heavyweight buildings have an earlier Q F, B peak.This agrees with others' finding that increasing thermal mass may cause larger cooling demand at night in the dwelling when the insulation level is high [44].
Similarly, the compensating effect between the U-value and thermal mass leads to contradicting roles in modulating Q F,B pattern phases for lightweight and heavyweight buildings.Hence, the impact of thermal mass and U-value cannot be determined independently, which is consistent with the conclusion that additional insulation may reduce or exacerbate overheating risk in summer [23].In addition, varying U-value causes negligible change to the daily mean Q F,B (Fig. 9b) due to compensating effects of improving opaque insulation and windows properties.Theoretically, smaller SHGC from windows (e.g., apply double or triple glazing windows) would effectively reduce building heat gain and cooling demand [18,45].But improved insulation traps nocturnal heat when outdoor environment is sufficiently cool, subsequently more stored heat may increase cooling energy use on the next day.
In summary, despite limited change in daily mean magnitude, both U-value and thermal mass can modulate the timing of Q F,B diurnal pattern in response to when buildings are occupied (i.e., o -uo), which may lead to different impacts on urban climate.For example, new construction with excellent insulation and heavyweight fabric could advance the Q F,B peak during the daytime, resulting in less nocturnal heat release when the boundary layer is shallow.Whilst lightweight fabric may be more suitable for building with less insulation in term of reducing nocturnal heat release and mitigate urban heat island.It is critical that both U-value and thermal mass are considered by building designers as they jointly determine the timing phase.

Shoulder season
The four clusters (Fig. 10) in the shoulder season are a combination of winter and summer patterns.Shoulder0 and shoulder3 (Fig. 10a and d) are similar to winter0 and winter1 (Fig. 5 a and b) with heating dominating the building operation.Whilst, shoulder1 and shoulder2 (Fig. 10b  and c) have patterns similar to summer0 and summer3 (Fig. 8a and d) with natural ventilation and mechanical cooling dominating.Such similarities indicate the Q F,B patterns in shoulder season are linked with the weather transitions.
Unlike in winter or summer, with only one dominant building operation mode per cluster, all shoulder season clusters have multiple operations modes during the course of the day, because of the wide weather range (e.g., daily mean air temperature (T day ) ranges from 1.7 • C to 21.5 • C).This makes understanding the influence of building parameters on Q F,B patterns more challenging.To reduce the weather variability, we separate the profiles into cool (MON [March, October and November, T day : 1.7 • C → 12.2 • C]) and warm (AMS [T day : 10. The cool months dominant pattern and impacts of envelope thermal properties are highly consistent with winter scenario (Fig. 11a).The shoulder0-a (53%) and shoulder3-a (25%) are nearly identical to winter0 and winter1 (Fig. 5a and b) because of a Q EC diurnal cycle linked to space heating.Higher heating demand in shoulder3-a contributes to larger change in heat storage flux (ΔS o-uo ) and different Q F,B patterns to Q EC .Uvalue is also the most important factor determining the pattern and daily Fig. 9.As Fig. 7, but for summer.mean distribution (Fig. 11i and j).
Poor insulation (U-2.1) is important in shoulder3-a (more heat is released).With improved insulation, less heating is required and shoulder0-a becomes the main pattern.Shoulder1-a can be regarded as an extension of shoulder3-a to shoulder0-a when less heating is required.Thus, its frequency increases with decreasing U-value, implying the buildings with more insulation release less Q F,B .More use of insulation could effectively reduce both energy use and corresponding heat release in this season.
In the warm months (AMS), natural ventilation become more important and both U-value and thermal mass play crucial roles in distinguishing human behaviour and corresponding Q F,B pattern.Shoul-der3-b (Fig. 12d) has dual Q EC peaks as building is heated at night but mechanically cooled in the afternoon.This mainly occurs in building cases with a combination of U-2.1 and lightweight (Fig. 12i), due to lacking thermal resistance and thermal inertia to dampen the indoor   temperature.Use of both heating and cooling energy results in considerably higher daily mean Q F,B (Fig. 12j) than other buildings.Shoulder2b has a typical summer pattern (as summer0) because of high cooling energy use in the afternoon when both much consumed energy and stored heat are ejected into the atmosphere.These buildings mainly are lightweight and mediumweight thermal mass with large/medium Uvalue, where thermal inertia effect is limited or solar heat gain through windows is relatively high.
With improving U-value or thermal mass, shoulder1-b become the dominant pattern, where the Q F,B shape is linked to heat release through natural ventilation.Peak Q F,B occurs at night when indoor and outdoor air temperature difference is sufficiently high and natural ventilation is used to cool the building.Pre-cooled buildings result in less cooling energy use in the afternoon.Shoulder0-b is dominated by natural ventilation but with a longer time with the windows closed.Most shoulder0-b cases have heavyweight fabrics that can minimize the use of mechanical cooling and even reduce the natural ventilation.
The effect of improving U-value varies with thermal mass level.For lightweight and mediumweight buildings, it has a moderate reduction in daily mean Q F,B (Fig. 12j) but shifts cooling-patterns (peak between 15:00-17:00 in Fig. 12c and d) into natural ventilation-pattern (peak between 01:00-06:00 Fig. 12a and b) with a lag of around 8-15 h.However, improving the U-value for a heavyweight building causes a negligible change in pattern and daily mean magnitude.It suggests energy-saving measures (i.e., more insulation, better glazing windows) does not reduce Q F,B for all buildings.Similarly, improving thermal mass also reduce magnitude and modulate the pattern for buildings with large U-value, but such effects are offset when the U-value is smaller than 0.5.
These results support the consensus that improving both U-value and thermal mass can reduce energy consumption from mechanical cooling thus impacts both diurnal pattern and magnitude of Q F,B in warm months.Suggesting that the appropriate designs of natural ventilation and building envelope could achieve both energy saving and modulation of the outdoor thermal environment.For example, for new construction following the high standard of insulation level in the building regulations, use of lightweight material releases most of Q F,B in afternoon and contributes to a smaller air temperature rise when the boundary layer is relatively deep.If buildings are difficult to insulate (e.g., solid wall), heavyweight thermal mass maybe preferred to reduce use of mechanical cooling and less heat will be released.
Overall, lightweight buildings with large U-values are likely to have a cooling-dominated pattern, which release relatively high Q F,B across a day.But it will have a peak of Q F,B in mid-afternoon when outdoor air temperature is likely highest.Whereas, a small U-value and high thermal mass are likely to have ventilation-dominated patterns with diurnal variation offset from the outdoor air temperature.The daily Q F,B is small, but with a large fraction of heat released at night when the boundary layer is shallow.

Inter-season comparison
As buildings have constant properties through the year, the link between seasons is critical to understand how things will influence the fluxes at different times of the year.To do this we evaluate the impact of U-value and thermal mass on daily mean (Fig. 13) and daily peak (Fig. 14) Q F,B between seasons.
When cooling use is likely (summer and shoulder season warm months), improving U-value reduces both the daily mean (for 50 th -95 th ) and peak Q F,B (all ranges).The reduction for lightweight buildings larger than for heavyweight buildings.The greater reduction of peak Q F,B for lightweight building indicate it may require higher standard insulation and glazing property to mitigate urban heating.The lightweight buildings daily peak Q F,B is much larger than the daily mean Q F,B, with a daily peak to mean ratio of 1.07-7.46 in these two seasons.This highlights the importance of both sub-daily variation of Q F,B and that omitting the diurnal profile (e.g., one fixed value [46]) is not sufficiently accurate.
For heavyweight buildings, improving the U-value decreases minimally both the mean and peak Q F,B because the large heat capacity dampens the indoor temperature with less extra energy use.Enhancing thermal mass (i.e., from light-to heavyweight) may contribute to a greater reduction in peak Q F,B than improving insulation only.However, large heat capacity could result in a large daily mean Q F,B in summer when heat could be trapped in the building fabric, particularly when buildings are well insulated.The trade-off between daily mean and peak magnitude of Q F,B should be explored in a future study to optimize building designs for the purpose of regulating urban heating.
In heating seasons (winter and cold shoulder season months), the effect of U-value and thermal mass on daily mean and peak magnitude is relatively consistent.The U-value is the most critical parameter to modulating the magnitude.When buildings are poorly insulated, the thermal mass has a moderate influence on the magnitudes.

Conclusions
Using K-mean clustering the representative diurnal patterns of Q F,B are identified, and the key building energy parameters impacting the Q F,B are also determined, for a city with both warm summers and cool winters (Beijing).The results address the relative importance of building parameters on Q F,B and provide a detailed physical understanding on how these parameters affect both diurnal patterns and mean magnitude in each season.Based on decision tree classification and distribution analysis, we find the U-value (combining thermal resistance of opaque envelope and glazing properties) is the most crucial building parameter influencing the shape of Q F,B diurnal patterns and this modulates the magnitude in all seasons.Thermal mass is the second most influential parameter, with its effect on Q F,B more pronounced in shoulder seasons with more mild outdoor weather, notably reducing daily peak Q F,B .But such effect could be constrained by improved U-value.So both parameters emerge as important to be considered by building designers to achieve energy-saving while retaining a comfortable outdoor thermal environment.Planners should be aware of the link between building materials and anthropogenic heat fluxes, and therefore local-scale urban climates.
The key conclusions by season for this warm summer/cool winter climate are:  mass play a similar role as winter, with both daily mean magnitude and pattern modulated.In warm months (AMS), low levels of insulation and thermal mass are more likely result in the Q F,B patterns dominated by space cooling, as in summer.Daily mean Q F,B is relatively large (e.g., 19.4 W m − 2 for U-2.1 and lightweight) with most heat ejected from mid-afternoon to evening when the outdoor air temperature is high.Buildings with heavyweight fabric or small Uvalue are dominated by natural ventilation.With less cooling energy use, the daily mean and daily peak of Q F,B is smaller with up to 38% reduction in the mean and 74% in the peak (cf.U-2.1 and lightweight) and its patterns are offset (8-15h) from the peak outdoor air temperature Combined with natural ventilation, appropriate building envelope designs (e.g., large U-value with heavyweight fabric, small U-value with lightweight fabric) should be considered to achieve both building energy saving and improving outdoor thermal environment.The large sub-daily variation of Q F,B (e.g., daily peak to daily mean ratio is between 1.07 and 7.46 for lightweight buildings) suggests Q F,B should not be simplified to fixed ratios for a day.The differences in Q F,B diurnal pattern implies the buildings with different design parameters will have different twoway impacts on neighbourhood air temperature with potential to modify the spatial and temporal pattern of canopy layer urban heat island.
Given we demonstrate the variation of diurnal patterns of anthropogenic heat flux at the building scale, future studies should explore: • More realistic building geometry (number of floors, roof shape etc) and internal thermal mass (internal partition and furniture).• Our occupied (o) cases assume 24 h occupancy Whereas inevitably in a neighbourhood of buildings a mix will occur [47].A mix of schedules should be used as they would modify diurnal patterns of Q EC and therefore Q F,B .• Our unoccupied (uo) baseline is ideally sealed but other cases (other scenarios in [1]) should be used.• Different climates and/or different socio-economic cultures will modify thermal comfort norms and/or the influence of building parameters, particularly for natural ventilation and nocturnal temperature in summer and shoulder season.• Q F,B impacts buildings, its feedback on neighbourhood scale and therefore the building climate.Better understanding the feedback between the two will help to bridge building design, local scale and urban climate.

Declaration of competing interest
The authors declare no financial interests.
Centroid of each cluster σ standard deviation of each data in dataset ΔBAE o- uo Difference in heat transfer by air exchange between building and atmosphere between the occupied (o) and unoccupied (uo) building (W m − 2 ) C Intra-cluster inertia of K-mean clustering algorithm ΔH o-uo Difference in Q H between the occupied (o) and unoccupied (uo) building (W m − 2 ) ΔL ↑, o-uo Difference in outgoing longwave radiation between the occupied (o) and unoccupied (uo) building (W m − 2 ) P k Set of clusters Q EC Energy consumption within building volume (W m − 2 ) Q F Anthropogenic heat flux (W m − 2 ) Q F, B Anthropogenic heat flux from building sector (W m − 2 ) Q Waste Waste heat released to outdoor by HVAC system (W m − 2 ) ΔS o-uo (continued on next column) (continued ) Change in storage heat flux induced by human activities between the occupied (o) and unoccupied building (uo) (W m − 2 ) T day Daily mean outdoor air temperature ( • C) T max Daily peak outdoor air temperature ( • C) T median Seasonal median hourly outdoor air temperature ( • C) T o (a) initialize K number of centroids (μ) randomly, (b) assign each point from dataset to nearest centroid by minimizing C(P, μ), (c) update the new centroids to the mean in each cluster, and (d) repeat (b) and (c) until convergence occurs.

Fig. 3 .
Fig. 3. Clustergram of the potential K for initial partitioning of Q F,B diurnal patterns in winter.

Fig. 4 .
Fig. 4. Flowchart of data pre-processing and K-mean clustering steps undertaken.

Fig. 5 .
Fig. 5.After clustering of winter profiles for K = 3, the (a-c) diurnal patterns, and (e-f) building operations for the three clusters (a,d) winter0, (b,e) winter1, (c,f) winter2 with the number (N) of profiles within the cluster, its relative percentage, and mean (black line).

Fig. 6 .
Fig. 6.Relative importance of building parameters on Q F,B diurnal patterns for different seasons clusters.

Fig. 7 .Fig. 8 .
Fig. 7. Three winter clusters (colour) relation with (a, b) building parameters (U-value and thermal mass) and (a) number of profiles (N = 360) and (b) daily mean Q F,B ; and (c-e) median (line) and interquartile range (IQR, shading) diurnal pattern of (c) Q F,B, (d) building energy consumption (Q EC ) and (e) change in storage heat flux from human behaviour (ΔS o-uo ).(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 11 .
Fig. 11.Shoulder season in March, October and November (MON) (a-d) median (line) and interquartile range (IQR, shading) diurnal pattern of Q F,B and Q EC and (e-h) corresponding building operation mode proportions for four clusters (a, e) shoulder0-a, (b, f) shoulder1-a, (c, g) shoulder2-a and (d, h) shoulder3-a.Four cluster (i) pattern and (j) magnitude relation with building parameters (U-value and thermal mass) as in Fig. 7(a and b).

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.Liu et al.

•Fig. 13 .
Fig. 13.Range of daily mean Q F,B with U-value and thermal mass by season with whiskers (5 th , 95 th percentile), box (25 th and 75 th percentile) and median (central line 50 th percentile) shown.Each box contains the data varying building parameters (insulation position, windows wall ratio and orientation) and daily weather (9 days in each season).Note difference in X-scales between season.

Table 1
Parameter types and values used in simulations (600 cases).mixed-mode ventilation and HVAC.The building geometry uses the ASHRAE standard 140 Case 900 test model with a south-facing window and single-sided ventilation (ASHRAE, 2017).The window area is 10% openable if the indoor air temperature is warmer than both the outdoor air temperature and the ventilation setpoint (23 • C).The idealised HVAC system has fixed heating (18 • C) and cooling (26 • C) setpoints.With a centralised heating system (as Beijing has changeover

Table 2
Clustergram analysis to determine the number of clusters K.