A stochastic dynamic building stock model for determining long-term district heating demand under future climate change

Abstract District heating networks will face major changes on the demand side resulting from future demographic change, building energy efficiency improvements and climate change in cities. A stochastic dynamic building stock model was developed to investigate the impact of climate change and renovation strategies on district heat demand. The model was applied to a representative city in Finland comprising 3880 real buildings with hourly-resolution data, for which heat demand scenarios for buildings were simulated up to 2050 using results from global and regional climate change models. The novel stochastic dynamic building stock model utilises the real building stock as a basis and considers demolition, construction of new buildings and renovation of existing buildings. It is used in the precised dynamic heat demand model (mean MAPE 7.7%) to calculate the future heat demand. Model outputs indicated that early adoption of building renovation will decrease long-term energy consumption by 3% for every 0.5% increase in the renovation rate by 2050. Increasing the yearly renovation rate from the current 1% to 3% could reduce the district heat demand by 22% (range 19–28%). Early adoption of building renovation could reduce the relative peak load by 50% compared with late adoption. Climate change will reduce the overall heat demand for district heating but will increase the annual relative daily variation from 3.6% to 4.5%, meaning that the peaks in heat demand will be more visible.

District heating networks will face major changes on the demand side resulting from future demographic change, building energy efficiency improvements and climate change in cities. A stochastic dynamic building stock model was developed to investigate the impact of climate change and renovation strategies on district heat demand. The model was applied to a representative city in Finland comprising 3880 real buildings with hourly-resolution data, for which heat demand scenarios for buildings were simulated up to 2050 using results from global and regional climate change models. The novel stochastic dynamic building stock model utilises the real building stock as a basis and considers demolition, construction of new buildings and renovation of existing buildings. It is used in the precised dynamic heat demand model (mean MAPE 7.7%) to calculate the future heat demand. Model outputs indicated that early adoption of building renovation will decrease long-term energy consumption by 3% for every 0.5% increase in the renovation rate by 2050. Increasing the yearly renovation rate from the current 1% to 3% could reduce the district heat demand by 22% (range 19-28%). Early adoption of building renovation could reduce the relative peak load by 50% compared with late adoption. Climate change will reduce the overall heat demand for district heating but will increase the annual relative daily variation from 3.6% to 4.5%, meaning that the peaks in heat demand will be more visible.

Introduction
According to the Intergovernmental Panel on Climate Change (IPCC), buildings were responsible for 32% of total global final energy consumption and 19% of energy-related emissions in 2010 [1]. At the European Union (EU) level, thermal energy represents 50% of the total energy consumption [2], of which two-third were dedicated for heating and cooling demand in buildings [3] as of 2020. In Finland, the heating sector is the second-largest consumer of energy (26%), after industry (55%). Within the Finnish heating sector, more than half (55%) of all energy use is for urban heating through district heating, while heating activities represented 70% of total energy use in residential buildings in 2017 [4]. Thus the building sector has large untapped potential for reducing energy use and emissions [1]. District heating is regarded as the most sustainable way of providing cleaner heat under predicted future climate change [5]. Future district heating systems will also be driven by externalities at the city/district scale, such as demographic projections, building renovation and urban planning (demolition and construction). The heat demand change due to renovation and climate change in a French district on the Atlantic coast has been estimated to be around − 18% by 2050 [6]. It has also been estimated that energy efficiency measures in the building sector could reduce the heat demand in Helsinki by 15-19% by 2050 [7]. A study examining the impact of climate change on a detached house in Helsinki, Finland, reported a decrease of 15-18% in heating energy demand under the Special Report on Emissions Scenarios by 2050 [8]. On specifically examining the change in delivered energy consumption for a building with district heating and mechanical cooling, the same study found a decrease in energy consumption of 13-16% by 2050 under the same emission scenarios [8]. However, research is currently limited by a lack of information on local-scale climate variation and on the large-scale real detailed building stock that would increase model fidelity and robustness.
The EU has issued directives on the energy performance of buildings (EPBD) [9] and on energy efficiency (EED) [10]. The EPBD requires all new buildings to be nearly zero-energy buildings (NZEBs) by the end of 2020. However, it has been reported that the replacement rate of old buildings with new buildings is too low to reduce the energy consumption of buildings solely through promotion of highly energyefficient new buildings, and therefore retrofitting practices also have to be considered [11]. Recent revisions to EPBD and EDD require EU member states to establish stronger long-term renovation strategies aimed at decarbonising national building stocks by 2050 [12]. To date (late 2020), only 13 member states, including Finland, have delivered their strategies. At the same time, the International Energy Agency (IEA) reports that the rate of progress in deep energy efficiency renovations of existing buildings is slow, with annual rates of 1-2% of the existing building stock, and that this must increase to 2-3% per year by 2025 to achieve the energy efficiency goals [13]. National strategies need to be supported by local actions and coordinated with local urban planning to apply these strategies to existing and future building stocks in cities. In Finland, this energy efficiency improvement will require a decrease in heat demand of 55% compared with 2005 for all types of buildings by 2050 [14]. Achieving this will require a detailed representation of future building stock dynamics, instead of sampling and upscaling representative buildings and extrapolating the results to the entire building stock. Existing models for calculating building stock dynamics are associated with limitations and inflexibility, due to the limited amount of information available on district topology. This results in inaccurate construction, renovation and demolition strategies and lack of building segmentation.
The main objective of this study was to evaluate the influence of climate change, energy efficiency (building renovation) policy and demographic change (surface area and population variation) in urban districts on the thermal heat load throughout the heating season. The analysis was based on complete and detailed building stock data and therefore provided a delineated view of the district dynamics. The model accuracy was increased by individually modelling each building present in the district and by applying a Monte-Carlo simulation to randomise the selected buildings for renovation and/or demolition based on their age category. The aim was to help define future heat load profiles and peak demand at full district scale and to estimate future heat demand, by developing a model specifically applicable to cities using district heating system.
The remainder of this paper is structured as follows: 2 presents a review of existing work in the field of urban planning and district. In Section 3, the methodology developed to account for changes in building stocks and future climate change is explained. Section 4 presents results from a case study on a Finnish city and from an associated sensitivity analysis, while Section 5 discusses the findings on future district heating in a cold climate.

Buildings and urban planning
On a global scale, the number of persons per household is expected to almost halve from 2010 to 2050 [11]. This will lead to a significant increase in the number of households and therefore in the number of residential buildings (RBs). The energy intensity (kWh/m 2 ) of heating is expected to decline in the same period, but the higher number of households will result overall in increasing heat consumption. For nonresidential buildings (NRBs) a similar development is expected, as the area of such buildings is expected to increase [11].
Through retrofitting, significant improvements in the energy efficiency of buildings can be achieved [15,16] e.g., in residential buildings (RBs) heating energy requirements can be reduced by up to a factor of ten [17]. As urban planning reshapes cities, including those in the countries, demolition of buildings must be considered when modelling the dynamics of the city.

Building stocks
Future energy consumption of building stocks has been extensively studied, but the assumptions made and methods used to model changes in building stocks and to calculate energy consumption vary widely. Many models consider only RBs [18,19], mainly because the residential stock is well investigated [20], and the timeframe of the modelling is typically up to 2050. Construction of new buildings has been modelled as a fixed rate or based on population projections, while the demolition rate has been modelled as a fixed rate or by probability functions. However, the renovation rate has typically been modelled as a fixed rate. Few previous studies have used stock-driven models or have employed a multi-type, multi-cohort, and multi-year approach to evaluate the energy demand of existing and future buildings [18]. Overall, studies to date have used six parameters to represent building stock dynamics: population, floor area per capita, type split of construction, mean lifetime of dwellings, lifetime standard deviation (σ), and energy intensity of dwellings.

Models
To include the effect of energy demand in buildings on the future district heating network, three types of urban simulation framework are available [21]: i) Representative building simulation, ii) representative building simulation with in-country climate variations, and iii) largescale building simulation. Models for calculating the energy use of building stocks can be characterised by the dimensions they incorporate, along with the modelling techniques [18]. Three dimensions to consider are: building type, cohort, and modelling timeframe, where cohorts are typically defined by the construction year or period of buildings. Modelling techniques can be classified into three categories: accounting models, quasi-stationary models, and dynamic models. Dynamic models can be further classified into activity-driven or stock-driven models [19]. In activity-driven models, construction and demolition rates are typically based on recent trends and are the main drivers for the model [22], whereas stock-driven models are based on changes in building stock demand, based on the population, lifestyle and economic growth [23]. Construction rate has to satisfy the demand and take into account the demolition rate of buildings. Demolition of buildings can be modelled by a fixed demolition rate [23] or a demolition probability function utilising either a normal distribution [18] or a Weibull distribution [24]. Renovation rate can be modelled using an endogenously defined renovation rate or a renovation probability function [25]. Comparison of modelling methods presented in recent studies is provided in Table 1.

Demolition rate
Future building stocks are typically estimated based on demolition of existing buildings and construction of new buildings. In a study covering the period 2000-2012, the demolition rate of buildings in Finland was found to be linked to demographic changes, new construction, and type and size of settlements, with larger cities with a growing population having more new buildings constructed and more buildings demolished than smaller municipalities [31]. Building type was also found to affect the demolition rate, with a higher rate for NRBs than for RBs, while building age was found not to be the primary reason for demolition, although NRBs were shown to be demolished at a younger age than RBs [31]. The average demolition rate in Finland between 2000 and 2012 was 0.25% [31]. This is much larger than the average demolition rate reported for other European countries, e.g., in the period 1980-2000 the average demolition rate in Western Europe was 0.09% (σ = 0.03), except for the Netherlands where it was 0.17% (σ = 0.04) [32].

Renovation rate
The renovation and replacement rates of buildings must also be considered alongside the demolition rate, when assessing the future energy consumption of buildings. In one study, simple calculation methods were used to estimate the energy use of building stocks from 2005 to 2050 [16]. Renovation and replacement of old buildings was considered in that study, together with improvements in energy intensity. In addition, the net increase and the energy intensity of the new floor space each year was accounted for. Six scenarios with low or high growth in floor area and one of three different cases of energy intensity improvements were considered [16]. Energy intensity was found to decrease by 30-60% by 2050, depending on the scenario. In two of the scenarios, energy use was 10-30% higher in 2050 than in 2005, while in the other scenarios energy use was 10-50% lower in 2050 [16]. These results indicate that improvements in the energy efficiency of new and renovated buildings have to be rapid to reduce energy use in buildings. This is because buildings have long lifetimes and buildings constructed and renovated today will exist long into the future. Therefore, state-ofthe-art performance levels are required for new and renovated buildings to avoid long-term sub-optimal outcomes [1].
According to most estimates, the renovation rate in European countries (EU27) is 0.5-2.5% of the building stock per year [22] with a mean renovation rate of 1%. The renovation frequency for buildings constructed in 2011-2020 is commonly set at once during a 10-year period, at a rate of 0.5% of the building stock each year.
In Finland, the actual renovation rate for building shells was 3.7% in 2000 [33]. However, when the reasons for renovation were examined, it was found that only 18% of these renovations were aimed at increasing the energy performance of the shell, while in over 60% of cases the reason for renovation was damage repair or maintenance [33]. Renovation of heating and ventilation systems showed a similar pattern. Therefore, it is clear that not all renovation activity results in improved performance of buildings, leading some studies to assume that only 20% of renovations result in significant energy efficiency improvements [34].

Surface living area
Another aspect influencing energy consumption in buildings is the surface area per person, which affects both total energy consumption and the energy intensity of the building. Methods to include the variation in surface living area vary, but most use exogenous variables such as gross domestic product (GDP) or population projections. A first approach estimated the future change in residential floor space from 2005 to 2050 by multiplying future population numbers by estimated future floor area per capita approximated using GDP per capita [35]. This approach indicated that the floor area would increase by 110% compared with the existing building stock, i.e., more than half of the building stock in 2050 would be new buildings and the majority of current buildings would still be present [35]. The total floor area in EU-27 has been estimated to increase by 27% by 2050 compared with 2005 [23]. A second approach considered the floor area for RBs based on floor area per capita estimates and population projections [23]. Floor area calculation for all NRBs except industrial buildings was based on GDP per capita in 2005, which was divided by the NRB floor area for the same year. This produced a constant which was then multiplied by GPD for a given year to give the future floor area demand for NRBs.

Energy efficiency improvements
Population growth, in combination with increased surface living area in districts, results in an increase in new buildings and renovated buildings in the building stock. Renovation rate was addressed in Section 2.1.3, so this section focuses on the level of the renovation. Renovation may be used as a mean to increase the energy efficiency of buildings [22], with renovations divided into four categories based on the estimated energy efficiency improvement: Minor renovation, i.e. implementation of a single measure to improve energy efficiency, with an assumed energy efficiency improvement of 15%; moderate renovation, i.e. implementation of multiple measures and with an assumed energy efficiency improvement of 45%; deep renovation, i.e. a holistic approach to renovation using a package of measures working together, with an assumed energy efficiency improvement of 75%; and profound renovation, i.e., where the building is renovated to the level of nearly Zero Energy Building (nZEB), with an assumed energy efficiency improvement of 95%.
Energy efficiency improvements may be used in various combinations to achieve e.g. deep renovation or business-as-usual (BAU) This study renovation. One previous study [23] considered three different scenarios (deep, moderate, frozen) for energy use dynamics. In the deep efficiency scenario, state-of-the-art building practices were implemented for new and renovated buildings from 2022, with most new and renovated buildings being highly energy efficient, achieving 90% energy savings compared with the existing stock average. The moderate efficiency scenario assumed an accelerated renovation rate from 1.4% in 2005 to 2.1% in 2020 in EU-27, but the new and renovated buildings had far lower efficiency levels than state-of-the-art solutions, achieving approximately 30% energy savings compared with the existing stock average as stated in the Finnish Building Code. The EPBD requires all new buildings and 50% of renovated buildings to achieve high energy performance by 2020, and all new and renovated buildings to achieve this by 2030. The frozen efficiency scenario assumed that the energy efficiency of new and renovated buildings was not improved compared with the 2005 level, that renovated buildings consumed 10% less heat energy than standard buildings and that new buildings had higher energy consumption than in the moderate scenario. The retrofit rate was assumed to be constant at 1.4% for the whole period [23].

Dynamic model description
The model developed in this work is of the large-scale building simulation type, where scenarios for future heat demand are constructed utilising real building stock data, in this work data for individual buildings. However, it utilises methods and approaches from the first two categories presented in [21] (see Section 2.1.1), thus forming a unique approach to district heating modelling. Future hourly heat demand for individual buildings is modelled using historical heat demand data and projections on building stocks and population. Changes in the building stock, including RBs and NRBs, are considered. Three subgroups of RB are considered: detached houses, row houses and apartment buildings.
A data-based dynamic heat demand model is used to calculate the future hourly heat demand of individual buildings. Future building stock is modelled by estimating the rates of demolition of buildings, construction of new buildings and renovation of old buildings. The approach combines stock-driven and activity-driven methods. Construction of new buildings is stock-driven as it is based on population growth and change in living area per person. Demolition and renovation are activity-driven as they are based on past trends and policies. Fig. 1 presents the framework for the calculation of scenarios of future heat demand, which also considers climate change. All modelling and simulations reported here were done in the MATLAB® environment (version R2018b). The building stock model (BSModel) is publicly available on GitHub [36].

Heat demand model
The dynamic heat demand model presented in [37] is used to predict the heat demand of individual buildings. For city level heat demand prediction, the model presented an average MAPE of 4%. The model was initially developed for the optimisation of the heat demand at the city level. Therefore, it has low number of free parameters and input variables to enable the ease of application to the whole building stock comprising hundreds or even thousands of buildings. The model predicts the long-term heat demand based on past heat demand and heat loss caused by the temperature difference between indoor and outdoor temperature variations while daily variations in heat demand are taken into account using a residual model: where P t is the predicted heat demand at time t [kWh], P t− 1 is the measured heat demand at time t -1 [kWh]. T in,t and T out,t are the indoor and outdoor temperature at time t [ • C] respectively. Parameters a and b are parameters estimated by fitting the model to historical heat demand data and minimising root mean squared error (RMSE) between the model predictions and the measurements. Parameter U is a buildingspecific physical heat loss coefficient [kW/K] that is estimated based on the volume of the building. Term w t is the value of the residual model at time t and it is the hourly average of the residuals of the output from the dynamic model (inside the brackets in (Eq. 1)) and the measured heat demand. Indoor temperature (T in ) at a constant value of +21 • C is assumed. For multiple hours ahead in heat demand predictions, previous prediction results are used as inputs to the model. For more details of the heat demand model, see [37].

Building stock model
The future building stock is generated using the existing building stock, which is modified taking into account the annual rate of demolition of buildings, construction of new buildings, renovation of old buildings, the floor area per person and population variation projections. The model for the building stock is then:  Table 2.
Existing buildings in the original building stock undergo normally distributed renovation for RBs and at a fixed rate for NRBs. Demolition of old buildings occurs based on a Weibull distribution rate for RBs and a fixed rate for NRBs. Construction of new buildings occurs based on demographic change i.e., population and floor area per person projections. This results in the building stock at the start of the next year. Calculations are continued until the building stock for the final year (2050) is produced. Renovation, demolition and new construction are discussed in more detail in the following sections.

Renovation of old buildings
Renovations are performed on many different components and systems in buildings and have different levels of impact on the performance of buildings. As the aim of this work was to estimate heating energy consumption, the renovation model is considered to include at least 'moderate' renovation measures [22] that significantly improve the energy efficiency of the buildings. The estimated renovation rates used in the model apply for renovations that result in significant improvements in energy efficiency. Regular maintenance and 'minor' renovations to maintain energy efficiency at the original level are assumed to happen, but are not considered separately in the model.
Four renovation scenarios (RS1-4) are considered to evaluate the impact of renovation rate policies of residential buildings in a city, ranging from a low renovation rate to active renovation of buildings Table 3. The renovation rate for 2013 (RS1) is the average renovation rate in Finland and the increased renovation rate scenarios (RS2-RS4) are set to end in 2050 with a renovation rate of 3% per year. For NRBs, a linear fit is used to give the renovation rate for each year (parameter REN NRB ). Renovation of RBs is modelled using a normal distribution, similarly to [25]. The mean of the normal distribution (parameter μ Ren ) is first set to 53 years, which equates to about 1% annual renovation rate for RBs, and is then adjusted each year to match the linear fit renovation rate.
Renovated RBs are randomly chosen from among the RBs with higher than average characteristic heat demand for their building and age group. This could mean that some buildings are never renovated and some buildings are renovated multiple times. A similar approach is used for NRBs. However, as information on age of the buildings is not available, renovated NRBs are randomly chosen from among the NRBs with higher than average characteristic heat demand. It is assumed that after renovation, the energy efficiency of the buildings increases by 30% (parameter η REN ) and there is a 10-year period (parameter t REN ) when the buildings do not undergo new renovation and are not demolished.

Demolition of buildings
Demolition of RBs is modelled using a Weibull distribution, which is considered the most adequate distribution for modelling demolition of buildings [24,31,38]. The three-parameter Weibull probability density function is defined as: where t⩾k 3 ⩾0, k 2 > 0 is the shape parameter, k 1 > 0 is the scale parameter and k 3 is the location parameter. The Weibull probability density function is zero at time t < k 3 , which can be used to set the initial time period after the construction when the building is not demolished. When 1 < k 2 < 2.6, the Weibull distribution produces a right tail representing the long lifetime of buildings. In Finland, a total of 50,818 buildings were demolished between 2000 and 2012 [31]. The average annual demolition rate for all buildings was 0.25%, while for RBs and NRBs it was 0.15% and 0.65%, respectively. The average age of RB at the time of demolition was 58 years [31]. Considering these findings, the parameters of the Weibull probability density function (Eq. 3) in the model are set so that the average annual demolition rate for RB is 0.15%. The mode of the Weibull distribution is assumed to be 58 years and the value of the location parameter k 3 is assumed to be 10 years. With 0.15% average annual demolition rate, the value of the scale and shape parameters k 1 and k 2 is 473.1 and 1.09, respectively. Considering the time t, these parameters produce a very long lifetime for the buildings (~468 years). This is probably not realistic, but gives the desired demolition rate. In [19], a mean lifetime of 125 years and a 40-year period of no demolition after construction was typically assumed for RB stocks in European countries. This would give an average annual demolition rate of >0.4%, which is much higher than the 0.15% found for the Finnish RB stock by [31].
As construction year or decade for NRBs was not included in the original dataset of buildings, the demolition rate for NRBs (parameter DEM NRB ) in the model is set to achieve the reported average annual demolition rate of 0.65% [31].

Construction of new buildings
The construction of new RBs is modelled using annual population projections and estimated floor area per person. This gives the annual total floor area needed for RBs. By subtracting the floor area in the previous year from the calculated floor area needed for the current year, and taking into account the demolition of RBs, the amount of new floor space needed can be calculated.
The original data for the buildings include information only on the volume of the buildings, and not on the floor area. Therefore, it is necessary to convert the calculated floor area needed to volume. Monthly data from Statistics Finland [4] for the volume and floor area of new RBs built from 1995 to July 2019 show the following linear correlation between volume and floor area of RB stock: where As the building stock using district heat is only part of the building stock in a city, it is necessary to calculate the annual percentage change in floor area and volume. Assuming that the demographic development is evenly spread throughout the city, the same change in building volume is considered throughout.
According to Statistic Finland [4], from 1995 to 2018 the annual total volume of new NRBs was around 50% larger than the annual total volume of new RBs. This was also the case for the last five years of the period (2014-2018). Therefore, it is assumed in the model that the annual total volume of new NRBs is 50% larger than the calculated annual total volume of new RBs (V New,NRB = 1.5⋅V New,RB ) in this work.
New RBs are duplicated from the RBs of the 2000s in the original dataset. The proportions of detached houses, row houses and apartment buildings among the new RBs in terms of volume are assumed to be similar to those in the original building stock. In the case of NRBs, the new buildings are duplicated from the NRBs of the original dataset with lower than average characteristic heat demand, as there is no information on the age of the buildings. Mixed-integer linear programming is used to determine the buildings and give the required volume increase. New buildings are not added in cases where the volume increase is negative or zero. The problem is defined as follows: where f is a vector containing the volume of all the buildings that could be added, and x is a vector of integers with values between zero and three representing the times a certain building is added. The inequality constraints are applied to allow a 0.1% deviation from the calculated volume increase V inc as it is possible that the exact value cannot be reached. Mixed-integer linear programming solver intlinprog in MAT-LAB® is used to solve the problem in Eq. 5.
In line with the Finnish Building Code and EPBD, new buildings built in the 2010s are considered in the model to be 30% more energyefficient (parameter η New,2010 ) and buildings built in 2020-2050s to be 50% more energy-efficient (parameter η New,2020 ) than buildings built in the 2000s.

Climate change scenario
The selection of the suitable future weather file creation depends on the available data, selected simulation scenarios and required output of the data. Currently, there are two sources of climate change data available for Finland for Representative Concentration Pathway (RCP) scenarios for 2030 and 2050: -Ensemble results from the recent Global Climate Models (GCMs) produced within the fifth Coupled Model Intercomparison Project (CMIP5) on long-and near-term changes [39]. This data is available for Finland in [40], and was downloaded and modified for long-term monthly means from [41] for years 1975-2085 and daily mean [42], maximum [43] and minimum outdoor temperature values [44] for years 1981-2100. The available climate change scenarios are RCP2.6, RCP4.5 and RCP8.5. -Regional down-scaled results simulated with Regional Climate Models (RCMs) [45] from the European Climatic Energy Mixes (ECEM) Demonstrator created by Copernicus Climate Change Service (C3S) 1 . This data is available as monthly and daily mean outdoor temperature values for South Finland cluster for 1979-2100 period and RCP4.5 and RCP8.5 scenarios.
Due to the available climate change data and the demand for an hourly based outdoor temperature data, the future weather datasets are created with a commonly used, statistical down-scaling method called morphing [46]. Morphing is based on a historical, hourly baseline weather data, and monthly and daily future climate change data. To take into account the change in monthly average temperature and the change in daily temperature variation, a method combining shifting and stretching Eq. 6 is used: where T is the morphed temperature [ • C], T 0 is baseline temperature where ΔT max,m is the change in daily maximum temperature in month m [ • C], ΔT min,m is the change in daily minimum temperature in month m [ • C], T max,m is the average daily maximum temperature on the baseline scenario on month m [ • C] and T min,m is the average daily minimum temperature on the baseline scenario on month m [ • C] [46]. A rather similar method was created and tested by Räisänen and Räty (method M2) [47] and used in [48] where stretching α m was conducted by using the change in monthly standard deviation of simulated climate change and baseline scenarios according to Eq. 8: where σ s is the daily standard deviation of the outdoor temperatures simulated scenario for the morphing period [-], and σ b is the standard deviation of the outdoor temperature in the baseline climate [-] [48]. In all calculation methods the absolute and relative changes are calculated according to their 30-year average values to reduce the impact of single year variation in the data.
To improve the reliability of the model results, 5 baseline scenarios (S1-S5) were selected to present both mean and extreme weather scenarios: -S1: Cold2010 -coldest January taken as a reference point for morphing future cold events.

Fig. 2.
Flow chart describing the future weather files creation process for creating outdoor temperature profiles. The method was applied using Jyväskylä's Airport weather observation station in January for two extreme weather datasets, Cold2010 and Warm2008, in scenarios S1 and S5, including each RCP 2.6, RCP 4.5 and RCP 8.5 for 2030 and 2050 morphed using the projections distributed by the Finnish Meteorological Institute [40]. (see electronic version for colours). The Finnish Meteorological Institute has released a test reference year (TRY) dataset representative of a "typical" weather for the years 1980 to 2009 (TRY2012) [50] that was used in building energy demand calculations in [8] A typical meteorological year (TMY) dataset has been created by [49] for the period 1952-2017 and a newer dataset for 2004-2018 according to TMY/ISO 15927-4:2005 methodologies. To increase the reliability of the model results in including extreme weather conditions when assessing changes in warm and cold winters, representative cold winter (S1) and warm winter (S5) datasets are used [51]. The selection and downloads are based on the coldest and warmest January in available localised datasets from the Finnish Meteorological Institute's open data repository 2 . All the datasets include hourly outdoor   [4], the red segment is a projection for 2019-2040 as reported by Statistics Finland [4] and the green segment is a projection made with a one-term. Gaussian model.
temperatures to be used in the simulations. To match the case study used for validating the model (see Section 3.4), the TRY dataset is taken from a created area III, and the TMY and representative cold and warm winters are taken and created based on observations from Jyväskylä Airport weather observation station. The basic principle for the creation of the future weather files with morphing by using historical and test year data as baselines, and climate change data as future projections, is presented in Fig. 2 together with an example for January baseline and future weather data files for Cold2010 and Warm2008 scenarios. The presentation of the morphed future weather files, additional information and detailed dataset on the baseline and climate change projection data are available as SI [52].

Case study: Jyväskylä
To test the model developed in this study, it was applied to the case of Jyväskylä, a city in central Finland, often taken as a trade-off city when considering the entire energy need in Finland. Jyväskylä has around 140,000 inhabitants and district heating covers almost 75% of the population (2018 data). It has the 10th largest district heating network in Finland, with a capacity for heat production of 940 GWh/y (2018 data).
Heating season data from 2013 consisting of hourly measured values of heat demand for individual buildings in Jyväskylä and of outdoor temperature are available. Data on the volume of all buildings are also available. Table 4 shows the number of buildings in different groups and the measured heat demand for Jyväskylä in the 2013 heating season (all months from October to April). The general terms of contract for DH in Finland [53] state that the measurement error for heat demand cannot exceed 5%.
Data on RBs, i.e. apartment buildings, detached houses and row houses, also contained information on the construction year. Table A.8 shows the number of RBs in different age groups and their measured demand for heating in the heating season 2013 [56].
Changes in population (pop) and floor area per person (A fp ) in the city of Jyväskylä in the period 2013-2049 are shown in Fig. 3. Recorded values for 2013-2018 and the population projection from 2019 to 2040 are taken from Statistics Finland [4], and the projection for 2041-2049 is made with a one-term Gaussian model. Country-wise, the floor area per person is projected for 2019-2049 by assuming 0.2 m 2 /person annual increase, which is close to the average increase between 2010 and 2018 (see also Section 4.1.2 for sensitivity analysis of this parameter). Jyväskylä's district heating network is expanding as the city grows. In 2013, the network served 94,025 individuals from among a total population of 134,719 inhabitants, and supplied 901.6 GWh. During the heating season (October-April) 2013, buildings (excluding 16.5% of buildings with large data gaps) used 657.2 GWh of heat. The heating period therefore represents 73% of the overall yearly production from the district heating network. The other 27% is heat use outside the heating season, e.g. hot water consumption.

Results
The results obtained in the case study were first screened through model validation of the heat demand and building stock models and sensitivity analysis. The results were then analysed to determine the impact of renovation strategy and climate change on overall heat demand and peak load variations.

Model validation
The accuracy of the developed modelling approach depends on the accuracy of both the heat demand model and the building stock model. Therefore, both models were validated against real data. The heat demand model was validated using measured data from the heating season 2013. The building stock model was validated with statistical building stock data from years 2013-2019 and by performing sensitivity analysis.

Heat demand model
A model for each month of the (seven-month) heating season was created for every building. One month of data was used for parameter estimation and data from the other six months were used for validation to estimate the model performance with unseen data. Parameter estimation and validation for 3880 buildings took approximately 10 min, using local parallel computing in MATLAB®. The results of the validation are summarised in Table 5 (detailed validation results can be found in Supplementary Information section S1.1 [57]).
The correlation with validation data was high for all monthly head demand models, with MAPE of 7.7% (σ = 4.6) on average (range 2.2-20.7%) as some months are considerably different from others with respect to outdoor temperature. As the heat demand model is databased, model performance could be expected to decrease with validation data that differ significantly from those used for parameter estimation. It was found that the MAPE with parameter estimation data was 5% or lower for all models when considering all buildings. The heat demand model proved to be much more accurate than other data-driven models developed for similar regions [7]. The model can be used to predict the heat demand with reasonable accuracy for datasets with a similar outdoor temperature range and weather conditions to Finland.

Building stock model
Statistical information on the buildings stock of Jyväskylä DH system from years 2013-2019 [58] was used to validate the building stock model. Composition of the modelled building stock in 2014-2019 was compared with the statistics. As the initial building stock data for 2013 used in this study did not include all the buildings that were in the Jyväskylä DH system in 2013 (see Table 4), the number of excluded buildings was assumed to be missing also from the building stock of 2014-2019. Validation results are shown in Table 6. On average, there is a 2.5% deviation between the statistical number of buildings and the modelled number of buildings in 2014-2019. Furthermore, both the modelling results and the statistics show a 10.7% increase in the volume of the building stock from 2013 to 2019. Applying the heat demand Table 5 Validation results for the heat demand model through the Pearson correlation coefficient r, Root Mean Squared Error (RMSE), Absolute Percentage Error (APE), and Absolute Error (AE), and their associated standard deviation σ. model for the modelled 2019 building stock revealed that the relative error between the modelled heat demand and recorded heat demand was 3.7%. These results indicate that the developed building stock model can be used to accurately model the changing building stock.
In sensitivity analysis to further validate the building stock model, the value of each parameter or variable was altered by 20%, while the others were kept constant, and the effect on the outputs (rates of annual renovation, demolition and new building construction, total and peak heat demand) were analysed. For pop and A fp this change meant that the annual growth or decrease was adjusted accordingly. Wilcoxon rank sum test was used to test the equality of the medians achieved with the base value of the parameter or variable and with the changed value. The results are presented in Table 7.
The results of the sensitivity analysis confirmed the accuracy of the building stock model, as altering the input parameters and variables had the expected effects on model outputs. Total and peak heat demand were most sensitive to the parameters η Ren and η New,2020 . The next largest impact was from μ Ren , DEM NRB , NEW NRB and pop. Full details of the analysis can be found in Supplementary Information section S1.2 [57].

Heat demand scenarios
The heating season heat demand for building stock in the year 2013 was calculated by applying the original outdoor temperature data from the different climate change scenarios (S1-S5). This heat demand was then used as a reference point for the future scenarios. For each scenario, 100 building stocks were generated using the building stock model developed. Future heat demand for the heating season of 2030 and 2050 was calculated for each building stock using the heat demand model and all future outdoor temperature data from each of the RCP climate scenarios. Total heat demand for each scenario, year, climate data and source is depicted in Fig. 4. The impact of the RCP scenario between all datasets was around 3.9%, meaning that the heat load reduction related to the effect of climate change was around 21.3% on average (σ=1.9). The remaining heat load reduction was due to the renovation strategy (RS1-RS4).

Renovation strategy 2030-2050
The energy efficiency renovation strategies for buildings were analysed through the four scenarios (RS1-RS4) explained in Table 3. The scenario S1-RCP4.5-GCM was used to analyse the impact of building renovation on the overall heat demand in the district. The renovation scenarios are compared in Fig. 5a and an in-depth analysis using the RS4 renovation scenario is provided in Fig. 6a.
Increasing the renovation rate of buildings had a significant impact on the long-term energy need of the district already in 2030 (Fig. 5a). The energy demand from district heating was reduced by 9.8% in the coldest scenario (S1) or by 12.2% in the warmest scenario (S5) by 2050 (Fig. 5a). However, the impact of increasing the renovation rate from the current 1% to 3% reduced the heat demand in the district by 21.1 to 23.2% for the same scenario. While the 2050 target of 3% renovation rate clearly reduced the heat demand overall, delaying the increase in renovation rate to after 2030 influenced the end target of heat demand reduction by 2050. Each 0.5% increase in the renovation rate of buildings by 2030 brought about a 3% decrease in energy demand by 2050. The spread of heat demand reduction by 2050 varies from − 7.9% to − 28.5%. This is in the range of heat demand reduction found in the literature from energy efficiency measures only [7] or using typical building stock model [6] as illustrated in Fig. 5b. The effect of renovation policy is clearly depicted on Fig. 5b, where the mean heat demand reduction reaches − 13% with the conservative renovation scenario RS1 and − 23% using the renovation policy scenario RS4.
In the most renovation-intensive scenario (RS4), the decrease in heat demand varied between 19.7% and 28.3% compared with the 2013 baseline with all climate scenarios. The results had to be adjusted by the demographic change in the city, and therefore the energy intensity variation was used to compare the energy efficiency improvement through the renovation scenario (Fig. 6b). The energy intensity was found to decrease from 24.5 to 15.45 kWh/m 3 representing a decrease of 34-58% for the whole building sector compared with the 2005 baseline. However, none of the buildings in the conservative policy scenario RS1 reached the 2050 target of − 55%, which was only fully reached in climate scenario S5 plus renovation policy scenario RS4.

Heat peak load variation
Peak load can be measured in two ways, peak load variation due to the combined effect of population and living space variation and peak load variation due to climate change. The effects of the four renovation scenarios on the daily heat load profile of the district heating network are shown in Fig. 7. Increasing the renovation rate of buildings was assumed to decrease the heat demand in buildings, while domestic hot water demand was assumed to remain at the same level. The daily and hourly variation in heat load was also analysed, through their relative

Table 7
Change in the median renovation, demolition and new construction rate and heat and peak demand when parameter or variable is changed by ±20%. Highlighted values mean that there is a difference between the medians at the 95% significance level according to Wilcoxon rank sum test and the difference is more than 1%.
variation in total annual energy demand of the district heating, using metrics previously established in the literature [59]. The average annual relative daily variation was found to be 4.02% for the year 2013 (Fig. 8).
Overall, the annual relative daily variation increased in almost all future scenarios, indicating a relative increase in the daily peak operations of the district heating system. The warmer the scenario (S1? S5), the higher the annual relative daily variation as the yearly heat demand decreased, confirming previous findings [59]. However, the reason for this correlation was different, with more visible peaks with increasingly warm scenarios although the overall heat demand base load decreased. The   Table 3 for details) on final heat demand in 2030 and 2050 for the entire heating season (October-April) for all buildings in the city of Jyväskylä. Climate scenario S1-RCP8.5-GCM. (b) net heat demand decrease in all climate scenarios (S1-S5) compared with the 2013 level for renovation scenario RS4.
relative hourly variation (Fig. 8) showed more hours with high peaks of up to +35% of the daily load variation, which was expected. The highest hourly variation in the warmest scenario (S5) (+16.5%) was half that the coldest scenario. However, relative analysis of the data provides only a comparison between the dataset of the same year, while the time dimension is required to examine absolute changes. Therefore, the daily heat load profile of the district heating network and associated standard deviation shown in Fig. 7 better represented the variation in absolute terms. The peak load variation was measured by calculating the difference of variation of the standard deviations of each peak load variation. The peak load variation due to the combined effect of population and living space variation was analysed as the variation in difference between indoor and outdoor temperature, with an indoor temperature setting of 21 • C, as specified by law in Finland. The slow renovation strategy (RS1) gave an increase in the heat load peak profile of 12% in 2030 and 7% in 2050. In all renovation scenarios (RS1-RS4), the heat load increased by 2030 due to the increase in living space and population (+12% and +9.1%, respectively) ( Fig. 7e-h). However, by 2050 the heat load had decreased in RS3 and RS4 in 2050 (− 3.3% and − 6.3%, respectively).
The peak load variation due to climate change is directly linked to the variation in outdoor temperature and was analysed through the variation in volume space in the building stock. The variation due to climate gave lower daily variation in the heat load profile of the district heating (σ =.32 in 2013) and, as the temperature increased overall in all climate and RCP scenarios, the load profile was always lower in 2030 (− 20%) and 2050 (− 35%) (σ between the RS1 and RS4. However, the impact of the difference in 2050 is much greater with a variation of − 26% to − 35% (Fig. 7(a-d)). The impact of renovation scenario in 2030 was minimal, with only a 2% difference in standard deviation between RS1 and RS4. However, the impact was much greater in 2050, with a variation of − 26% to − 35% in load profile for RS1 and RS4, respectively. This reflected the intensity of the renovation strategy, as seen in Section 4.2.1.
Finally, combining both effects gave the heat demand profile in terms of energy intensity (Fig. 7i-l). The high decrease in peak heat load profile due to climate change was balanced by the increase in living space. Overall, however, there was a decrease in peak heat load profile from 20% to 30% (− 50% relative change) in 2050 for RS1-RS4, respectively.

Discussion
The results obtained using our new modelling approach confirmed that simply increasing the energy efficiency of new buildings is not sufficient to achieve a significant reduction in heat demand of the building stock. Renovation of old buildings was shown to produce major reductions in the heat demand, but an annual renovation rate of 2-3% would be needed, instead of the current 1%, to achieve a significant impact. The results indicated that an average improvement of 30% in energy efficiency through renovation of old buildings will not be enough to support the goal in Finland of reducing heat demand in the building sector by 55% by 2050. A greater proportion of moderate to deep renovation energy efficiency actions and an increased rate of new buildings would be required when considering heat demand as the main key performance indicator. In urban planning, it would therefore be more pragmatic to use energy intensity (kWh/m 3 ) as an indicator, to fully consider demographic change in cities. In the case study city of Jyväskylä, an improvement in energy intensity (kWh/m 3 ) of 42-58% compared with the 2005 baseline can be expected, depending on the climate scenario (S1-S5). In other words, large cities with heat demand on the decline in 2005 will have little problem reaching the 2050 goal, while medium-sized cities with heat demand on the rise in 2005 will face major challenges in complying with the 2050 policy target for energy reduction in the building sector.
In different scenarios, the final volume and heat demand of NRBs varied more than those of RBs. This was to be expected, as NRBs are a very heterogeneous group, including buildings with widely different volumes and heat demands. Another factor that contributed to the difference between RBs and NRBs was the demolition of buildings. For RBs, the age of the buildings was known and, at a particular demolition rate, the same number of buildings of a certain age will be demolished. Although the demolition of RBs was random, the group of RBs that could be demolished was smaller than in the case of NRB.
In this work, it was assumed that the calculated heat demand was supplied to the building stock by the district heating system. However, local production is likely to increase in future, which would reduce the heat production requirement from district heating. Some buildings could be entirely self-sufficient in heating and need no additional supply of heat from district heating.
This work considered heat consumption and changes in future due to changes in the climate and in building stock. Energy efficiency improvements on the consumption side through renovation and more energy-efficient new buildings were considered. The energy efficiency was assumed to increase due to better insulation and more effective heating equipment. However, possible changes in the way people use heating or implementation of advanced control systems [60] could also affect the heat demand, but were not considered. In all climate change scenarios tested, the results showed that renovation policies to improve the energy efficiency of buildings need to be implemented rapidly, instead of defining long-term suboptimal outcomes.

Conclusions
A dynamic stock-driven model was developed to assess the impact of climate change and urban planning strategies on heat demand in cities. This model, which is generalisable to other locations, requires district heating historical data, including base statistics on the characteristics of the building stock. The model was applied to the case of Jyväskylä, a representative city in Finland. This novel approach to analysing heat demand in district heating increased the model precision, with average MAPE of 7.7%.
Model outcomes indicated that building renovation and actions to raise the energy efficiency level of existing and new buildings are critical in decreasing the heat demand in cities and respond to policy targets. However, non-linear population variation, combined with increasing living space per capita, was shown to limit the impact of energy efficiency actions. The 2050 target was partially met in terms of energy intensity reduction but not in energy consumption terms. Intermediate and fast actions to implement energy efficiency actions had an even greater impact on the heat load reduction. It is therefore necessary to combine long-term and short-term efforts to meet the energy reduction requirement. Energy efficiency actions had a similar effect on the peak load, but with higher renovation rate decreasing the peaks in absolute heat load profile.
The current renovation level of 30% increased efficiency in buildings is not sufficient for reaching the 2050 goal, even if the renovation rate is increased from 1% to 3%. An estimated average renovation level of 60% increased efficiency in buildings will be necessary to reach a heat demand reduction of 50% in the building sector by 2050. When translating national targets into regional and/or municipal plans, demographic change in the city should be carefully assessed, and therefore energy intensity may be a more relevant metric for cities.
Future district heating will face changes in peak load that should be considered when planning future investments. However, as the overall demand will tend to decrease, the absolute peak will be lower than at present (reference 2013). Energy efficiency policies in the Energy Performance in Buildings (EPBD) and Energy Efficiency (EED) directives should enforce stronger mid-term renovation strategies, to support the long-term goals for decarbonising the building stock by 2050.