As presented in the Introduction (see Sect. ), the parameters Tb(c) and f(c) are critical in the formulation of HDDs, influencing the daily distribution of total pollutants emitted. f is generally fixed at a constant value in the scientific literature e.g., with no variation by country or species. The reference value of f is defined here at 0.2, following (hereafter referred to as fref.). In this work we propose a spatialization of these parameters for the 27 member countries of the European Union (EU) based on national statistics on household energy use from countries with necessary information. The fraction of emissions from the residential and commercial sector that is not related to heating, designated as the f(c) parameter, is calculated for each country on the basis of the “Disaggregated final energy consumption in households” dataset . This dataset provides the quantity of energy consumed in households in European countries, disaggregated by type of fuels (according to the Standard International Energy Classification, SIEC) and activity (mainly space heating and cooling, water heating, cooking, and lighting). The statistics for 2018 are used (as that year is selected in Sect.  for the simulations with the CHIMERE model).

Several energy sources are generally used in European households, and their proportions allocated to space heating are different. As PM and NO_x emissions come from very different energy types, the parameter f(c) can be estimated for the two pollutants (fPM(c) and fNOx(c)). PM emissions from residential heating come mainly from the consumption of solid fuels and oil that are used in fireplaces, stoves and oil-fired boilers. Based on the Eurostat dataset, the average fractions of the energy classes “solid fossil fuels, peat products, oil shale and oil sands” (SFF-P1000-S2000 SIEC code) and “primary solid biofuels” (R5110-5150-W6000RI SIEC code) consumed for space heating in relation to all household activities are calculated for each EU 27 country, to derive fPM(c). The same fraction is calculated for the energy type “natural gas” (G3000 SIEC code) to represent the fraction of NO_x emissions from space heating (fNOx(c)) that comes mainly from the use of gas boilers. As biogas is mainly used for transport, it is not included. Other pollutants, such as carbon monoxide (CO) and volatile organic compounds (VOCs) for example, are characterized by the reference value (0.2, ).

Figure  presents fPM(c) and fNOx(c) for each EU 27 country. With the exception of a few countries, fNOx(c) remains between 0.1 and 0.4. Latvia (0.48), Poland (0.47), Romania (0.41) and Spain (0.54) use more than 40 % of natural gas for household activities other than heating (e.g. water heating, cooking). Portugal stands out from the other countries, with a high fNOx(c) value (0.94). Portugal uses very little gas in its energy mix for domestic activities (9 % compared to 32 % for the EU 27 average), and this small fraction is mainly used for heating water (62 % compared to 19 % for the EU 27) and for cooking (35 % compared to 6 % for the EU 27). For most countries, fPM(c) is less than 0.10. It is even equal to 0.01 for Belgium, Greece, Hungary, Malta and the Netherlands, which means that almost all solid fossil fuels are used exclusively for heating. With Portugal (0.29), Slovakia (0.25) and Finland (0.24) the highest, fPM(c) does not exceed 0.30 in the EU 27 countries.

Tb(c) is calculated by fitting it to the national domestic gas consumption statistics used as a proxy of heating use (hereafter referred to as Tbfit(c)) taken from the Transparency Platform provided by the European Network of Transmission System Operators for Gas . In this article, Tbfit(c) is compared with the reference threshold of 15.5 °C, which does not vary by country (hereafter referred to as Tbref.).

The Transparency Platform is a web tool that provides technical and commercial data on gas transmission systems for several countries. Measurements of physical gas flow at a daily frequency are available at interconnection points and connections to different types of infrastructure: liquefied natural gas terminals, production facilities, storage facilities, transmission systems, distribution systems and consumer metering systems. As industrial consumers require large quantities of high-pressure gas for their plants, they are generally directly connected to the pipelines. This ensures that the distribution network (carrying low-pressure gas) is used for domestic purposes (both commercial and residential). For the purposes of this study, only data related to distribution systems and consumer metering systems are retained. In addition, only countries for which the proportion of gas used by households for space heating is at least 60 % are kept, which ensures that daily gas consumption is an appropriate proxy for assessing the temperature threshold. Based on these criteria and available data, data are gathered for eight countries (Hungary, Romania, Italy, France, Belgium, the Netherlands, Latvia and Estonia). These countries cover the different regions of Europe, being as representative as possible of the diversity of weather conditions and building construction. The operator and the temporal coverage of gas flow data for each country can be found in the Supplement (Table S2).

Tbfit(c) is calculated by fitting the country-averaged TFHDD(c) (see Eq. ) to the temporal factor of domestic gas consumption (TFgas(c); see Eq. ) by country using an optimization solver by machine learning. Based on non-linear optimization, the Nelder–Mead algorithm provides the minimized RMSE as the successful solution. The daily TFgas(c,d) for the year n is calculated as follows: 4TFgas(c,d,n)=Q(c,d,n)Q(c,n)‾, where Q(c,n)‾ is the yearly average of distribution gas flow [kWh d⁻¹] . In order to reduce dependence on daily data for a specific year, which could be not representative of the country's domestic consumption, the fitting was based on data over several years (from 2 to 6 years over the 2016–2021 period depending on the country). TFHDD(c) is calculated from the daily average temperature, using hourly T2m data from the ERA5 reanalyses .

An example with Belgium and Romania is shown in Fig. , where TFgas(c) shows a marked seasonal cycle with a maximum in winter and a minimum in summer. It presents significant day-to-day variations during the winter period. Using the calculated Tbfit(c) (15.92 and 16.63 °C for Belgium and Romania respectively), TFHDD(c) manages to closely follow the evolution of TFgas(c). The peaks of gas consumption, corresponding to colder periods, are reproduced by the HDD parameterization. The time series of TFgas(c) and TFHDD(c) (for both Tbfit(c) and Tbref.(c)) for the other six countries are available in Fig. S1 in the Supplement.

Calculated Tbfit(c) values by country are shown in Table . TFHDD(c) using Tbfit(c) and Tbref. can be compared. The mean RMSE between TFgas(c) and TFHDD(c) is lower by -36% using Tbfit(c) compared to Tbref. on average over the eight countries. The Tbfit(c) values found for the eight European countries highlight a latitudinal gradient decreasing from 15.68 °C for Italy to 11.49 °C for Latvia. A lower Tbfit(c) means that heating in a given country is activated for a lower threshold of ambient temperature. obtained a similar south–north gradient (ranging from 16.4 to 13.5 °C) by applying linear regressions between natural gas consumption and temperature data over 2016–2019. used observed BaP in situ concentrations, as a proxy of wood burning emissions, at five urban sites in Norway to determine a Tb around 10 °C for Norway rather than the usual value of 15 °C. The Finnish Meteorological Institute applies a Tb value for calculating HDDs that varies according to the season: 10 °C from spring onwards and 12 °C from autumn onwards .

Finally, the European map of Tbfit is derived by interpolating the values of the 8 fitted countries to the other EU 27 countries using the inverse distance weighting (IDW) (Fig. ). As Sweden and Finland are not in the interpolated domain, they have been assigned the averaged value of Estonia and Latvia (11.99 °C). The interpolated value is calculated as the distance-weighted average of the central coordinates of the eight neighbouring fitted countries, as follows: 5xp=∑c=1Zxcdc∑c=1Z1dc, where xp is the interpolated value, xc the Tbfit(c) value of the Z(=8) neighbouring countries c, and d the distance (in km) between the national central coordinates. For countries outside the EU 27, the value assigned is the average Tbfit of the eight countries, namely 15.16 °C.

Several sets of emissions data are used to meet the objectives of this work. Firstly, annual gridded totals of anthropogenic emissions are provided by the Regional Inventory for Air Pollutant “CAMS-REG-AP-v5.1” . The national totals by country come from the EMEP Centre on Emission Inventories and Projections , which is responsible at the European level for compiling the emissions of the State Parties to the “Convention on long-range transboundary air pollution” (LRTAP) for official publication. The annual emission totals reported for a given year are recalculated each subsequent year in accordance with any updated guidelines and/or datasets.

Based on specific spatial proxies for the distribution of emissions, “CAMS-REG-AP-v5.1” covers the European domain at a 0.05°×0.10° grid resolution. Specifically designed for air quality modellers, it provides emission for the main pollutants (NO_x, SO₂, non-methane VOCs (NMVOCs), NH₃, CO, PM₁₀, PM_2.5 and CH₄) at a wide range of sector levels. Following , condensable PM is represented in this inventory in a consistent way for all European countries. In addition to emissions from stationary residential combustion, the “other stationary combustion” sector (GNFR_C) also includes stationary commercial combustion (which can be assumed to behave in the same way as the residential sector) and stationary combustion from agriculture, forestry and fishing, which may not behave in the same way but whose contribution to the total GNFR_C is negligible. Emissions from power stations and other industries are not covered by sector C but by GNFR_A and B respectively. The annual average spatialized contribution of sector C to total anthropogenic emissions of NO_x and PM over the period 2009–2018 (based on CAMS-REG-AP-v5.1) can be found in the Supplement (Fig. S3). On average over EU 27 countries (national totals from ), the contribution of GNFR_C is 9.1 % for NO_x, 33.4 % for PM₁₀ and 51.6 % for PM_2.5. Emissions of PM are split into primary organic aerosol (POA), elemental carbon (EC) and other primary PM based on the CAMS speciation table.

Temporal profiles for other sectors than GNFR_C are taken from the “CAMS-TEMPOv3.2” product that provides temporal profiles of European emissions of the main atmospheric pollutants. Those gridded temporal factors are available for monthly, daily, weekly and hourly cycles. Identifying the main emission drivers for each sector, the profiles are calculated on the basis of statistical information linked to the variability of the emissions (e.g. traffic counts) and parameters dependent on meteorology.

The CHIMERE v2020r1 model , a regional three-dimensional Eulerian CTM, is used to simulate air quality over the year 2018 by testing different HDD parameterizations. CHIMERE represents the processes of gas-phase chemistry, aerosol formation, atmospheric transport and deposition. The chemical scheme used is MELCHIOR2 , which includes 44 species and around 120 reactions. Aerosol microphysics and thermodynamics as well as secondary aerosol formation mechanisms are represented in the inorganic and organic aerosol module from . POAs are assumed to be semivolatile and can partition between the gas and particle phase as a function of temperature and the concentration of organic aerosols. The gas-phase fraction can react with the hydroxyl radical and form lower-volatility compounds via ageing. Secondary organic aerosols (SOAs) are formed with the hydrophilic/hydrophobic organic (H²O) mechanism. The Fast-Jx module version 7.0b calculates the photolysis rates accounting for the radiative impacts of aerosols online. Vertical advection and horizontal advection follow the scheme of . The physical and chemical time steps are 10 min. The simulated domain covers Europe, with the following coordinates as corners: 30–72° N, 25–45° E. The spatial resolution is 0.2°×0.2° (around 20 km). Nine vertical layers from 998 up to 500 hPa are used. The meteorological fields are from the operational analysis of the Integrated Forecasting System (IFS) model of the European Centre for Medium-Range Weather Forecasts (ECMWF). Time-varying boundary conditions for gas and dust aerosols are also provided by the IFS .

Natural emissions are calculated online: biogenic emissions using the MEGAN model , sea salt and dimethyl sulfide marine emissions following the scheme of and respectively, and finally mineral dust emissions based on the parameterization of and . Emissions from forest fires are not included.

In situ measurements of surface concentration are used to evaluate air quality simulations based on the CHIMERE model. These observations are taken from the European air quality observation database AQ e-Reporting , which gathers air quality data provided by EU members states and other EEA collaborating countries.

The analyses presented in this work focus mainly on NO₂, PM₁₀ and PM_2.5 species. The stations selected are background stations (urban, suburban and rural type). For the calculation of daily averages and maximums, stations that do not cover an availability ratio of at least 75% of hourly measurements are excluded. Over the whole domain, our study considers 1831 stations for NO₂, 1070 for PM₁₀ and 540 for PM_2.5 for the year 2018.

Total annual emissions from GNFR_C can be projected over several years by calculating HDDs. While emission inventories take at least 2 years to be officially published, temperature reanalyses are available in a much shorter time frame (from a few weeks to a few months). By assuming that changes in emissions from residential and commercial heating are dominated by the effect of the meteorology (rather than changes in emission factors and changes in heating habits), projected emissions (Eproj(i,j)) can be calculated using the total gridded emissions E(i,j) of the reference year nref and comparing HDD factors between the projected year nref+x and the reference year nref (Eq. ). 6Eproj(i,j,nref+x)=E(i,j,nref)×1N×f+∑d=1NHDD(i,j,d,nref+x)∑d=1NHDD(i,j,d,nref)×(1-f) Gridded emission totals from the CAMS-REG-AP-v5.1 inventory are used to model emissions of PM_2.5, PM₁₀ and NO_x from GNFR_C between 2009 and 2018. The multi-year projections using the HDD method are calculated for x=2 (equivalent to the delay in the official publication of emissions) and for x=3 (to assess the feasibility of the method in a longer publication scenario). They are compared with persistence (also for x=2 and x=3), which assumes that emissions in subsequent years are identical to those in the reference year.

In the process of emission reporting of the LRTAP Convention, countries have to update emissions for several recent years when they introduce a change in the emission calculation methodology. Therefore, to assess if the uncertainties introduced in the modelling of emission with HDDs are comparable to emissions uncertainties, we compare those different reporting years for the same target year. As suggested in the Informative Inventory Report from CEIP/EMEP , the magnitude of the recalculation can provide a general estimate of the uncertainty of released emissions. This uncertainty (U+z), expressed as a percentage, is calculated based on the average relative difference between total national emissions (E(c)) of the year (n) reported for a given year (yr) and the total for the same year but reported in subsequent years (z) up to 2 years (U+2 with z={1,2}) and 3 years (U+3 with z={1,2,3}), as follows: 7U+z(c,n)=Eyr+z(c,n)-Eyr(c,n)Eyr(c,n)×100. U+2(c,n) and U+3(c,n) are calculated in this work for the official publication of national emissions totals for each year n between 2009 and 2018 and then averaged over this period. Finally, the national totals of EU 27 countries in GNFR_C supplied by CEIP are used. This method enables uncertainty to be calculated quickly for a specific sector and by country.

In order to provide a general validation of the baseline simulation, surface concentrations simulated with the MonthTF experiment are compared with AQ e-Reporting observations over the whole of 2018, with a focus on winter (defined here from January to March) and autumn (from October to December). Table  shows the scores on daily concentrations averaged over all the European background stations. On average, annually, the bias (model minus observations) is negative for PM_2.5 (-3.09 µg m⁻³), PM₁₀ (-9.07 µg m⁻³) and NO₂ (-7.45 µg m⁻³) and positive for O3 (+8.27 µg m⁻³). In winter, the bias for PM_2.5 becomes positive (+1.99 µg m⁻³). The RMSE calculated over winter is lower (e.g. 4.30 µg m⁻³ for PM_2.5) than over the whole year (5.95 µg m⁻³ for PM_2.5) for each species analysed. The correlation coefficient R on annual average is almost equal to or greater than 0.5 for all species (between 0.47 and 0.73). It increases considerably when calculated for winter, between 0.63 and 0.81.

It should also be pointed out that these mean values show considerable spatial and temporal variability. The temporal distribution of the daily bias (see Fig. S4) and the spatial distribution of the stations with their corresponding annual bias (see Fig. S5) are presented in the Supplement. The majority of background stations included in the validation calculation are of the urban or suburban type (between 69 % and 77 % depending on the species). A representativeness bias may lead to a reduction in PM and NO₂ peaks at station points when the regional CTM simulates average concentrations over 20 km grids. Nevertheless, these scores show an overall agreement with those presented in the latest articles using the 2020 version of CHIMERE e.g., as well as with other regional CTMs e.g..

The effect of the different HDD parameterizations integrated in the emissions used in CHIMERE is analysed by comparing the Spearman correlation and RMSE scores in concentration with the available observations (stations averaged by country) for each experiment and more specifically for each country for which the Tb parameter has been calculated based on the national gas data. Using an HDD-based temporal profile, therefore with daily variation by comparison to the baseline simulation MonthTF experiment, mainly affects the simulated concentrations of PM_2.5, PM₁₀ and NO₂ from January to March and from October to December (see Fig. S4). As a result, the spring and summer seasons, when wood heating is almost non-existent in both southern and northern Europe, are not included in the analysis here. The case of the beginning of 2018, characterized by negative temperature anomalies (corresponding to cold spells occurring on a European scale) and high residential heating emissions, will be detailed in Sect. , “Threshold level exceedance during the cold spells at the beginning of 2018”, with a specific analysis on peak concentrations. Figure  shows the performance metrics for PM_2.5. There are no observations available from AQ e-Reporting for this pollutant in 2018 for Hungary, Romania, Estonia and Latvia. Analysed individually by country, performance between experiments can vary significantly. For Italy, France, Belgium and the Netherlands in winter, the DayTF_Tbfit_fspec. experiment presents the best temporal correlation, with an increase of the Spearman coefficient by +8.7%, +7.9%, +10.5% and +8.6% compared to the MonthTF experiment. In terms of RMSE scores, DayTF_Tbfit_fspec. remains close to the MonthTF experiment, although there is a slight decrease for France and the Netherlands in winter (-0.5 and -1.3 µg m⁻³ respectively). The DayTF_Tbfit experiment leads to a significant decrease in the RMSE for Belgium and the Netherlands (-1.6 and -3.0 µg m⁻³ compared to MonthTF respectively), which can be explained by a lower overestimation of the modelled concentration peaks in these countries. Indeed, the fPM parameter is lower in DayTF_Tbfit_fspec. (0.01 for Belgium and the Netherlands) than fref. (0.20). As the simulations show a positive bias for these two countries (already the case with MonthTF; see Fig. S5), the RMSE scores are higher for DayTF_Tbfit_fspec. than for DayTF_Tbfit. The validation scores obtained also depend on the accuracy of the values provided by the Eurostat dataset. The bias scores can be found in the Supplement (see Fig. S11).

For the autumn season, the HDD parameterization does not appear to have any beneficial effect on performance scores. While the correlation varies very little (about -0.03 for R compared to MonthTF), the RMSE increases, whatever the parameterization (+2.9 µg m⁻³ on average over the four countries compared to MonthTF). However, autumn 2018 does not appear to be the most relevant period for assessing the impact of HDDs, as it was relatively warmer than the average, with no major European cold spell (see Fig. S12).

Performance scores can vary considerably from one country to another (and even more so than between experiments, which, as a reminder, only differ in the parameters of the temporal distribution of heating emissions). This is discussed in more detail in the “Discussion and conclusions” section (see Sect. ), but national differences in the calculation of emissions and the representation of certain processes such as long-distance transport have an impact on the simulation scores for each country.

The equivalent figure for PM₁₀ can be found in the Supplement (see Fig. S10), with results similar to those for PM_2.5.

The spatial distribution of score variations induced by the DayTF_Tbfit_fspec. experiment (shown in Fig.  for PM_2.5 in JFM) allows us to identify the regions most sensitive to the adjusted HDD parameters. The Spearman temporal correlation is considerably better (compared to MonthTF), relatively uniformly between and within countries (up to +0.2), with the exception of Belgium, the southern Netherlands and western Poland, where the increase in the R coefficient is smaller (about +0.05). This analysis also shows that the improvement in scores also concerns countries for which the Tbfit has been interpolated. Being larger in eastern Europe (about -2 µg m⁻³), the decrease in RMSE with experience DayTF_Tbfit_fspec. does not concern all countries. The change in RMSE is almost zero in Belgium, the Netherlands, southwestern Germany, eastern Poland and Portugal. The spatial variations in scores for PM₁₀ are similar to those for PM_2.5, while they are very small for NO₂ (as discussed below).

Figure  shows the performance metrics for NO₂. With the exception of the Netherlands, Romania and Latvia, the correlation coefficient in winter varies slightly between the CHIMERE experiments. However, DayTF_Tbfit_fspec. has the lowest RMSE in winter for Italy, France, Hungary, Romania, Estonia and Latvia, with an average decrease of -4.4% compared to MonthTF. For the autumn season, HDD-based experiments do not improve the correlation coefficient (for all parameterizations tested), but the RMSE decreases by -3.6% on average for Hungary, Romania, Estonia and Latvia for DayTF_Tbfit_fspec. compared to MonthTF.

February and March 2018 were considerably colder than seasonal normals (up to -4 °C on average across Europe). Several periods of intense cold have been identified and documented by the Copernicus Climate Change Service (C3S) (see Figs. S12 and S13). Three cold spells were reported to have affected most of the European region: from 7 to 10 February, from 26 February to 4 March and from 18 to 27 March. These periods are particularly relevant for analysing the use of HDDs when residential heating increases considerably and therefore for assessing the model capabilities to capture threshold exceedance e.g..

Figure  shows the temporal evolution of simulated concentrations of PM_2.5, PM₁₀ and NO₂ during JFM, averaged over Europe. The example of France is also shown, with an adjusted identification of cold periods throughout the country from Météo-France . Time series for other countries can be found in the Supplement (see Figs. S7, S8 and S9). The simulation without HDDs (MonthTF) fails to correctly reproduce the variability driven by cold spells and relatively warmer winter periods, especially from February to March. Compared to PM_2.5 and PM₁₀ observations averaged over Europe, the MonthTF simulation completely misses the concentration peaks of 3 March (underestimation of around 20 µg m⁻³) and, in the case of PM_2.5, overestimates concentrations over the periods 15–20 February and 7–17 March (by +2 to +5 µg m⁻³).

The various peak concentrations of PM_2.5 and PM₁₀ observed during cold periods were relatively well simulated by the HDD-based simulations. The different parameterizations can lead to differences of several µg m⁻³ during PM peaks. The DayTF_Tbfit_fspec. simulation is the experiment that best reproduces the PM peaks during periods of intense cold at the European scale, with the exception of the last PM_2.5 peak around 25 March, when concentrations were slightly overestimated (up to 2 µg m⁻³).

For NO₂ species, concentrations between HDD-based experiments can vary slightly (up to 2 µg m⁻³) and more widely compared with MonthTF (up to 6 µg m⁻³). Compared to the European observations, all experiments tend to underestimate daily concentrations by -5 to -10 µg m⁻³. This does not apply to all countries, such as Estonia, Belgium and the Netherlands (see Figs. S7 and S9). Except for the peak on 8 February which was well modelled, NO₂ peaks are less well represented than PM. However, NO₂ peaks do not always correspond to cold periods. It should be pointed out that observations of NO₂ concentration levels during cold spells are not significantly higher than during other periods. This suggests that background NO₂ concentrations are less sensitive to abrupt variations in emissions linked to residential heating, such as during cold weather events. The recent literature e.g. highlights a possible significant sensitivity of NO₂ concentrations to changes in road transport emissions linked to temperature changes.

The same analysis was carried out with the maximum daily concentration (see Fig. S6), and the findings are similar. To complete this spatially averaged analysis of JFM 2018, a specific study of threshold exceedance calculated at each measurement station is presented below, detailing the differences in performance in simulating high concentrations between HDD configurations.

The numbers of exceedance of daily concentration thresholds of 25 µg m⁻³ for PM_2.5, 50 µg m⁻³ for PM₁₀ and 40 µg m⁻³ for NO₂ (based on the Directive 2008/50/EC of the European Parliament and of the Council on ambient air quality and cleaner air for Europe) have been calculated at each monitoring station over Europe for JFM months of 2018. Table  shows the average number (per station) of good detection, false alarms and missed alarms, in regards to the observed concentrations.

Compared to the MonthTF experiment, the number of good detection increases and the number of missed alarm decreases when HDDs are included, for all combinations of parameters for the species PM_2.5 (+6% on average for good detection and -4% for missed alarms), PM₁₀ (+41% and -7%) and NO₂ (+6% and -2%). The countries most concerned by these changes, according to the network of measuring stations available, are Belgium, the Netherlands, Poland and Slovakia. The number of false alarms decreases with DayTF_ref. (-12% for PM₁₀ and -2% for NO₂) and DayTF_Tbfit (-12% for PM_2.5, -20% for PM_2.5 and -11% for NO₂) and increases with DayTF_Tbfit_fspec. (+3% for PM_2.5, +1% for PM_2.5 and +19% for NO₂). However, this percentage increase in false alarms for DayTF_Tbfit_fspec. remains lower than its increase in good detection for PM_2.5 and PM₁₀.

Among the different HDD configurations, the experiment DayTF_Tbfit_fspec. has the largest increase of good detection (+11% for PM_2.5, +57% for PM₁₀ and -15% for NO₂) and the largest decrease of missed alarms (-7% for PM_2.5, -9% for PM₁₀ and -5% for NO₂). Finally, DayTF_Tbfit_fspec. presents the best probability of detection for PM_2.5 (0.45), PM₁₀ (0.21) and NO₂ (0.31), as illustrated on the performance diagrams (designed by ) in the Supplement (see Fig. S14).