New External Design Temperatures and Geospatial Models for Poland and Central Europe for Building Heat Load Calculations

: This article proposes new values and geospatial models of winter and summer external design temperatures for designing buildings’ heating, ventilation, and air-conditioning (HVAC) systems. The climatic design parameters applicable in Poland for the sizing of these installations are approximately 50 years old and do not correspond to Poland’s current climate. New values of climatic design parameters were determined following the methods described in European standards and the American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) Handbook of Fundamentals. The determined climatic design parameters, particularly the winter and summer external design temperatures, were compared with those currently in force by law in Poland. The external air design dry-bulb temperatures presented in the article were developed based on meteorological and climatic data from the years 1991–2020 from two data sources: synoptic data from the Institute of Meteorology and Water Management (IMWM) in Poland and reanalysis models of the ERA5 database of the European Centre for Medium-Range Weather Forecasts (ECMWF). According to ASHRAE, with 99.6% and 0.4% frequency of occurrence, external air design dry-bulb temperatures for winter and summer were used to develop mathematical geospatial models of external design temperatures for the Central Europe area with Poland’s territory in the centre part. Scattered data from 667 meteorological stations were interpolated to 40,000 uniform mesh points using a biharmonic spline interpolation method to develop these models. Linear regression and ANOVA analysis for the ERA5-generated data from 900 checkpoint data items were used to estimate the correctness of these models. Veriﬁed models were used to calculate winter and summer external design temperature isolines presented together with colour space representation on Mercator projected maps of Central Europe.


Introduction
High-quality climate data and weather statistics have become the foremost information in building optimisation and design.There is wide application of weather data in energy and structural building design, from environmentally imposed loads for construction to thermal influences on buildings.In most cases, the databases developed based on the averaged data are used to determine climate zones generally [1] or according to the parameters under consideration: temperature [2], snow cover, wind pressure [3], etc.However, in the case of building energy performance analyses, the datasets are much more extensive, including statistically processed different formats such as the number of degree days [4], extreme weather year [5], design weather year [6], typical meteorological year [7], etc.
The growing interest in building energy optimisation [8,9], renewable energy systems application [10] and methods of energy performance analyses [11] requires exact and Energies 2024, 17, 3905 2 of 21 up-to-date design data.The climatic database [7] is one of the standard datasets used in building performance simulation (BPS) and system design.The basic sets of PBS climate files according to EPW (EnergyPlus [12] weather file format) and CLM (ESP-r [13] weather files format) consist of the following climatic design parameters: dry-bulb temperature, relative humidity, solar radiation, wind speed and direction.The external temperature and solar radiation also determined the climate classifications [1] and selected class divisions.
The dry-bulb temperature of external air is the basic parameter in design methods for calculating heat loads for buildings' heating or cooling systems.These methods also use other parameters of the external climate, such as coincident wind speed, wet-bulb temperature and dew-point temperature with the dry-bulb temperature, specific enthalpy of moist air and others.This article focuses on determining and modelling external winter and summer design air dry-bulb temperatures.The external air dry-bulb temperature is treated as one of the most sensitive parameters to climate change and has a great impact on building performance [14].Most future climate assessment efforts focus on seasonal or annual increases in air temperature [15].Rebecca Cole et al. [16] hypothesised that capturing the building's ability to cope with extreme heat events should consider absolute temperature or how these temperatures are distributed throughout the year.In the following research study, Farah S. et al. [17] presented a method that separated hourly dry-bulb temperature into three time series components to simplify the integration of three climate change features into historical weather data.Bamdad K. et al. [18] revealed that climate change and variations in simulation parameters over the building's life span may impact the optimised design.Also, some studies performed energy simulations of residential rooms under present and future climatic conditions to evaluate the impact of climate change on their heating/cooling load components.Temperate, mid-latitude climates will see the largest change, but it will be swapping from heating to cooling, including a significant reduction of 25% or more in heating energy and up to 15% increase in cooling energy [14].Spandagos and Ng [19] predicted the climate change impacts on building cooling and heating energy in large Asian cities.As an example, in Indian cities, increasing temperature and relative humidity conditions will significantly reduce people's thermal comfort, necessitating the need for more cooling [20].The impacts of a predicted increase in external air dry-bulb temperature on heating and cooling energy use were also confirmed for European countries [21].The results show an overall increase in total energy consumption with a relative decrease in heating demand and an increase in cooling demand.Changes in climatic parameters can be presented as the shifting or changing of climate zones [22].Forecasting the impact of climate change on building stocks offers valuable quantitative insights for city and local authorities to plan their adaptations.Building codes and standards need to incorporate these climate change predictions.Demonstrating the effects of climate change by highlighting shifts in climate zones could be an effective way to influence standard makers in the building and construction industries.These changes in climate zones also offer a broader perspective on climate change.Presenting climate changes as changing climate zones is inappropriate for designing buildings' heat loads.Then, climatic parameter changes should be presented in another form, e.g., maps of climatic parameters and maps of changes in values.
Climatic design parameters play a crucial role in designing the heat loads and dimensioning installations and sources of heat and cooling for installations, ensuring thermal comfort and indoor air quality in buildings.These parameters form the foundation for all calculations in determining the size of building installations.Consequently, they influence the investment costs for installing these systems in new constructions or renovating existing buildings.In Poland, the calculation parameters were defined about 50 years ago.In the case of designing the heating installation, only the design values of the external air temperature were specified.In contrast, in designing the cooling and air-conditioning installations, in addition to the monthly design values of the external air dry-bulb temperature, the monthly external design wet-bulb temperatures were determined for six months from April to September.
The main aim of this study was to update the existing winter and summer design temperatures for Central Europe, with the main emphasis on Poland.According to EN ISO 15927 standards [23][24][25][26] and the ASHRAE Handbook of Fundamentals [27], new climatic design parameters for Poland were calculated.The synoptic source data were obtained from the Institute of Meteorology and Water Management (IMWM) and reanalysis models of the ERA5 database of the European Centre for Medium-Range Weather Forecasts (ECMWF).The most up-to-date meteorological stations' synoptic data and ECMWF ERA5 meteorological data from 1991-2020 were used in the analyses.These mostly hourly datasets fully represent the climatic characteristics of the region and include all extreme weather events that took place during these years.External air design dry-bulb temperatures for the location of meteorological stations were calculated among other climatic parameters.
The current design climate parameters used in Poland were determined based on meteorological and climatic data from the middle of the last century and do not reflect Poland's current climate.The design external temperature values for winter for the border areas of Poland are significantly different from those adopted in neighbouring countries.For example, for the town of Zgorzelec on the Polish-German border, the value of −20 • C is assumed, while, for Görlitz in Germany, which is on the other bank of the Nysa Łu życka River, it is −14.4 • C according to the German national annexe of the EN 12831:2006 [28].
Due to observable climate changes [29] and bearing in mind that the heating and cooling design parameters of outdoor air are the fundamental values used for dimensioning HVAC installations in buildings, and taking into account the fact that these parameters in Poland have not been officially updated since the mid-1900s, updated climatic design parameters should be introduced into the Polish applicable regulations and made available to HVAC engineers.The final results of this work are winter and summer external dry-bulb design temperatures for 81 meteorological stations in Poland and geospatial mathematical models of these temperatures for Central Europe used to draw colour space maps of external design with isotherms.

Winter Design Parameters
In Poland, the designers of building heating systems are obliged by law to use the external air design temperature values specified in the Polish standard PN 82/B 02403 [30] and the national annexe of the EN 12831:2006 standard [28] when calculating the heat load.It should be noted that the PN 82/B 02403 standard was withdrawn from the Polish standards in 2014, while the PN EN 12831:2006  The Polish national annexe of the EN 12831:2006 [28] standard presents a map that retains the division of the Polish territory into five climatic zones presented in the earlier Polish standards from 1974.It should be noted that the 1974 standard specifying the external design temperatures for heating is a minor modification of the standard from 1957.It presented six climatic zones of Poland with design temperature values for heating from −14 • C to −24 • C with two-centigrade steps.The map of division into climate zones was almost identical to the current one, with the separation of the Baltic Sea coast zone, which was assigned a calculation temperature of −14 • C. The Polish standard PN/B 02403 changes are described in detail in the paper [31].
It is worth noting that Poland's climatic zones were plotted in the 1960s based on the then-available meteorological data covering the 1940s, 1950s and 1960s.Subsequent changes in the standard specifying the external design temperature values remained the same.They also did not alter the division of Poland's territory into a climatic zone.
Additionally, it should be emphasised that the cited standards do not consider the change in the design temperature value with the change in the town's location above sea level.Interestingly, in the old PN/B-102 standard from 1934 for the territory of Poland within other borders than currently, the design external winter temperature value was set at −25 • C for areas above 650 m above sea level.

Summer Design Parameters
Unlike the design of heating systems, there are no legal requirements in Poland for summer external design temperatures used for dimensioning air-conditioning systems in buildings.This means that designers are not legally obliged to use any particular parameters.Customarily, when adopting so-called good design practice, HVAC engineers in Poland still use the PN-B-03420:1976 standard [32], withdrawn in 2011, and manuals and studies [33][34][35] in which this standard or its earlier version from 1964 is referenced.
The old Polish PN-B-03420:1976 standard contains a map of Poland divided into two climatic zones with assigned calculation values of external air temperature according to a dry bulb and according to a wet bulb for six months from April to September.Zone number I, on the Baltic coast, was assigned dry-bulb temperatures ranging from 18.6 • C to 28 This standard also provides seasonal values of the specific enthalpy of moist air, relative humidity, moisture content and daily temperature differences according to a dry bulb for both climate zones.The standard also includes hourly deviations from the calculated temperature values according to a dry-and wet-bulb thermometer, which allows the determination of temperature values from 8 a.m. to 8 p.m. in 2 h steps.The disadvantage of this solution is that this standard cannot be used to determine the values of external air parameters with hourly steps for the entire representative design day of a given month for cooling, ventilation and air-conditioning systems design in buildings.

Calculation Methods for New Climatic Design Parameters for Poland and Design Temperature Geospatial Models for Central Europe
New climatic parameters were determined as part of the research work to update external design temperatures for Poland.Winter and summer design temperatures were determined, among many other parameters, for Polish synoptic stations according to the methods described in the EN ISO 15927 standards [23][24][25][26] and methods presented in the ASHRAE Handbook of Fundamentals [27].These new parameters were calculated using 30 years of meteorological and climatic data measurement sequences from 1991-2020.
The development of geospatial models of winter and summer design temperatures enabling the determination of design temperatures for any location in Poland requires a geospatial analysis of data for an area of Europe with a meridional and latitudinal extent twice as large as the extent of the territory of Poland.Such a large area is necessary to minimise the impact of model approximation errors on the edge of the analysed area on the values calculated in the central part.The land territory of Poland is located between 49 • 00 N and 54 • 50 N latitude and 14 • 07 E and 24 • 09 E longitude.
For the geospatial analysis of the winter and summer external design temperatures, the area of Central Europe between 45 • and 60 • north latitude and 7 • and 31 • east longitude was assumed.This area includes a large part of the Baltic Sea basin, partly the Alps and the Carpathians, and the southern part of the Scandinavian peninsula.Developing a model of design temperature values for this area required collecting synoptic data from meteorological stations in Poland and outside the country.
To determine the design temperature geospatial models for Central Europe, it was assumed that the external design dry-bulb temperature for 81 meteorological stations in Poland and 586 outside Poland have to be defined similarly and include sequences of measurement data with the same accuracy and frequency from the same range of 1991-2020 calendar years.
All weather stations in the analysed area are listed in the ASHRAE Handbook of Fundamentals 2021 [27].Poland's new climatic design parameters were calculated using EN ISO 15927 standards [23][24][25][26] and the ASHRAE methodology based on IMWM source data from 81 Polish stations.The design temperature models presented in this article were developed based on data from 667 meteorological stations in the analysed area of Central Europe.In the case of 586 stations outside Poland, the ERA5 database was used for the same calendar years.To obtain design temperature geospatial models, the same algorithm was used to determine the design temperature values for winter and summer of all meteorological stations in the analysed Central Europe area.

Meteorological and Climatic Data Sources
To determine the climatic design parameters described in the EN ISO 15927 and in the ASHRAE Handbook of Fundamentals, synoptic data sequences and solar irradiation values from a period of at least 20 years for selected geographical locations are necessary, preferably with a measurement period of 1 h.New climatic parameters for Poland and design temperatures for stations outside Poland were calculated based on 30-year data sequences from 1991 to 2020.Values from the publicly available IMWM synoptic database and ERA5 data from the ECMWF were used to determine these parameters.
The IMWM measurement and observation database in the meteorological data section contains three datasets-from synoptic, climatological and precipitation stations for various time intervals-monthly, daily and timely data.Synoptic timely data from IMWM observation stations were used to calculate the climatic design parameters.IMWM observation and measurement data are saved in CSV format files.The data contained in the CSV files are consistent with the data of the WMO SYNOP FM-12 standard [36].
The timely synoptic data of IMWM do not contain information on the intensity of solar radiation, which is necessary to determine some design climatic parameters (design days) according to EN ISO 15927.The IMWM measurement and observation database includes a catalogue with actinometric data for 28 locations in Poland, which do not cover the location of synoptic stations.The time range of available data on solar irradiation and longwave radiation of the atmosphere made it impossible to use these synoptic data to calculate the climatic design parameters.Therefore, modelled solar irradiation data were used to determine Poland's new winter and summer climatic design parameters.These data were determined by ERA5 database reanalysis of the atmosphere state using archived meteorological data from ground stations and satellite observations of the ECMWF [37].
The lack of the actinometric measurements at meteorological stations necessary to determine climatic design parameters or typical meteorological years for building energy simulations, or determining climatic design parameters exists worldwide.For example, typical meteorological years (TMY2) for locations in the USA were calculated using data from 239 measurement stations, of which only 56 contain solar irradiation measurement data [38].For this reason, meteorological solar radiation models are commonly used to calculate solar irradiation and longwave atmospheric radiation [39].
ERA5 data reanalysis processes use advanced models of atmosphere state and deep machine learning tools that determine the state of the Earth's atmosphere over a given area at a specific time.ERA5 data enable the atmosphere state to be found in a grid of 0.25 degrees of latitude, longitude and exact time intervals.
As mentioned above, the ERA5 database was used to reconstruct the values of solar irradiation on the Earth's surface split into direct normal and diffuse irradiation and atmosphere longwave radiation for the analysed synoptic stations in Poland in the calendar years 1991-2020 with an hourly step.Solar irradiation and longwave atmosphere radiation, together with synoptic station data, were used to determine new climatic design parameters for Poland, and to calculate the winter and summer external design temperature for meteorological stations in the considered area of Central Europe except Poland.The ERA5 database was also used to determine the winter and summer external design temperatures of 900 checkpoints.The checkpoints were used to verify the correctness of the winter and summer external design temperature models, which were built based on data from 677 meteorological stations in the analysed geographical area of Central Europe.
Since data from the IMWM and the ERA5 system were saved in many CSV files and with different time steps, it became necessary to integrate this data into a uniform database with hourly time steps.It was assumed that these data would be integrated into an SQL database to determine new climatic design parameters for Poland.Both data resources were imported from CSV files into the SQL database using database tools with a uniform hourly time step.The SQL database was used as a data source for Visual Studio 2022 C++ and Python 3. As mentioned above, the ERA5 database was used to reconstruct the values of solar irradiation on the Earth's surface split into direct normal and diffuse irradiation and atmosphere longwave radiation for the analysed synoptic stations in Poland in the calendar years 1991-2020 with an hourly step.Solar irradiation and longwave atmosphere radiation, together with synoptic station data, were used to determine new climatic design parameters for Poland, and to calculate the winter and summer external design temperature for meteorological stations in the considered area of Central Europe except Poland.The ERA5 database was also used to determine the winter and summer external design temperatures of 900 checkpoints.The checkpoints were used to verify the correctness of the winter and summer external design temperature models, which were built based on data from 677 meteorological stations in the analysed geographical area of Central Europe.
Since data from the IMWM and the ERA5 system were saved in many CSV files and with different time steps, it became necessary to integrate this data into a uniform database with hourly time steps.It was assumed that these data would be integrated into an SQL database to determine new climatic design parameters for Poland.Both data resources were imported from CSV files into the SQL database using database tools with a uniform hourly time step.The SQL database was used as a data source for Visual Studio 2022 C++ and Python 3.

New Winter and Summer External Design Temperatures for Poland
The external winter and summer design dry-bulb temperatures discussed in the article are some of the many calculation parameters.New climatic design parameters for Poland were determined according to the EN 15289 standards and the ASHRAE Handbook of Fundamentals.These new climatic design parameters are based on synoptic data from Polish meteorological stations and ERA5 data.These parameters include winter and summer external design dry-bulb temperature, coincident wind speed and prevailing wind direction, and coincident wet-bulb and dew-point temperatures.Monthly, annual and seasonal statistics of meteorological parameters were also determined.Two kinds of design days were also chosen for each Polish meteorological station and each calendar month based on the following basic parameters: dry-bulb temperature, total solar

New Winter and Summer External Design Temperatures for Poland
The external winter and summer design dry-bulb temperatures discussed in the article are some of the many calculation parameters.New climatic design parameters for Poland were determined according to the EN 15289 standards and the ASHRAE Handbook of Fundamentals.These new climatic design parameters are based on synoptic data from Polish meteorological stations and ERA5 data.These parameters include winter and summer external design dry-bulb temperature, coincident wind speed and prevailing wind direction, and coincident wet-bulb and dew-point temperatures.Monthly, annual and seasonal statistics of meteorological parameters were also determined.Two kinds of design days were also chosen for each Polish meteorological station and each calendar month based on the following basic parameters: dry-bulb temperature, total solar irradiation on the horizontal surface and dew-point temperature.These design days were calculated for the frequency of exceedances equal to 1%, 2% and 5% of the days of the adopted period of 1991-2020.
Due to the vast number of determined new climatic design parameters for Poland's climate, the following sections of the article discuss only the external winter and summer design dry-bulb temperatures, which are fundamental for the calculation of the heat loads of heating, ventilation, cooling and air-conditioning systems in buildings.The external design dry-bulb temperatures calculated for 81 Polish meteorological stations (IMWM) and 586 outside Poland (ERA5) were used to develop geospatial models of winter and summer design temperatures for Central Europe, as described in the following parts of the article.Tables 1 and 2 present the new external design temperature values for winter and summer for locations of the IMWM meteorological stations in Poland.Long-term analysis of temperature data used to calculate external winter design temperature shows an upward trend.This is due to observable climate changes [28].Table 3 shows changes in the design temperature values for Suwałki city, referred to as the Polish "Pole of Cold", located northeast of Poland.The temperatures in the table are based on data published in the ASHRAE Handbook of Fundamentals and in the literature.Tables 4 and 5 present the actual and newly calculated external design temperatures for winter and summer for representative meteorological stations located in the currently applicable Polish climate zones according to the PN 82/B 02403 and PN 76/B 03420 standards.Table 4 presents winter external design temperature changes in the given towns, ranging from 4.8 • C to 7.4 • C. For the entire territory of Poland, out of 81 analysed meteorological stations, the minimum change in the winter external design temperature is 2 • C for the Cewice-Łebunia airport station.The maximum change in the design temperature value for winter is 8.2 • C at the Świnoujście station in northwestern Poland.The average winter external temperature change in all analysed Polish meteorological stations is approximately 4.9 • C. Based on these observations, Poland's current mandatory winter external design temperatures are lower by about 5 • C on average than the actual values.This change in the winter design temperatures for Poland's area leads to a decrease in the designed heat loads of building heating systems by approximately 11%, assuming linear dependency between building heat loads and internal and external temperature differences.
Similarly, Table 5 compares the external design temperatures used for summer for selected meteorological stations with the newly calculated values.The table shows that the design temperatures have been changed only slightly.In some cases, the currently used summer external design temperatures should be corrected.In the case of Zakopane, located at the base of the Tatra Mountains, the change in the design temperature for summer results from the height above sea level, which was not considered in the Polish standard PN 76/B 03420.
Among all 81 analysed meteorological stations in Poland, the most significant summer design temperature changes are −4.2 • C and −4.4 • C, which is an effect of the altitude of the Zakopane meteorological station and the meteorological station located on the top of Kasprowy Wierch summit.For both stations, the current design temperature is assumed to be 30 • C without considering the location of these stations in the mountains.The most significant positive correction of +1.6 • C was recorded at the Zielona Góra meteorological station.The average value of changes in the calculation temperature value for summer in Poland is −0.75 • C.This is probably due to neglecting the altitude above sea level in the 1976 standard.
A comparative analysis of the new and current external design temperature values for winter and summer shows that adjustments should be made to the map of the climate zones of Poland.To define the new climate zones with isolines, it is necessary to determine the geospatial design temperature models described below.

Geospatial Winter and Summer External Design Temperature Models for the Central Europe Area
The design temperatures for winter and summer are among the basic parameters for calculating heat loads for HVAC systems in buildings.For this reason, it is necessary to develop methods for presenting these temperatures on maps or lists to make it easier for designers to precisely determine these temperatures for any building location.
The EN ISO 15927 standards describe various ways of presenting the climatic design parameters.They may be among the following: Tables with a list of towns or country territorial division areas (counties or communes) to which the value of the design parameter is assigned; Maps with isolines of climatic design parameters, with different gradations, which divide the analysed area into zones with assigned values of the design parameter; Maps with area divisions to which the value of the design parameter is designated from a meteorological station, e.g., Voronoi cells.
All three presentation methods have their advantages and disadvantages.The first and second methods enable the precise determination of values for any point in space, but they require determining geospatial models of climate parameters.The third method is more straightforward to plot on maps and less accurate, but only if the first and second methods provide high-accuracy geospatial design parameter models.
In the case of the external design temperature for winter and summer, the first and second methods described above require the determination of a mathematical geospatial model approximating the design temperature surface over the geographical area based on the values assigned to meteorological stations.Geospatial approximation requires expanding the area due to the approximation boundary conditions to move the errors from the area for which high accuracy is needed, in this case, the territory of Poland.This assumption defined the area of Central Europe, as described above, for which winter and summer external design temperature geospatial models were determined.The geospatial models of design temperature enable finding the design external temperatures for any geographical location and draw isotherms on maps with the desired gradation.In the case of the third method of presentation, it becomes natural to designate areas on the map that minimise the distance to a meteorological station located inside this area, for which the external design temperature is known.These areas are obtained by performing Delaunay triangularisation and Voronoi tessellation [40,41] based on the spatial location of meteorological stations.
Determining geospatial models of the external design temperature requires calculations in a geographic coordinate grid.The maps presented in this article were developed based on the Mercator projection for the Central Europe area between latitudes 45 • and 60 • north and longitudes 7 • and 31 • east.The geographical coordinates of the points were projected to the XY coordinates of the map using the WKID 3395 WGS 1984 World Mercator projection.Using the inverse transformation of this projection, the geographical coordinates of the points were obtained for the XY coordinates of points calculated during the determination of models approximating the winter and summer external air design dry-bulb temperature.The interpolation surfaces of the geospatial models of the winter DBT 99.6% design temperature and summer DBT 0.4% design temperature for Central Europe are shown in Figures 2 and 3, respectively.Determining geospatial models of the external design temperature requires calculations in a geographic coordinate grid.The maps presented in this article were developed based on the Mercator projection for the Central Europe area between latitudes 45° and 60° north and longitudes 7° and 31° east.The geographical coordinates of the points were projected to the XY coordinates of the map using the WKID 3395 WGS 1984 World Mercator projection.Using the inverse transformation of this projection, the geographical coordinates of the points were obtained for the XY coordinates of points calculated during the determination of models approximating the winter and summer external air design dry-bulb temperature.The interpolation surfaces of the geospatial models of the winter DBT 99.6% design temperature and summer DBT 0.4% design temperature for Central Europe are shown in Figures 2 and 3, respectively.

Geospatial Model Verification and Error Analysis
To determine the accuracy of the external design temperature models, model residuals were determined at the points of meteorological stations and additionally at 900 checkpoints of a regular 30 × 30 grid in the XY coordinate system of the Mercator map.The model values at selected points were determined based on the barycentric coordinates of these points in the triangles of the computational temperature model facets.The facet grid of the computational temperature model was built based on 40,000 points of a regular interpolation grid.The model residual was determined as the difference between the calculation temperature values at meteorological stations or checkpoints, and the model values at these points' coordinates.
External design temperature values at control points were determined similarly to meteorological stations, using hourly outdoor air temperature sequences generated from Both geospatial models interpolating the winter and summer external design temperatures were determined based on a uniform mesh of 200 × 200 points in the XY coordinate system of the Mercator map for a given area of Central Europe, in which there are scattered data of 667 meteorological stations for which the design temperature values were determined.This division generated 40,000 points on Mercator's map.The distance between the grid points varies due to the adopted WKID 3395 projection.The uniform grid on the Mercator map corresponds to the variable density grid in geographic coordinates with a mean division of 0.0648 • (0 • 3 53.28 ) latitude and 0.0998 • (0 • 5 59.28 ) longitude.There are many methods for interpolating scattered data using a uniform mesh of points, such as linear, cubic spline, nearest neighbour and natural neighbour interpolation or inverse distance weighted method.The external ASHRAE DBT 99.6% and DBT 0.4% design temperature values from 667 meteorological stations were interpolated using the biharmonic spline curves method [42] to 40,000 uniform mesh points.This method requires a uniform mesh of even distributed points on the Mercator map.The mesh of points was not refined in areas with high variability in terrain elevation or in areas with high variability in climatic parameters, e.g., the sea coast.Using a variable density mesh requires generating mesh points based on analysing terrain height variability or climatic parameter variability, and using variable density mesh interpolation models of scattered data.

Geospatial Model Verification and Error Analysis
To determine the accuracy of the external design temperature models, model residuals were determined at the points of meteorological stations and additionally at 900 checkpoints of a regular 30 × 30 grid in the XY coordinate system of the Mercator map.The model values at selected points were determined based on the barycentric coordinates of these points in the triangles of the computational temperature model facets.The facet grid of the computational temperature model was built based on 40,000 points of a regular interpolation grid.The model residual was determined as the difference between the calculation temperature values at meteorological stations or checkpoints, and the model values at these points' coordinates.
External design temperature values at control points were determined similarly to meteorological stations, using hourly outdoor air temperature sequences generated from the ERA5 database for 1991-2020.The control points were divided into two groups: central points located within Poland's latitudinal and meridional extent, and other coastal points of the analysed area of Central Europe.The residual values determined for meteorological stations and control points were used to calculate model error statistics for Central Europe's central part and the analysed area.Figures 4 and 5 show the location of meteorological station points and checkpoints along with the residuals for the winter and summer computational temperature models.In both figures, it can be observed that the residuals have higher values in areas where there are very few stations and a high gradient of design temperature (Baltic Sea coast), on the edges of the analysed area and in mountainous regions (the Alps and Carpathians) where there is a significant variation in the height of the land above sea level.the central points.In the case of border-area checkpoints, a greater spread of values is observed, resulting from interpolation errors at the edge of the area.As mentioned above, the dispersion of values for checkpoints is also due to the limited number of meteorological stations over large areas or areas with significant variations in terrain altitude.Figure 6 shows comparison charts of the external design temperature values and modelled values for winter ASHRAE 99.6% DBT and summer ASHRAE 0.4% DBT design temperatures.Points on these charts distinguish between meteorological stations, and central-area and border-area checkpoints.These charts show a high consistency of model interpolation at the points of the meteorological stations based on which the model was determined.In the case of checkpoints, most of the convergence of values is observed at the central points.In the case of border-area checkpoints, a greater spread of values is observed, resulting from interpolation errors at the edge of the area.As mentioned above, the dispersion of values for checkpoints is also due to the limited number of meteorological stations over large areas or areas with significant variations in terrain altitude.
The quality assessment of the designated external design temperature geospatial models was based on statistics, linear regression and ANOVA analysis.The adopted null hypothesis with a significance level of 0.05 assumes that the designated external design temperature model does not correctly describe the new external design temperature values for the studied area of Central Europe, i.e., it is incorrect.According to Wilkinson's notation, y ~1 + x, a linear regression model and ANOVA analysis were used for the calculations.Tables 6 and 7 present the results of linear regression calculations and the ANOVA summary for the winter external design temperature geospatial model.Tables 8 and 9, respectively, present the results for the summer external design temperature geospatial model.The quality assessment of the designated external design temperature geospatial models was based on statistics, linear regression and ANOVA analysis.The adopted null hypothesis with a significance level of 0.05 assumes that the designated external design temperature model does not correctly describe the new external design temperature values for the studied area of Central Europe, i.e., it is incorrect.According to Wilkinson's notation, y ~ 1 + x, a linear regression model and ANOVA analysis were used for the calculations.Tables 6 and 7 present the results of linear regression calculations and the ANOVA summary for the winter external design temperature geospatial model.Tables 8  and 9, respectively, present the results for the summer external design temperature geospatial model.The values of R-squared > 0.95, p-value < 0.05 and F-statistic > 1000 determined in the linear regression and analysis of variance support the rejection of the null hypothesis.Therefore, the determined external design temperature models are assumed to be correct.

Colour Scale Maps and Isotherms of Winter and Summer External Design Temperatures for Central Europe
The adopted alternative hypothesis that the developed external design temperature models correctly describe its geospatial variability allowed for determining the course of isotherms of these values in the analysed area of Central Europe.The external design temperature isotherms, along with a coloured representation of their values for the entire analysed area of Central Europe, are shown on the maps in Figure 7 for winter and Figure 8 for summer.The main isotherms were determined with a step of 1 degree and drawn with a solid line, and the auxiliary isotherms with a step of 0.5 degrees were drawn with a dashed line.These maps also show the location of 667 meteorological stations and 900 checkpoints, including 224 in the separated central area.On both maps presented, characteristic areas with reduced or increased temperature values can be observed in the spatial distribution of these values, which are related to the topography of the analysed area.Particularly visible is the stabilisation of temperature in the Baltic Sea basin, which means that the design temperature in this area has the highest values during winter and lower values during summer.In the case of the highlands and mountain areas of the Alps, Sudetes, Beskids and Carpathians mountains, lower values of the design temperature can be observed for both winter and summer, resulting from the location of these areas above sea level and the presence of a vertical air temperature gradient in the troposphere, as described in U.S. Standard Atmosphere [43] and International Standard Atmosphere [44].The main isotherms were determined with a step of 1 degree and drawn with a solid line, and the auxiliary isotherms with a step of 0.5 degrees were drawn with a dashed line.These maps also show the location of 667 meteorological stations and 900 checkpoints, including 224 in the separated central area.On both maps presented, characteristic areas with reduced or increased temperature values can be observed in the spatial distribution of these values, which are related to the topography of the analysed area.Particularly visible is the stabilisation of temperature in the Baltic Sea basin, which means that the design temperature in this area has the highest values during winter and lower values during summer.In the case of the highlands and mountain areas of the Alps, Sudetes, Beskids and Carpathians mountains, lower values of the design temperature can be observed for both winter and summer, resulting from the location of these areas above sea level and the presence of a vertical air temperature gradient in the troposphere, as described in U.S. Standard Atmosphere [43] and International Standard Atmosphere [44].
On the map with the winter external design temperature model, one can observe a characteristic, meridional-like arrangement of isotherms in the European lowlands resulting from the influence of the continental climate of Europe and Asia during winter.In the case of the summer external design temperature, an isoline's system is close to the latitudinal in the lowlands of Poland and Germany areas, resulting from the change in the value of the sum of solar irradiation energy with a change in latitude and from the influence of the continental climate of Europe and Asia and the impact of the maritime climate shaped by the Atlantic Ocean, the North and Baltic Seas.
Comparing maps of Poland's climate zones in standards [30,32] with the new maps shown in Figures 7 and 8, one can notice similarities in the primary system of isotherms.The new geospatial models introduce local corrections to the course of isotherms and change the external design temperature values, especially for winter.

Conclusions
There is an urgent need to update the climatic design parameters applicable in Poland for dimensioning heating, cooling, ventilation and air-conditioning installations in buildings.The winter and summer external design temperatures that were mandatory or commonly used in Poland were determined in the mid-20th century and still need to be updated in law regulations.The climatic design parameters for meteorological stations located in Poland were constantly updated and published in the ASHRAE Handbook of Fundamentals.Still, they could not be used due to the law in force in Poland.As shown above, Poland's new winter external temperature values increased by an average of about 4.9 • C compared to the current values.A change in the winter design temperatures for Poland's area is estimated to decrease the designed heat loads of building heating systems by approximately 11%, which is a significant amount.Oversized heating devices have lower seasonal efficiency and increased investment costs for building heating installations.Evidence that the currently applicable winter external design temperatures in Poland are lowered is the fact that the maximum ordered heat power for buildings substations supplied from district heating systems, calculated based on these temperatures, is commonly reduced due to owners bearing the costs of a fixed fee related to the amount of ordered thermal power.
Regarding the summer external design temperature, the values commonly used in Poland for designing building cooling and air-conditioning systems are usually correct and consistent with the actual values.Still, there are places in Poland where corrections to these values should be made.
The developed geospatial models of the external design temperature for a large area of Central Europe make it possible to determine winter and summer design temperatures for any geographical location.This enables the creation of tables with the external design temperature for any units of country territorial division-communes, counties or cities.Such tables can be an alternative to maps of design temperatures.A national annexe in DIN EN 12831 adopted this solution in Germany, where one can find design temperatures for about 500 locations.
The external design temperature models described in the article were determined based on interpolation with biharmonic spline curves.Many other methods of interpolating geospatial data, such as linear models, cubic spline interpolation, inverse distance weighted interpolation, etc., can demonstrate a different, higher or lower accuracy than the interpolation method selected for the external design temperature geospatial models described in the article.Therefore, further research is required to compare geospatial design temperature models developed using different interpolation or approximation methods.Other ways of presenting data on maps should also be considered and compared.An example would be the comparison of design temperature maps using isolines and areas with constant design temperature values assigned to different places, for instance, in the form of Voronoi cells.
The developed methods for determining external designing temperature models and their presentation on maps can be used for geospatial analysis of other climatic design parameters for synoptic stations.Maps of such parameters or their complex indices can give new impetus to the analysis of criteria for assessing the energy performance of buildings depending on their geographical location.
The discussed external design temperature geospatial models were determined based on values calculated for synoptic meteorological stations, often airport stations located standard was replaced in 2017 by the EN 12831-1:2017-08 standard.The national annexe of the EN 12831:2006 standard presents the actual map of Poland divided into five climatic zones with assigned heating design external temperatures equal −16 • C, −18 • C, −20 • C, −22 • C and −24 • C, respectively, for zones I, II, III, IV and V. Climate zones are assigned temperature values that are even numbers, so the isotherms on this map have odd values from −17 • C to −23 • C. The map of the division of Poland into climatic zones in the EN 12831:2006 standard is identical to the map in the Polish standard PN 82/B 02403.
11 programs determining the climatic design parameters according to the EN ISO 15927 and ASHRAE Handbook of Fundamentals.A diagram showing the data flow in calculating climatic design parameters and typical meteorological years for Poland is shown in Figure 1.
11 programs determining the climatic design parameters according to the EN ISO 15927 and ASHRAE Handbook of Fundamentals.A diagram showing the data flow in calculating climatic design parameters and typical meteorological years for Poland is shown in Figure 1.

Figure 1 .
Figure 1.Authors' proposed meteorological data flow diagram for calculating climatic design parameters and typical meteorological year for Poland.Arrows in the figure mean data flow.

Figure 1 .
Figure 1.Authors' proposed meteorological data flow diagram for calculating climatic design parameters and typical meteorological year for Poland.Arrows in the figure mean data flow.

Figure 2 .
Figure 2. Winter external design temperature geospatial model (ASHRAE DBT 99.6%) for Central Europe based on data from 667 meteorological stations.

Figure 2 .
Figure 2. Winter external design temperature geospatial model (ASHRAE DBT 99.6%) for Central Europe based on data from 667 meteorological stations.

Figure 3 .
Figure 3. Summer external design temperature geospatial model (ASHRAE DBT 0.4%) for Central Europe based on data from 667 meteorological stations.

Figure 3 .
Figure 3. Summer external design temperature geospatial model (ASHRAE DBT 0.4%) for Central Europe based on data from 667 meteorological stations.

26 Figure 4 .
Figure 4. Residual values of winter external design temperature geospatial model (ASHRAE DBT 99.6%) for Central Europe at 667 meteorological stations and 900 checkpoints split into central and border areas.

Figure 6
Figure 6 shows comparison charts of the external design temperature values and modelled values for winter ASHRAE 99.6% DBT and summer ASHRAE 0.4% DBT design temperatures.Points on these charts distinguish between meteorological stations, and central-area and border-area checkpoints.These charts show a high consistency of model interpolation at the points of the meteorological stations based on which the model was determined.In the case of checkpoints, most of the convergence of values is observed at

Figure 4 .
Figure 4. Residual values of winter external design temperature geospatial model (ASHRAE DBT 99.6%) for Central Europe at 667 meteorological stations and 900 checkpoints split into central and border areas.

Figure 5 .
Figure 5. Residual values of summer external design temperature geospatial model (ASHRAE DBT 0.4%) for Central Europe at 667 meteorological stations and 900 checkpoints split into central and border areas.

Figure 5 .
Figure 5. Residual values of summer external design temperature geospatial model (ASHRAE DBT 0.4%) for Central Europe at 667 meteorological stations and 900 checkpoints split into central and border areas.

Energies 2024 , 26 Figure 7 .
Figure 7. Map of winter external design temperature (ASHRAE DBT 99.6%) with isotherms for the Central Europe area.

Figure 7 .
Figure 7. Map of winter external design temperature (ASHRAE DBT 99.6%) with isotherms for the Central Europe area.

Figure 8 .
Figure 8. Map of summer external design temperature (ASHRAE DBT 0.4%) with isotherms for the Central Europe area.
• C and wet-bulb temperatures ranging from 15.8 • C to 21 • C. The remaining part of Poland was assigned to zone number II with dry-bulb temperature values from 19.5 • C to 30 • C and wet-bulb temperature values from 15.5 • C to 21 • C.

Table 1 .
New external design temperatures [ • C] for winter calculated for synoptic stations in Poland.

Table 2 .
New external design temperatures [ • C] for summer calculated for synoptic stations in Poland.Table1presents new external design dry-bulb temperature values for winter according to the EN ISO 15927-5:2006/A1:2012 standard, including hourly mean design temperature, 1-, 2-, 3-and 4-day mean design temperature, as well as the ASHRAE dry-bulb temperature corresponding to 99.6% and 99.0% cumulative frequencies of occurrence.Table2presents new dry-bulb design temperature values for summer according to the EN ISO 15927-5:2006/A1:2012, including values for the cumulative frequency of 5%, 2% and 1% of occurrence, and design dry-bulb temperatures corresponding to a 0.4%, 1.0% and 2.0% cumulative frequency of occurrence according to ASHRAE.At this point, it should be noted that the current obligatory external design temperatures for winter in Poland range from −24 • C to −16 • C and are significantly lower than the newly developed values.The calculation temperatures applicable in Poland for the summer months are equal to +28 • C and +30 • C.

Table 3 .
Long-term variability of the winter design dry-bulb temperature for Suwałki meteorological station.
* Actual winter design temperature.

Table 4 .
Change in the winter external design dry-bulb temperature for selected meteorological stations located in the currently applicable Polish climate zones according to PN 82/B 02403 Polish standard.

Table 5 .
Change in the summer external design dry-bulb temperature for selected meteorological stations located in the currently applicable Polish climate zones according to PN 76/B 03420 standard.

Table 6 .
Results of linear regression analysis for the winter external design temperature geospatial model for all checkpoints and central-area-only checkpoints.

Table 6 .
Results of linear regression analysis for the winter external design temperature geospatial model for all checkpoints and central-area-only checkpoints.

Table 7 .
Summary of the ANOVA analysis for the winter external design model for all control points and checkpoints and central-area-only checkpoints.

Table 8 .
Results of linear regression analysis for the summer external design temperature geospatial model for all checkpoints and central-area-only checkpoints.

Table 9 .
Summary of the ANOVA analysis for the summer external design model for all control points and checkpoints and central-area-only checkpoints.