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METreport No. 02/2023 ISSN 2387-4201 Climate Calculation of design temperatures Proposed use of Bayesian GEV to calculate design summer and design winter temperatures Hans Olav Hygen, Lars Grinde and Helga Therese Tilley Tajet METreport Title Calculation of design temperatures Date 21.04.2023 Section Climate services Report no. No. 02/2023 Author(s) Hans Olav Hygen, Lars Grinde, Helga Therese Tilley Tajet Classification ● Free ○ Restricted Client(s) Standard Norge Client's reference [Client's reference] Abstract This report presents methods to calculate design temperature for summer and winter. It is a new probabilistic approach to design temperatures based on Bayesian statistics and GEV. Previous methods extracted data from meteorological observation sites and interpolated these to municipality centres. MET Norway calculates operationally gridded climatology of 1*1 km for daily mean temperatures. The new method uses daily mean temperatures extracted at municipality centres from this gridded dataset. Unlike previous calculations, consisting of one value, these new calculations give a distribution based on return periods from 2 to 200 years and 1 to 5 days mean. This provides the possibility to consider the needs and the risk of the building in the future calculation, but also a need for guidance in applying the right temperatures. In addition to the design temperatures for summer and winter,a simple method to calculate diurnal variation in temperature and humidity is presented, and the idea that the warmest and coldest days coincide with clear weather conditions. Keywords Design temperatures, Standardisation Disiplinary signature Hans Olav Hygen Responsible signature Cecilie Stenersen 2 MET report 3 Abstract This report presents methods to calculate design temperature for summer and winter. It is a new probabilistic approach to design temperatures based on Bayesian statistics and GEV. Previous methods extracted data from meteorological observation sites and interpolated these to municipality centres. MET Norway calculates operationally gridded climatology of 1*1 km for daily mean temperatures. The new method uses daily mean temperatures extracted at municipality centres from this gridded dataset. Unlike previous calculations, consisting of one value, these new calculations give a distribution based on return periods from 2 to 200 years and 1 to 5 days mean. This provides the possibility to consider the needs and the risk of the building in the future calculation, but also a need for guidance in applying the right temperatures. In addition to the design temperatures for summer and winter,a simple method to calculate diurnal variation in temperature and humidity is presented, and the idea that the warmest and coldest days coincide with clear weather conditions. Meteorologisk institutt Meteorological Institute Org.no 971274042 [email protected] Oslo P.O. Box 43 Blindern 0313 Oslo, Norway T. +47 22 96 30 00 Bergen Allégaten 70 5007 Bergen, Norway T. +47 55 23 66 00 Tromsø P.O. Box 6314, Langnes 9293 Tromsø, Norway T. +47 77 62 13 00 www.met.no Table of contents 1 Background 7 1.1 Design winter temperature 7 1.1.1 The challenge of an unclear definition 7 1.1.2 The challenge of spatial resolution and short periods of measurements 7 1.2 Design summer temperature 8 1.2.1 The challenge of spatial resolution and choice of reference period 8 1.2.2 The challenge of the definition 8 2 Suggested method 11 2.1 Availability of data 11 2.2 Description of calculations 12 2.2.1 GEV, Bayesian approach 12 2.2.2 Correction of inconsistencies 13 3 Example of calculated return values for winter and summer design values for Oslo 17 3.1 Design temperatures winter 17 3.2 Design temperatures summer 17 3.2.1 Comparison of GEV calculated summer design values and other values 18 4 Populating a more complete reference dataset 19 4.1 Daily temperature range (DTR / ΔT) 19 4.2 Clear day hypothesis and radiation 22 4.3 Humidity 24 5 Recommendation 29 References 31 A1 Appendix: County-wise table with associated observational station 32 Troms og Finnmark 32 Nordland 34 Trøndelag 36 Møre og Romsdal 38 Vestland 39 Rogaland 41 Agder 42 Vestfold og Telemark 43 Oslo og Viken 44 Innlandet 46 5 6 1 Background Design winter/summer temperatures are extensively used in the design and construction of the built environment. The calculation of these values are standardised in ISO 15927-5:2004(E) and 15927-2:2009(E). Some troubling parts with these standards will be highlighted in chapter 1.1 and 1.2. The following chapters will present an alternate method to calculate robust values and provide a broader set of information. 1.1 Design winter temperature 1.1.1 The challenge of an unclear definition The current definition of Design winter temperature in ISO 15927-5:2004(E) is: “The n-day mean design temperature, θ*nd , is calculated as the n-day mean air temperature, where n is one, two, three or four, having an average return period of 1 year (e.g. occurring on average 20 times in 20 years). The n-day mean air temperature on which it is based may be calculated, for every combination of n successive days, in one of several ways, depending on the data available.” For the record, there is a different nuance in the definitions «return period of 1 year» and «occurring on average 20 times in 20 years», but this is outside the scope of this report. We will further point out that in standard tools to calculate return periods there exists no definition of “average return period of 1 year”, and that most systems to calculate this fail when using 1 year return period. 1.1.2 The challenge of spatial resolution and short periods of measurements The current calculations are based on in situ measurements at the site of observations. At sites with good continuous observations for the period used to calculate design values, this is a good approach. The challenge with this approach for a major part of Norwegian municipalities is the lack of a stable reference near the centre of the municipality. Their challenge is composed of two not exclusive problems: No relevant station and stations with short or broken timeseries. In figure 1, the daily mean temperatures of Trondheim-Voll (purple) and Værnes (blue) are shown. There are two points worth attention: The records at Trondheim – Voll start in 1996, and Værnes, which is geographically the closest observation site, is slightly colder in winter. 7 Figure 1: Daily mean temperature at Trondheim - Voll (purple) and Værnes (blue) for the periode 1991-2022 show that the records in Trondheim are incomplete, and that Værnes tends to be colder winters than Trondheim - Voll. The example above from Trondheim illustrates both the challenge of short and broken records and spatial resolution. If the intention is to create design values based on the current normal period, 1991-2020, one needs to either merge the Trondheim series with the Værnes series or adjust the Værnes series to fit the statistics of the Trondheim series. In this case with almost 25 years overlap, the task of merging and/or adjusting is manageable, at other sites it can be less fortunate. 1.2 Design summer temperature 1.2.1 The challenge of spatial resolution and choice of reference period As pointed out for design winter temperature there is a challenge in the temporal resolution. The definition states that a station must have “at least 10 years of hourly data”, however, there are several stations that don't have a complete record of 10 years of hourly data. Good climatological practice would be, if possible, to use 30 years of data to avoid annual and decadal variations. 1.2.2 The challenge of the definition In ISO 15927-2:2009(E) chapter 4 and 5 contains definitions on the construction. The design reference temperature in question is defined in 5: “For all the hourly data in the data set, calculate the dry-bulb temperature exceeded on 1 %, 2 % and 5 % of occasions. These are θ99%, θ98% and θ95%”. 8 Numbers of hours in a year is 365*24=8760. One percent of this is 88, two percent is 175 and 5 percent is 438. It is a tradition in Norway to use temperatures that exceed maximum 50 hours a year, which finds no reference in the standard. Figure 2 shows these temperatures calculated at Oslo - Blindern. The average for the normal period, 1991-2020, is θ99% = 25,0 °C, θ98% = 23,2 °C, θ95% = 20,3 °C, 50H = 26,3 °C. Figure 2: Annual variations in dry-bulb temperature θ99%, θ98% and θ95% and 50 hours. The use of hourly data for the current normal period is a challenge since most stations, as mentioned above, do not have 30 years of hourly data. This challenge may be overcome by different approaches. ● One may interpolate less frequent data to hourly data by introducing certain assumptions, e.g., minimum temperature reflects early morning temperature, and maximum temperature is recorded in the afternoon. This kind of interpolation may amend the problem if there are observations at a relevant site. ● As stated above many municipalities do not have a homogeneous relevant series of observations. For the municipalities without relevant observations, one would need to adjust nearby observations to fit the site, thus requiring methods for spatial interpolation in addition to temporal interpolation. As mentioned above, the definition does contain “at least 10 years of hourly data”. Figure 3 shows the θ99% based on various 10-year periods (solid red lines) and 30 years (dotted line). θ99% based on the 10-year reference period show a variation from 24,3 °C (2008 -2017) to 25,3 °C (2011 – 2020), while θ99% based on the normal period (1991 – 2020) is 25,0 °C and stable. The variability in shorter reference periods leads to a recommendation of a reference period of 9 Figure 8: Uncertainty estimates for 2 and 200 years return period at Røros. 16 3 Example of calculated return values for winter and summer design values for Oslo In the following chapter design temperatures for winter and summer are presented for Oslo municipality centre as an example. In the summer chapter a comparison of design temperatures according to current standard, the Norwegian practice and the proposed method will be presented. 3.1 Design temperatures winter The following table shows the winter design temperatures, for 1-5 days and return period of 2-200 years, calculated at Oslo municipality centre with gridded data from seNorge 2018. Table 1: Design temperatures winter for Oslo. 3.2 Design temperatures summer The following table shows the summer design temperatures, for 1-5 days and return period of 2-200 years, calculated for Oslo municipality centre. Table 2: Design temperatures summer for Oslo. 17 3.2.1 Comparison of GEV calculated summer design values and other values Figure 9 compares the design values for Oslo from the Bayesian GEV and the current standard calculations. The standard used value of temperatures exceeding max 50 hours in a normal year is 26.3 °C, which is comparative to e.g. a 20 year return period of 3 days of 26.5 °C. Figure 9: Comparison of design values from the GEV based method, the standard and the Norwegian practice of temperatures exceeding max 50 hours per year. 18 4 Populating a more complete reference dataset Dimensioning of cooling and heating of houses are dependent on more data than just one value for winter and summer. Ideally one should have a reference year, or similar. To create a reference year is a huge task. As a substitute for a reference year, three supporting datasets/thesis are explored: ● A description of local standardised temperature variations on extreme days (Daily temperature range, DTR/ΔT) ● A matching set of humidity values ● A test if one can assume that the coldest and warmest days coincide with clear weather For DTR and humidity there are chosen to calculate this on representative stations and associate municipalities with these (Figure 10). 4.1 Daily temperature range (DTR / ΔT) The amplitude of diurnal temperature variations is considered a valid and relevant substitute for a full detailed hourly temperature profile. The most important description of this amplitude is connected to the most extreme days. Instead of generating this via extreme value distributions, we may use the assumption that the warmest and coldest days may also represent the seasonal greater variations. Figure 11 illustrates this, and verifies that the greater temperature ranges for summer, and in lesser degree for winter, is associated with the warmer and colder days. Based on this is an assumption that a warm and cold period are periods with greater DTR verified. This verification leads to the possibility that extracting DTR from warm and cold periods is a valid DTR to describe the temperature variations associated with the Design temperatures. The proposed method is to extract the DTR/ΔT from identified warm days at selected locations where also absolute humidity is calculated. The selection of locations are based on MET Norway's climatological regions and administrative regions (municipalities and counties. The result is presented in the appendix sorted by county. 19 Figure 10: Map of Norway with municipalities coloured according to the observational site recommended for the municipality and observational stations presented. 20 Figure 11: Daily temperature range at Blindern compared to mean temperatures. The five warmest days are shown in red. 21 4.2 Clear day hypothesis and radiation The thermal response and properties of the buildings are affected by solar radiation, thus the knowledge of cloudiness and solar radiation is very relevant. Unfortunately the measurements of radiation are severely limited in Norway. One assumption to be explored is whether the coldest and warmest days coincide with clear days. Figure 12 explores the connection on a monthly basis. This plot is rather complex and has three lines for each month. The upper line, marked with triangles, indicates days which were classified as “Fair-Weather-days”, while the lower, marked with squares, is for overcast days. The middle line, with circles, is neither. The classification is based on cloud observations in octa three times a day. Fair weather requires a sum of 9 or less and no observation above 4, while overcast is a sum of 20 and more. For the three winter months (December, top blue, January bottom blue and February in purple) the extreme cold days coincide with Fair weather. For the summer (orange, yellow and green) it’s clear that the extreme warm days do not coincide with overcast. Some of them might be on neither, this is usually due observations with octa higher than 4 in either morning or afternoon. Testing on other stations reveals the same pattern, here represented with Bergen-Florida and Værnes, Figure 13 and 14. The conclusion: The assumption that the warmest and coldest days are associated with clear, or almost clear skies, is valid. Figure 12: Monthly distribution of temperature sorted by cloudiness for Oslo-Blindern. Upper line in each month has clear days, lower lines are cloudy days, and the middle line is partly cloudy. 22 Figure 13: Monthly distribution of temperature sorted by cloudiness for Bergen-Florida. Upper line in each month has clear days, lower lines are cloudy days, and the middle line is partly cloudy. 23 Figure 14: Monthly distribution of temperature sorted by cloudiness for Værnes. Upper line in each month has clear days, lower lines are cloudy days, and the middle line is partly cloudy. 4.3 Humidity What is the typical humidity of the days matching the dimensioning temperatures? The following simple exploration is based on Oslo-Blindern for the period of 2016 to 2020. Conversion between relative humidity and temperature to absolute humidity is performed with: (6) 𝐴𝑏𝑠𝐻𝑢𝑚. = 6.112 *𝑒((16,67*𝑇)/(𝑇+243,5)*𝑅𝐻*18,2 (273,15+𝑇)*100*0,08314 ● AbsHum is the absolute humidity in g/m3 ● T is temperature in ℃ ● RH is relative temperature in % Figures 15 and 16 explore the five warmest and coldest days at Oslo-Blindern, and show how the absolute humidity reveals minor variations throughout the day even though the relative humidity has large variations. For warm days, relative humidity in the morning is typically 70-75 %, and decreases to about 30 % in the afternoon as temperature increases. Absolute humidity on the other hand is fairly stable throughout the day at 10 to 15 g/m3. In the colder days the relative humidity for all but one of the days is about 80% throughout the day. The absolute humidity these 5 cold days is about 1 g/m3throughout the day. 24 Figure 15: Relative and absolute humidity of the five warmest days at Oslo-Blindern. 25 A1 Appendix: County-wise table with associated observational station Troms og Finnmark Kommunenummer Kommune Stasjonsnummer Sted 5401 Tromsø 90450 Tromsø 5402 Harstad 90450 Tromsø 5403 Alta 93140 Alta 5404 Vardø 98550 Vardø 5405 Vadsø 98550 Vardø 5406 Hammerfest 93140 Alta 5411 Kvæfjord 90450 Tromsø 5412 Tjeldsund 90450 Tromsø 5413 Ibestad 90450 Tromsø 5414 Gratangen 90450 Tromsø 5415 Lavangen 90450 Tromsø 5416 Bardu 90450 Tromsø 5417 Salangen 90450 Tromsø 5418 Målselv 90450 Tromsø 5419 Sørreisa 90450 Tromsø 5420 Dyrøy 90450 Tromsø 5421 Senja 90450 Tromsø 5422 Balsfjord 90450 Tromsø 5423 Karlsøy 90450 Tromsø 5424 Lyngen 90450 Tromsø 5425 Storfjord 90450 Tromsø 5426 Kåfjord 90450 Tromsø 5427 Skjervøy 93140 Alta 32 5428 Nordreisa 93140 Alta 5429 Kvænangen 93140 Alta 5430 Kautokeino 97250 Karasjok 5432 Loppa 93140 Alta 5433 Hasvik 93140 Alta 5434 Måsøy 93140 Alta 5435 Nordkapp 93140 Alta 5436 Porsanger 93140 Alta 5437 Karasjok 97250 Karasjok 5438 Lebesby 98550 Vardø 5439 Gamvik 98550 Vardø 5440 Berlevåg 98550 Vardø 5441 Tana 98550 Vardø 5442 Nesseby 98550 Vardø 5443 Båtsfjord 98550 Vardø 5444 Sør-Varanger 98550 Vardø 33 Nordland Kommunenummer Kommune Stasjonsnummer Sted 1804 Bodø 82290 Bodø 1806 Narvik 82290 Bodø 1811 Bindal 82290 Bodø 1812 Sømna 82290 Bodø 1813 Brønnøy 82290 Bodø 1815 Vega 82290 Bodø 1816 Vevelstad 82290 Bodø 1818 Herøy 82290 Bodø 1820 Alstahaug 82290 Bodø 1822 Leirfjord 82290 Bodø 1824 Vefsn 82290 Bodø 1825 Grane 82290 Bodø 1826 Hattfjelldal 82290 Bodø 1827 Dønna 82290 Bodø 1828 Nesna 82290 Bodø 1832 Hemnes 82290 Bodø 1833 Rana 82290 Bodø 1834 Lurøy 82290 Bodø 1835 Træna 82290 Bodø 1836 Rødøy 82290 Bodø 1837 Meløy 82290 Bodø 1838 Gildeskål 82290 Bodø 1839 Beiarn 82290 Bodø 1840 Saltdal 82290 Bodø 1841 Fauske 82290 Bodø 1845 Sørfold 82290 Bodø 1848 Steigen 82290 Bodø 1851 Lødingen 82290 Bodø 1853 Evenes 82290 Bodø 34 1856 Røst 82290 Bodø 1857 Værøy 82290 Bodø 1859 Flakstad 82290 Bodø 1860 Vestvågøy 82290 Bodø 1865 Vågan 82290 Bodø 1866 Hadsel 82290 Bodø 1867 Bø 82290 Bodø 1868 Øksnes 82290 Bodø 1870 Sortland 82290 Bodø 1871 Andøy 82290 Bodø 1874 Moskenes 82290 Bodø 1875 Hamarøy 82290 Bodø 35 Trøndelag Kommunenummer Kommune Stasjonsnummerr Sted 5001 Trondheim 69100 Værnes 5006 Steinkjer 69100 Værnes 5007 Namsos 69100 Værnes 5014 Frøya 69100 Værnes 5020 Osen 69100 Værnes 5021 Oppdal 10400 Røros 5022 Rennebu 10400 Røros 5025 Røros 10400 Røros 5026 Holtålen 10400 Røros 5027 Midtre Gauldal 10400 Røros 5028 Melhus 69100 Værnes 5029 Skaun 69100 Værnes 5031 Malvik 69100 Værnes 5032 Selbu 69100 Værnes 5033 Tydal 10400 Røros 5034 Meråker 69100 Værnes 5035 Stjørdal 69100 Værnes 5036 Frosta 69100 Værnes 5037 Levanger 69100 Værnes 5038 Verdal 69100 Værnes 5041 Snåsa 69100 Værnes 5042 Lierne 69100 Værnes 5043 Røyrvik 69100 Værnes 5044 Namsskogan 69100 Værnes 5045 Grong 69100 Værnes 5046 Høylandet 69100 Værnes 5047 Overhalla 69100 Værnes 5049 Flatanger 69100 Værnes 36 5052 Leka 69100 Værnes 5053 Inderøy 69100 Værnes 5054 Indre Fosen 69100 Værnes 5055 Heim 69100 Værnes 5056 Hitra 69100 Værnes 5057 Ørland 69100 Værnes 5058 Åfjord 69100 Værnes 5059 Orkland 69100 Værnes 5060 Nærøysund 69100 Værnes 5061 Rindal 69100 Værnes 37 Møre og Romsdal Kommunenummer Kommune Stasjonsnummer Sted 1507 Ålesund 60990 Vigra 1506 Molde 60990 Vigra 1505 Kristiansund 60990 Vigra 1511 Vanylven 60990 Vigra 1514 Sande 60990 Vigra 1515 Herøy 60990 Vigra 1516 Ulstein 60990 Vigra 1517 Hareid 60990 Vigra 1520 Ørsta 60990 Vigra 1525 Stranda 60990 Vigra 1528 Sykkylven 60990 Vigra 1531 Sula 60990 Vigra 1532 Giske 60990 Vigra 1535 Vestnes 60990 Vigra 1539 Rauma 60990 Vigra 1547 Aukra 60990 Vigra 1554 Averøy 60990 Vigra 1557 Gjemnes 60990 Vigra 1560 Tingvoll 60990 Vigra 1563 Sunndal 60990 Vigra 1566 Surnadal 60990 Vigra 1573 Smøla 60990 Vigra 1576 Aure 60990 Vigra 1577 Volda 60990 Vigra 1578 Fjord 60990 Vigra 1579 Hustadvika 60990 Vigra 38 Vestland Kommunenummer Kommune Stasjonsnummer Sted 4601 Bergen 50540 Bergen 4602 Kinn 50540 Bergen 4611 Etne 50540 Bergen 4612 Sveio 50540 Bergen 4613 Bømlo 50540 Bergen 4614 Stord 50540 Bergen 4615 Fitjar 50540 Bergen 4616 Tysnes 50540 Bergen 4617 Kvinnherad 50540 Bergen 4618 Ullensvang 50540 Bergen 4619 Eidfjord 25840 Finse 4620 Ulvik 25840 Finse 4621 Voss 50540 Bergen 4622 Kvam 50540 Bergen 4623 Samnanger 50540 Bergen 4624 Bjørnafjorden 50540 Bergen 4625 Austevoll 50540 Bergen 4626 Øygarden 50540 Bergen 4627 Askøy 50540 Bergen 4628 Vaksdal 50540 Bergen 4629 Modalen 50540 Bergen 4630 Osterøy 50540 Bergen 4631 Alver 50540 Bergen 4632 Austrheim 50540 Bergen 4633 Fedje 50540 Bergen 4634 Masfjorden 50540 Bergen 4635 Gulen 50540 Bergen 39 4636 Solund 50540 Bergen 4637 Hyllestad 50540 Bergen 4638 Høyanger 50540 Bergen 4639 Vik 50540 Bergen 4640 Sogndal 50540 Bergen 4641 Aurland 25840 Finse 4642 Lærdal 25840 Finse 4643 Årdal 25840 Finse 4644 Luster 25840 Finse 4645 Askvoll 50540 Bergen 4646 Fjaler 50540 Bergen 4647 Sunnfjord 50540 Bergen 4648 Bremanger 50540 Bergen 4649 Stad 50540 Bergen 4650 Gloppen 50540 Bergen 4651 Stryn 25840 Finse 40 Rogaland Kommunenummer Kommune Stasjonsnummer Sted 1101 Eigersund 44560 Sola 1103 Stavanger 44560 Sola 1106 Haugesund 44560 Sola 1108 Sandnes 44560 Sola 1111 Sokndal 44560 Sola 1112 Lund 44560 Sola 1114 Bjerkreim 44560 Sola 1119 Hå 44560 Sola 1120 Klepp 44560 Sola 1121 Time 44560 Sola 1122 Gjesdal 44560 Sola 1124 Sola 44560 Sola 1127 Randaberg 44560 Sola 1130 Strand 44560 Sola 1133 Hjelmeland 44560 Sola 1134 Suldal 44560 Sola 1135 Sauda 44560 Sola 1144 Kvitsøy 44560 Sola 1145 Bokn 44560 Sola 1146 Tysvær 44560 Sola 1149 Karmøy 44560 Sola 1151 Utsira 44560 Sola 1160 Vindafjord 44560 Sola 41